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<li><a class="reference internal" href="#">pymatgen.symmetry package</a><ul>
<li><a class="reference internal" href="#submodules">Submodules</a></li>
<li><a class="reference internal" href="#module-pymatgen.symmetry.analyzer">pymatgen.symmetry.analyzer module</a><ul>
<li><a class="reference internal" href="#pymatgen.symmetry.analyzer.PointGroupAnalyzer"><code class="docutils literal notranslate"><span class="pre">PointGroupAnalyzer</span></code></a><ul>
<li><a class="reference internal" href="#pymatgen.symmetry.analyzer.PointGroupAnalyzer.get_equivalent_atoms"><code class="docutils literal notranslate"><span class="pre">PointGroupAnalyzer.get_equivalent_atoms()</span></code></a></li>
<li><a class="reference internal" href="#pymatgen.symmetry.analyzer.PointGroupAnalyzer.get_pointgroup"><code class="docutils literal notranslate"><span class="pre">PointGroupAnalyzer.get_pointgroup()</span></code></a></li>
<li><a class="reference internal" href="#pymatgen.symmetry.analyzer.PointGroupAnalyzer.get_rotational_symmetry_number"><code class="docutils literal notranslate"><span class="pre">PointGroupAnalyzer.get_rotational_symmetry_number()</span></code></a></li>
<li><a class="reference internal" href="#pymatgen.symmetry.analyzer.PointGroupAnalyzer.get_symmetry_operations"><code class="docutils literal notranslate"><span class="pre">PointGroupAnalyzer.get_symmetry_operations()</span></code></a></li>
<li><a class="reference internal" href="#pymatgen.symmetry.analyzer.PointGroupAnalyzer.inversion_op"><code class="docutils literal notranslate"><span class="pre">PointGroupAnalyzer.inversion_op</span></code></a></li>
<li><a class="reference internal" href="#pymatgen.symmetry.analyzer.PointGroupAnalyzer.is_valid_op"><code class="docutils literal notranslate"><span class="pre">PointGroupAnalyzer.is_valid_op()</span></code></a></li>
<li><a class="reference internal" href="#pymatgen.symmetry.analyzer.PointGroupAnalyzer.symmetrize_molecule"><code class="docutils literal notranslate"><span class="pre">PointGroupAnalyzer.symmetrize_molecule()</span></code></a></li>
</ul>
</li>
<li><a class="reference internal" href="#pymatgen.symmetry.analyzer.PointGroupOperations"><code class="docutils literal notranslate"><span class="pre">PointGroupOperations</span></code></a><ul>
<li><a class="reference internal" href="#pymatgen.symmetry.analyzer.PointGroupOperations.sch_symbol"><code class="docutils literal notranslate"><span class="pre">PointGroupOperations.sch_symbol</span></code></a></li>
</ul>
</li>
<li><a class="reference internal" href="#pymatgen.symmetry.analyzer.SpacegroupAnalyzer"><code class="docutils literal notranslate"><span class="pre">SpacegroupAnalyzer</span></code></a><ul>
<li><a class="reference internal" href="#pymatgen.symmetry.analyzer.SpacegroupAnalyzer.find_primitive"><code class="docutils literal notranslate"><span class="pre">SpacegroupAnalyzer.find_primitive()</span></code></a></li>
<li><a class="reference internal" href="#pymatgen.symmetry.analyzer.SpacegroupAnalyzer.get_conventional_standard_structure"><code class="docutils literal notranslate"><span class="pre">SpacegroupAnalyzer.get_conventional_standard_structure()</span></code></a></li>
<li><a class="reference internal" href="#pymatgen.symmetry.analyzer.SpacegroupAnalyzer.get_conventional_to_primitive_transformation_matrix"><code class="docutils literal notranslate"><span class="pre">SpacegroupAnalyzer.get_conventional_to_primitive_transformation_matrix()</span></code></a></li>
<li><a class="reference internal" href="#pymatgen.symmetry.analyzer.SpacegroupAnalyzer.get_crystal_system"><code class="docutils literal notranslate"><span class="pre">SpacegroupAnalyzer.get_crystal_system()</span></code></a></li>
<li><a class="reference internal" href="#pymatgen.symmetry.analyzer.SpacegroupAnalyzer.get_hall"><code class="docutils literal notranslate"><span class="pre">SpacegroupAnalyzer.get_hall()</span></code></a></li>
<li><a class="reference internal" href="#pymatgen.symmetry.analyzer.SpacegroupAnalyzer.get_ir_reciprocal_mesh"><code class="docutils literal notranslate"><span class="pre">SpacegroupAnalyzer.get_ir_reciprocal_mesh()</span></code></a></li>
<li><a class="reference internal" href="#pymatgen.symmetry.analyzer.SpacegroupAnalyzer.get_ir_reciprocal_mesh_map"><code class="docutils literal notranslate"><span class="pre">SpacegroupAnalyzer.get_ir_reciprocal_mesh_map()</span></code></a></li>
<li><a class="reference internal" href="#pymatgen.symmetry.analyzer.SpacegroupAnalyzer.get_kpoint_weights"><code class="docutils literal notranslate"><span class="pre">SpacegroupAnalyzer.get_kpoint_weights()</span></code></a></li>
<li><a class="reference internal" href="#pymatgen.symmetry.analyzer.SpacegroupAnalyzer.get_lattice_type"><code class="docutils literal notranslate"><span class="pre">SpacegroupAnalyzer.get_lattice_type()</span></code></a></li>
<li><a class="reference internal" href="#pymatgen.symmetry.analyzer.SpacegroupAnalyzer.get_point_group_operations"><code class="docutils literal notranslate"><span class="pre">SpacegroupAnalyzer.get_point_group_operations()</span></code></a></li>
<li><a class="reference internal" href="#pymatgen.symmetry.analyzer.SpacegroupAnalyzer.get_point_group_symbol"><code class="docutils literal notranslate"><span class="pre">SpacegroupAnalyzer.get_point_group_symbol()</span></code></a></li>
<li><a class="reference internal" href="#pymatgen.symmetry.analyzer.SpacegroupAnalyzer.get_primitive_standard_structure"><code class="docutils literal notranslate"><span class="pre">SpacegroupAnalyzer.get_primitive_standard_structure()</span></code></a></li>
<li><a class="reference internal" href="#pymatgen.symmetry.analyzer.SpacegroupAnalyzer.get_refined_structure"><code class="docutils literal notranslate"><span class="pre">SpacegroupAnalyzer.get_refined_structure()</span></code></a></li>
<li><a class="reference internal" href="#pymatgen.symmetry.analyzer.SpacegroupAnalyzer.get_space_group_number"><code class="docutils literal notranslate"><span class="pre">SpacegroupAnalyzer.get_space_group_number()</span></code></a></li>
<li><a class="reference internal" href="#pymatgen.symmetry.analyzer.SpacegroupAnalyzer.get_space_group_operations"><code class="docutils literal notranslate"><span class="pre">SpacegroupAnalyzer.get_space_group_operations()</span></code></a></li>
<li><a class="reference internal" href="#pymatgen.symmetry.analyzer.SpacegroupAnalyzer.get_space_group_symbol"><code class="docutils literal notranslate"><span class="pre">SpacegroupAnalyzer.get_space_group_symbol()</span></code></a></li>
<li><a class="reference internal" href="#pymatgen.symmetry.analyzer.SpacegroupAnalyzer.get_symmetrized_structure"><code class="docutils literal notranslate"><span class="pre">SpacegroupAnalyzer.get_symmetrized_structure()</span></code></a></li>
<li><a class="reference internal" href="#pymatgen.symmetry.analyzer.SpacegroupAnalyzer.get_symmetry_dataset"><code class="docutils literal notranslate"><span class="pre">SpacegroupAnalyzer.get_symmetry_dataset()</span></code></a></li>
<li><a class="reference internal" href="#pymatgen.symmetry.analyzer.SpacegroupAnalyzer.get_symmetry_operations"><code class="docutils literal notranslate"><span class="pre">SpacegroupAnalyzer.get_symmetry_operations()</span></code></a></li>
<li><a class="reference internal" href="#pymatgen.symmetry.analyzer.SpacegroupAnalyzer.is_laue"><code class="docutils literal notranslate"><span class="pre">SpacegroupAnalyzer.is_laue()</span></code></a></li>
</ul>
</li>
<li><a class="reference internal" href="#pymatgen.symmetry.analyzer.SpacegroupOperations"><code class="docutils literal notranslate"><span class="pre">SpacegroupOperations</span></code></a><ul>
<li><a class="reference internal" href="#pymatgen.symmetry.analyzer.SpacegroupOperations.are_symmetrically_equivalent"><code class="docutils literal notranslate"><span class="pre">SpacegroupOperations.are_symmetrically_equivalent()</span></code></a></li>
</ul>
</li>
<li><a class="reference internal" href="#pymatgen.symmetry.analyzer.SymmetryUndeterminedError"><code class="docutils literal notranslate"><span class="pre">SymmetryUndeterminedError</span></code></a></li>
<li><a class="reference internal" href="#pymatgen.symmetry.analyzer.cluster_sites"><code class="docutils literal notranslate"><span class="pre">cluster_sites()</span></code></a></li>
<li><a class="reference internal" href="#pymatgen.symmetry.analyzer.generate_full_symmops"><code class="docutils literal notranslate"><span class="pre">generate_full_symmops()</span></code></a></li>
<li><a class="reference internal" href="#pymatgen.symmetry.analyzer.iterative_symmetrize"><code class="docutils literal notranslate"><span class="pre">iterative_symmetrize()</span></code></a></li>
</ul>
</li>
<li><a class="reference internal" href="#module-pymatgen.symmetry.bandstructure">pymatgen.symmetry.bandstructure module</a><ul>
<li><a class="reference internal" href="#pymatgen.symmetry.bandstructure.HighSymmKpath"><code class="docutils literal notranslate"><span class="pre">HighSymmKpath</span></code></a><ul>
<li><a class="reference internal" href="#pymatgen.symmetry.bandstructure.HighSymmKpath.equiv_labels"><code class="docutils literal notranslate"><span class="pre">HighSymmKpath.equiv_labels</span></code></a></li>
<li><a class="reference internal" href="#pymatgen.symmetry.bandstructure.HighSymmKpath.get_continuous_path"><code class="docutils literal notranslate"><span class="pre">HighSymmKpath.get_continuous_path()</span></code></a></li>
<li><a class="reference internal" href="#pymatgen.symmetry.bandstructure.HighSymmKpath.label_index"><code class="docutils literal notranslate"><span class="pre">HighSymmKpath.label_index</span></code></a></li>
<li><a class="reference internal" href="#pymatgen.symmetry.bandstructure.HighSymmKpath.path_lengths"><code class="docutils literal notranslate"><span class="pre">HighSymmKpath.path_lengths</span></code></a></li>
<li><a class="reference internal" href="#pymatgen.symmetry.bandstructure.HighSymmKpath.path_type"><code class="docutils literal notranslate"><span class="pre">HighSymmKpath.path_type</span></code></a></li>
</ul>
</li>
</ul>
</li>
<li><a class="reference internal" href="#module-pymatgen.symmetry.groups">pymatgen.symmetry.groups module</a><ul>
<li><a class="reference internal" href="#pymatgen.symmetry.groups.PointGroup"><code class="docutils literal notranslate"><span class="pre">PointGroup</span></code></a><ul>
<li><a class="reference internal" href="#pymatgen.symmetry.groups.PointGroup.symbol"><code class="docutils literal notranslate"><span class="pre">PointGroup.symbol</span></code></a></li>
<li><a class="reference internal" href="#pymatgen.symmetry.groups.PointGroup.generators"><code class="docutils literal notranslate"><span class="pre">PointGroup.generators</span></code></a></li>
<li><a class="reference internal" href="#pymatgen.symmetry.groups.PointGroup.symmetry_ops"><code class="docutils literal notranslate"><span class="pre">PointGroup.symmetry_ops</span></code></a></li>
<li><a class="reference internal" href="#pymatgen.symmetry.groups.PointGroup.from_space_group"><code class="docutils literal notranslate"><span class="pre">PointGroup.from_space_group()</span></code></a></li>
<li><a class="reference internal" href="#pymatgen.symmetry.groups.PointGroup.get_orbit"><code class="docutils literal notranslate"><span class="pre">PointGroup.get_orbit()</span></code></a></li>
<li><a class="reference internal" href="#pymatgen.symmetry.groups.PointGroup.is_subgroup"><code class="docutils literal notranslate"><span class="pre">PointGroup.is_subgroup()</span></code></a></li>
<li><a class="reference internal" href="#pymatgen.symmetry.groups.PointGroup.is_supergroup"><code class="docutils literal notranslate"><span class="pre">PointGroup.is_supergroup()</span></code></a></li>
<li><a class="reference internal" href="#id0"><code class="docutils literal notranslate"><span class="pre">PointGroup.symmetry_ops</span></code></a></li>
</ul>
</li>
<li><a class="reference internal" href="#pymatgen.symmetry.groups.SpaceGroup"><code class="docutils literal notranslate"><span class="pre">SpaceGroup</span></code></a><ul>
<li><a class="reference internal" href="#pymatgen.symmetry.groups.SpaceGroup.symbol"><code class="docutils literal notranslate"><span class="pre">SpaceGroup.symbol</span></code></a></li>
<li><a class="reference internal" href="#pymatgen.symmetry.groups.SpaceGroup.int_number"><code class="docutils literal notranslate"><span class="pre">SpaceGroup.int_number</span></code></a></li>
<li><a class="reference internal" href="#pymatgen.symmetry.groups.SpaceGroup.generators"><code class="docutils literal notranslate"><span class="pre">SpaceGroup.generators</span></code></a></li>
<li><a class="reference internal" href="#pymatgen.symmetry.groups.SpaceGroup.order"><code class="docutils literal notranslate"><span class="pre">SpaceGroup.order</span></code></a></li>
<li><a class="reference internal" href="#pymatgen.symmetry.groups.SpaceGroup.SG_SYMBOLS"><code class="docutils literal notranslate"><span class="pre">SpaceGroup.SG_SYMBOLS</span></code></a></li>
<li><a class="reference internal" href="#pymatgen.symmetry.groups.SpaceGroup.SYMM_OPS"><code class="docutils literal notranslate"><span class="pre">SpaceGroup.SYMM_OPS</span></code></a></li>
<li><a class="reference internal" href="#pymatgen.symmetry.groups.SpaceGroup.abbrev_sg_mapping"><code class="docutils literal notranslate"><span class="pre">SpaceGroup.abbrev_sg_mapping</span></code></a></li>
<li><a class="reference internal" href="#pymatgen.symmetry.groups.SpaceGroup.crystal_system"><code class="docutils literal notranslate"><span class="pre">SpaceGroup.crystal_system</span></code></a></li>
<li><a class="reference internal" href="#pymatgen.symmetry.groups.SpaceGroup.from_int_number"><code class="docutils literal notranslate"><span class="pre">SpaceGroup.from_int_number()</span></code></a></li>
<li><a class="reference internal" href="#pymatgen.symmetry.groups.SpaceGroup.full_sg_mapping"><code class="docutils literal notranslate"><span class="pre">SpaceGroup.full_sg_mapping</span></code></a></li>
<li><a class="reference internal" href="#pymatgen.symmetry.groups.SpaceGroup.gen_matrices"><code class="docutils literal notranslate"><span class="pre">SpaceGroup.gen_matrices</span></code></a></li>
<li><a class="reference internal" href="#pymatgen.symmetry.groups.SpaceGroup.get_orbit"><code class="docutils literal notranslate"><span class="pre">SpaceGroup.get_orbit()</span></code></a></li>
<li><a class="reference internal" href="#pymatgen.symmetry.groups.SpaceGroup.get_orbit_and_generators"><code class="docutils literal notranslate"><span class="pre">SpaceGroup.get_orbit_and_generators()</span></code></a></li>
<li><a class="reference internal" href="#pymatgen.symmetry.groups.SpaceGroup.get_settings"><code class="docutils literal notranslate"><span class="pre">SpaceGroup.get_settings()</span></code></a></li>
<li><a class="reference internal" href="#pymatgen.symmetry.groups.SpaceGroup.is_compatible"><code class="docutils literal notranslate"><span class="pre">SpaceGroup.is_compatible()</span></code></a></li>
<li><a class="reference internal" href="#pymatgen.symmetry.groups.SpaceGroup.is_subgroup"><code class="docutils literal notranslate"><span class="pre">SpaceGroup.is_subgroup()</span></code></a></li>
<li><a class="reference internal" href="#pymatgen.symmetry.groups.SpaceGroup.is_supergroup"><code class="docutils literal notranslate"><span class="pre">SpaceGroup.is_supergroup()</span></code></a></li>
<li><a class="reference internal" href="#pymatgen.symmetry.groups.SpaceGroup.op"><code class="docutils literal notranslate"><span class="pre">SpaceGroup.op</span></code></a></li>
<li><a class="reference internal" href="#pymatgen.symmetry.groups.SpaceGroup.sg_encoding"><code class="docutils literal notranslate"><span class="pre">SpaceGroup.sg_encoding</span></code></a></li>
<li><a class="reference internal" href="#pymatgen.symmetry.groups.SpaceGroup.symmetry_ops"><code class="docutils literal notranslate"><span class="pre">SpaceGroup.symmetry_ops</span></code></a></li>
<li><a class="reference internal" href="#pymatgen.symmetry.groups.SpaceGroup.to_pretty_string"><code class="docutils literal notranslate"><span class="pre">SpaceGroup.to_pretty_string()</span></code></a></li>
<li><a class="reference internal" href="#pymatgen.symmetry.groups.SpaceGroup.translations"><code class="docutils literal notranslate"><span class="pre">SpaceGroup.translations</span></code></a></li>
</ul>
</li>
<li><a class="reference internal" href="#pymatgen.symmetry.groups.SymmetryGroup"><code class="docutils literal notranslate"><span class="pre">SymmetryGroup</span></code></a><ul>
<li><a class="reference internal" href="#pymatgen.symmetry.groups.SymmetryGroup.is_subgroup"><code class="docutils literal notranslate"><span class="pre">SymmetryGroup.is_subgroup()</span></code></a></li>
<li><a class="reference internal" href="#pymatgen.symmetry.groups.SymmetryGroup.is_supergroup"><code class="docutils literal notranslate"><span class="pre">SymmetryGroup.is_supergroup()</span></code></a></li>
<li><a class="reference internal" href="#pymatgen.symmetry.groups.SymmetryGroup.symmetry_ops"><code class="docutils literal notranslate"><span class="pre">SymmetryGroup.symmetry_ops</span></code></a></li>
<li><a class="reference internal" href="#pymatgen.symmetry.groups.SymmetryGroup.to_latex_string"><code class="docutils literal notranslate"><span class="pre">SymmetryGroup.to_latex_string()</span></code></a></li>
</ul>
</li>
<li><a class="reference internal" href="#pymatgen.symmetry.groups.in_array_list"><code class="docutils literal notranslate"><span class="pre">in_array_list()</span></code></a></li>
<li><a class="reference internal" href="#pymatgen.symmetry.groups.sg_symbol_from_int_number"><code class="docutils literal notranslate"><span class="pre">sg_symbol_from_int_number()</span></code></a></li>
</ul>
</li>
<li><a class="reference internal" href="#module-pymatgen.symmetry.kpath">pymatgen.symmetry.kpath module</a><ul>
<li><a class="reference internal" href="#pymatgen.symmetry.kpath.KPathBase"><code class="docutils literal notranslate"><span class="pre">KPathBase</span></code></a><ul>
<li><a class="reference internal" href="#pymatgen.symmetry.kpath.KPathBase.get_kpoints"><code class="docutils literal notranslate"><span class="pre">KPathBase.get_kpoints()</span></code></a></li>
<li><a class="reference internal" href="#pymatgen.symmetry.kpath.KPathBase.kpath"><code class="docutils literal notranslate"><span class="pre">KPathBase.kpath</span></code></a></li>
<li><a class="reference internal" href="#pymatgen.symmetry.kpath.KPathBase.lattice"><code class="docutils literal notranslate"><span class="pre">KPathBase.lattice</span></code></a></li>
<li><a class="reference internal" href="#pymatgen.symmetry.kpath.KPathBase.rec_lattice"><code class="docutils literal notranslate"><span class="pre">KPathBase.rec_lattice</span></code></a></li>
<li><a class="reference internal" href="#pymatgen.symmetry.kpath.KPathBase.structure"><code class="docutils literal notranslate"><span class="pre">KPathBase.structure</span></code></a></li>
</ul>
</li>
<li><a class="reference internal" href="#pymatgen.symmetry.kpath.KPathLatimerMunro"><code class="docutils literal notranslate"><span class="pre">KPathLatimerMunro</span></code></a><ul>
<li><a class="reference internal" href="#pymatgen.symmetry.kpath.KPathLatimerMunro.label_points"><code class="docutils literal notranslate"><span class="pre">KPathLatimerMunro.label_points()</span></code></a></li>
<li><a class="reference internal" href="#pymatgen.symmetry.kpath.KPathLatimerMunro.label_symbol"><code class="docutils literal notranslate"><span class="pre">KPathLatimerMunro.label_symbol()</span></code></a></li>
<li><a class="reference internal" href="#pymatgen.symmetry.kpath.KPathLatimerMunro.mag_type"><code class="docutils literal notranslate"><span class="pre">KPathLatimerMunro.mag_type</span></code></a></li>
</ul>
</li>
<li><a class="reference internal" href="#pymatgen.symmetry.kpath.KPathSeek"><code class="docutils literal notranslate"><span class="pre">KPathSeek</span></code></a></li>
<li><a class="reference internal" href="#pymatgen.symmetry.kpath.KPathSetyawanCurtarolo"><code class="docutils literal notranslate"><span class="pre">KPathSetyawanCurtarolo</span></code></a><ul>
<li><a class="reference internal" href="#pymatgen.symmetry.kpath.KPathSetyawanCurtarolo.bcc"><code class="docutils literal notranslate"><span class="pre">KPathSetyawanCurtarolo.bcc()</span></code></a></li>
<li><a class="reference internal" href="#pymatgen.symmetry.kpath.KPathSetyawanCurtarolo.bctet1"><code class="docutils literal notranslate"><span class="pre">KPathSetyawanCurtarolo.bctet1()</span></code></a></li>
<li><a class="reference internal" href="#pymatgen.symmetry.kpath.KPathSetyawanCurtarolo.bctet2"><code class="docutils literal notranslate"><span class="pre">KPathSetyawanCurtarolo.bctet2()</span></code></a></li>
<li><a class="reference internal" href="#pymatgen.symmetry.kpath.KPathSetyawanCurtarolo.conventional"><code class="docutils literal notranslate"><span class="pre">KPathSetyawanCurtarolo.conventional</span></code></a></li>
<li><a class="reference internal" href="#pymatgen.symmetry.kpath.KPathSetyawanCurtarolo.cubic"><code class="docutils literal notranslate"><span class="pre">KPathSetyawanCurtarolo.cubic()</span></code></a></li>
<li><a class="reference internal" href="#pymatgen.symmetry.kpath.KPathSetyawanCurtarolo.fcc"><code class="docutils literal notranslate"><span class="pre">KPathSetyawanCurtarolo.fcc()</span></code></a></li>
<li><a class="reference internal" href="#pymatgen.symmetry.kpath.KPathSetyawanCurtarolo.hex"><code class="docutils literal notranslate"><span class="pre">KPathSetyawanCurtarolo.hex()</span></code></a></li>
<li><a class="reference internal" href="#pymatgen.symmetry.kpath.KPathSetyawanCurtarolo.mcl"><code class="docutils literal notranslate"><span class="pre">KPathSetyawanCurtarolo.mcl()</span></code></a></li>
<li><a class="reference internal" href="#pymatgen.symmetry.kpath.KPathSetyawanCurtarolo.mclc1"><code class="docutils literal notranslate"><span class="pre">KPathSetyawanCurtarolo.mclc1()</span></code></a></li>
<li><a class="reference internal" href="#pymatgen.symmetry.kpath.KPathSetyawanCurtarolo.mclc2"><code class="docutils literal notranslate"><span class="pre">KPathSetyawanCurtarolo.mclc2()</span></code></a></li>
<li><a class="reference internal" href="#pymatgen.symmetry.kpath.KPathSetyawanCurtarolo.mclc3"><code class="docutils literal notranslate"><span class="pre">KPathSetyawanCurtarolo.mclc3()</span></code></a></li>
<li><a class="reference internal" href="#pymatgen.symmetry.kpath.KPathSetyawanCurtarolo.mclc4"><code class="docutils literal notranslate"><span class="pre">KPathSetyawanCurtarolo.mclc4()</span></code></a></li>
<li><a class="reference internal" href="#pymatgen.symmetry.kpath.KPathSetyawanCurtarolo.mclc5"><code class="docutils literal notranslate"><span class="pre">KPathSetyawanCurtarolo.mclc5()</span></code></a></li>
<li><a class="reference internal" href="#pymatgen.symmetry.kpath.KPathSetyawanCurtarolo.orc"><code class="docutils literal notranslate"><span class="pre">KPathSetyawanCurtarolo.orc()</span></code></a></li>
<li><a class="reference internal" href="#pymatgen.symmetry.kpath.KPathSetyawanCurtarolo.orcc"><code class="docutils literal notranslate"><span class="pre">KPathSetyawanCurtarolo.orcc()</span></code></a></li>
<li><a class="reference internal" href="#pymatgen.symmetry.kpath.KPathSetyawanCurtarolo.orcf1"><code class="docutils literal notranslate"><span class="pre">KPathSetyawanCurtarolo.orcf1()</span></code></a></li>
<li><a class="reference internal" href="#pymatgen.symmetry.kpath.KPathSetyawanCurtarolo.orcf2"><code class="docutils literal notranslate"><span class="pre">KPathSetyawanCurtarolo.orcf2()</span></code></a></li>
<li><a class="reference internal" href="#pymatgen.symmetry.kpath.KPathSetyawanCurtarolo.orcf3"><code class="docutils literal notranslate"><span class="pre">KPathSetyawanCurtarolo.orcf3()</span></code></a></li>
<li><a class="reference internal" href="#pymatgen.symmetry.kpath.KPathSetyawanCurtarolo.orci"><code class="docutils literal notranslate"><span class="pre">KPathSetyawanCurtarolo.orci()</span></code></a></li>
<li><a class="reference internal" href="#pymatgen.symmetry.kpath.KPathSetyawanCurtarolo.prim"><code class="docutils literal notranslate"><span class="pre">KPathSetyawanCurtarolo.prim</span></code></a></li>
<li><a class="reference internal" href="#pymatgen.symmetry.kpath.KPathSetyawanCurtarolo.prim_rec"><code class="docutils literal notranslate"><span class="pre">KPathSetyawanCurtarolo.prim_rec</span></code></a></li>
<li><a class="reference internal" href="#pymatgen.symmetry.kpath.KPathSetyawanCurtarolo.rhl1"><code class="docutils literal notranslate"><span class="pre">KPathSetyawanCurtarolo.rhl1()</span></code></a></li>
<li><a class="reference internal" href="#pymatgen.symmetry.kpath.KPathSetyawanCurtarolo.rhl2"><code class="docutils literal notranslate"><span class="pre">KPathSetyawanCurtarolo.rhl2()</span></code></a></li>
<li><a class="reference internal" href="#pymatgen.symmetry.kpath.KPathSetyawanCurtarolo.tet"><code class="docutils literal notranslate"><span class="pre">KPathSetyawanCurtarolo.tet()</span></code></a></li>
<li><a class="reference internal" href="#pymatgen.symmetry.kpath.KPathSetyawanCurtarolo.tria"><code class="docutils literal notranslate"><span class="pre">KPathSetyawanCurtarolo.tria()</span></code></a></li>
<li><a class="reference internal" href="#pymatgen.symmetry.kpath.KPathSetyawanCurtarolo.trib"><code class="docutils literal notranslate"><span class="pre">KPathSetyawanCurtarolo.trib()</span></code></a></li>
</ul>
</li>
</ul>
</li>
<li><a class="reference internal" href="#module-pymatgen.symmetry.maggroups">pymatgen.symmetry.maggroups module</a><ul>
<li><a class="reference internal" href="#pymatgen.symmetry.maggroups.MagneticSpaceGroup"><code class="docutils literal notranslate"><span class="pre">MagneticSpaceGroup</span></code></a><ul>
<li><a class="reference internal" href="#pymatgen.symmetry.maggroups.MagneticSpaceGroup.crystal_system"><code class="docutils literal notranslate"><span class="pre">MagneticSpaceGroup.crystal_system</span></code></a></li>
<li><a class="reference internal" href="#pymatgen.symmetry.maggroups.MagneticSpaceGroup.data_str"><code class="docutils literal notranslate"><span class="pre">MagneticSpaceGroup.data_str()</span></code></a></li>
<li><a class="reference internal" href="#pymatgen.symmetry.maggroups.MagneticSpaceGroup.from_og"><code class="docutils literal notranslate"><span class="pre">MagneticSpaceGroup.from_og()</span></code></a></li>
<li><a class="reference internal" href="#pymatgen.symmetry.maggroups.MagneticSpaceGroup.get_orbit"><code class="docutils literal notranslate"><span class="pre">MagneticSpaceGroup.get_orbit()</span></code></a></li>
<li><a class="reference internal" href="#pymatgen.symmetry.maggroups.MagneticSpaceGroup.is_compatible"><code class="docutils literal notranslate"><span class="pre">MagneticSpaceGroup.is_compatible()</span></code></a></li>
<li><a class="reference internal" href="#pymatgen.symmetry.maggroups.MagneticSpaceGroup.sg_symbol"><code class="docutils literal notranslate"><span class="pre">MagneticSpaceGroup.sg_symbol</span></code></a></li>
<li><a class="reference internal" href="#pymatgen.symmetry.maggroups.MagneticSpaceGroup.symmetry_ops"><code class="docutils literal notranslate"><span class="pre">MagneticSpaceGroup.symmetry_ops</span></code></a></li>
</ul>
</li>
</ul>
</li>
<li><a class="reference internal" href="#module-pymatgen.symmetry.settings">pymatgen.symmetry.settings module</a><ul>
<li><a class="reference internal" href="#pymatgen.symmetry.settings.JonesFaithfulTransformation"><code class="docutils literal notranslate"><span class="pre">JonesFaithfulTransformation</span></code></a><ul>
<li><a class="reference internal" href="#pymatgen.symmetry.settings.JonesFaithfulTransformation.P"><code class="docutils literal notranslate"><span class="pre">JonesFaithfulTransformation.P</span></code></a></li>
<li><a class="reference internal" href="#pymatgen.symmetry.settings.JonesFaithfulTransformation.from_origin_shift"><code class="docutils literal notranslate"><span class="pre">JonesFaithfulTransformation.from_origin_shift()</span></code></a></li>
<li><a class="reference internal" href="#pymatgen.symmetry.settings.JonesFaithfulTransformation.from_transformation_str"><code class="docutils literal notranslate"><span class="pre">JonesFaithfulTransformation.from_transformation_str()</span></code></a></li>
<li><a class="reference internal" href="#pymatgen.symmetry.settings.JonesFaithfulTransformation.inverse"><code class="docutils literal notranslate"><span class="pre">JonesFaithfulTransformation.inverse</span></code></a></li>
<li><a class="reference internal" href="#pymatgen.symmetry.settings.JonesFaithfulTransformation.p"><code class="docutils literal notranslate"><span class="pre">JonesFaithfulTransformation.p</span></code></a></li>
<li><a class="reference internal" href="#pymatgen.symmetry.settings.JonesFaithfulTransformation.parse_transformation_string"><code class="docutils literal notranslate"><span class="pre">JonesFaithfulTransformation.parse_transformation_string()</span></code></a></li>
<li><a class="reference internal" href="#pymatgen.symmetry.settings.JonesFaithfulTransformation.transform_coords"><code class="docutils literal notranslate"><span class="pre">JonesFaithfulTransformation.transform_coords()</span></code></a></li>
<li><a class="reference internal" href="#pymatgen.symmetry.settings.JonesFaithfulTransformation.transform_lattice"><code class="docutils literal notranslate"><span class="pre">JonesFaithfulTransformation.transform_lattice()</span></code></a></li>
<li><a class="reference internal" href="#pymatgen.symmetry.settings.JonesFaithfulTransformation.transform_symmop"><code class="docutils literal notranslate"><span class="pre">JonesFaithfulTransformation.transform_symmop()</span></code></a></li>
<li><a class="reference internal" href="#pymatgen.symmetry.settings.JonesFaithfulTransformation.transformation_string"><code class="docutils literal notranslate"><span class="pre">JonesFaithfulTransformation.transformation_string</span></code></a></li>
</ul>
</li>
</ul>
</li>
<li><a class="reference internal" href="#module-pymatgen.symmetry.site_symmetries">pymatgen.symmetry.site_symmetries module</a><ul>
<li><a class="reference internal" href="#pymatgen.symmetry.site_symmetries.get_shared_symmetry_operations"><code class="docutils literal notranslate"><span class="pre">get_shared_symmetry_operations()</span></code></a></li>
<li><a class="reference internal" href="#pymatgen.symmetry.site_symmetries.get_site_symmetries"><code class="docutils literal notranslate"><span class="pre">get_site_symmetries()</span></code></a></li>
</ul>
</li>
<li><a class="reference internal" href="#module-pymatgen.symmetry.structure">pymatgen.symmetry.structure module</a><ul>
<li><a class="reference internal" href="#pymatgen.symmetry.structure.SymmetrizedStructure"><code class="docutils literal notranslate"><span class="pre">SymmetrizedStructure</span></code></a><ul>
<li><a class="reference internal" href="#pymatgen.symmetry.structure.SymmetrizedStructure.equivalent_indices"><code class="docutils literal notranslate"><span class="pre">SymmetrizedStructure.equivalent_indices</span></code></a></li>
<li><a class="reference internal" href="#pymatgen.symmetry.structure.SymmetrizedStructure.as_dict"><code class="docutils literal notranslate"><span class="pre">SymmetrizedStructure.as_dict()</span></code></a></li>
<li><a class="reference internal" href="#pymatgen.symmetry.structure.SymmetrizedStructure.copy"><code class="docutils literal notranslate"><span class="pre">SymmetrizedStructure.copy()</span></code></a></li>
<li><a class="reference internal" href="#pymatgen.symmetry.structure.SymmetrizedStructure.find_equivalent_sites"><code class="docutils literal notranslate"><span class="pre">SymmetrizedStructure.find_equivalent_sites()</span></code></a></li>
<li><a class="reference internal" href="#pymatgen.symmetry.structure.SymmetrizedStructure.from_dict"><code class="docutils literal notranslate"><span class="pre">SymmetrizedStructure.from_dict()</span></code></a></li>
</ul>
</li>
</ul>
</li>
</ul>
</li>
</ul>
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  <section id="module-pymatgen.symmetry">
<span id="pymatgen-symmetry-package"></span><h1>pymatgen.symmetry package<a class="headerlink" href="#module-pymatgen.symmetry" title="Link to this heading"></a></h1>
<p>The symmetry package implements symmetry tools like spacegroup determination, etc.</p>
<section id="submodules">
<h2>Submodules<a class="headerlink" href="#submodules" title="Link to this heading"></a></h2>
</section>
<section id="module-pymatgen.symmetry.analyzer">
<span id="pymatgen-symmetry-analyzer-module"></span><h2>pymatgen.symmetry.analyzer module<a class="headerlink" href="#module-pymatgen.symmetry.analyzer" title="Link to this heading"></a></h2>
<p>An interface to the excellent spglib library by Atsushi Togo
(<a class="reference external" href="https://github.com/spglib/spglib">https://github.com/spglib/spglib</a>) for pymatgen.</p>
<p>v1.0 - Now works with both ordered and disordered structure.
v2.0 - Updated for spglib 1.6.
v3.0 - pymatgen no longer ships with spglib. Instead, spglib (the python</p>
<blockquote>
<div><p>version) is now a dependency and the SpacegroupAnalyzer merely serves
as an interface to spglib for pymatgen Structures.</p>
</div></blockquote>
<dl class="py class">
<dt class="sig sig-object py" id="pymatgen.symmetry.analyzer.PointGroupAnalyzer">
<em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">PointGroupAnalyzer</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">mol</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><a class="reference internal" href="pymatgen.core.html#pymatgen.core.structure.Molecule" title="pymatgen.core.structure.Molecule"><span class="pre">Molecule</span></a></span></em>, <em class="sig-param"><span class="n"><span class="pre">tolerance</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">float</span></span><span class="w"> </span><span class="o"><span class="pre">=</span></span><span class="w"> </span><span class="default_value"><span class="pre">0.3</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">eigen_tolerance</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">float</span></span><span class="w"> </span><span class="o"><span class="pre">=</span></span><span class="w"> </span><span class="default_value"><span class="pre">0.01</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">matrix_tolerance</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">float</span></span><span class="w"> </span><span class="o"><span class="pre">=</span></span><span class="w"> </span><span class="default_value"><span class="pre">0.1</span></span></em><span class="sig-paren">)</span><a class="reference external" href="https://github.com/materialsproject/pymatgen/blob/v2025.1.24/src/pymatgen/core/../symmetry/analyzer.py#L1014-L1557"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pymatgen.symmetry.analyzer.PointGroupAnalyzer" title="Link to this definition"></a></dt>
<dd><p>Bases: <code class="xref py py-class docutils literal notranslate"><span class="pre">object</span></code></p>
<p>A class to analyze the point group of a molecule.</p>
<p>The general outline of the algorithm is as follows:</p>
<ol class="arabic">
<li><p>Center the molecule around its center of mass.</p></li>
<li><p>Compute the inertia tensor and the eigenvalues and eigenvectors.</p></li>
<li><p>Handle the symmetry detection based on eigenvalues.</p>
<blockquote>
<div><ol class="loweralpha simple">
<li><p>Linear molecules have one zero eigenvalue. Possible symmetry
operations are C*v or D*v</p></li>
<li><p>Asymmetric top molecules have all different eigenvalues. The
maximum rotational symmetry in such molecules is 2</p></li>
<li><p>Symmetric top molecules have 1 unique eigenvalue, which gives a
unique rotation axis. All axial point groups are possible
except the cubic groups (T &amp; O) and I.</p></li>
<li><p>Spherical top molecules have all three eigenvalues equal. They
have the rare T, O or I point groups.</p></li>
</ol>
</div></blockquote>
</li>
</ol>
<dl class="simple">
<dt>Attribute:</dt><dd><p>sch_symbol (str): Schoenflies symbol of the detected point group.</p>
</dd>
</dl>
<p>The default settings are usually sufficient.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>mol</strong> (<a class="reference internal" href="pymatgen.core.html#pymatgen.core.structure.Molecule" title="pymatgen.core.structure.Molecule"><em>Molecule</em></a>) – Molecule to determine point group for.</p></li>
<li><p><strong>tolerance</strong> (<em>float</em>) – Distance tolerance to consider sites as
symmetrically equivalent. Defaults to 0.3 Angstrom.</p></li>
<li><p><strong>eigen_tolerance</strong> (<em>float</em>) – Tolerance to compare eigen values of
the inertia tensor. Defaults to 0.01.</p></li>
<li><p><strong>matrix_tolerance</strong> (<em>float</em>) – Tolerance used to generate the full set of
symmetry operations of the point group.</p></li>
</ul>
</dd>
</dl>
<dl class="py method">
<dt class="sig sig-object py" id="pymatgen.symmetry.analyzer.PointGroupAnalyzer.get_equivalent_atoms">
<span class="sig-name descname"><span class="pre">get_equivalent_atoms</span></span><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="reference external" href="https://github.com/materialsproject/pymatgen/blob/v2025.1.24/src/pymatgen/core/../symmetry/analyzer.py#L1512-L1523"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pymatgen.symmetry.analyzer.PointGroupAnalyzer.get_equivalent_atoms" title="Link to this definition"></a></dt>
<dd><p>Get sets of equivalent atoms with symmetry operations.</p>
<dl class="field-list simple">
<dt class="field-odd">Returns<span class="colon">:</span></dt>
<dd class="field-odd"><p><dl class="simple">
<dt>with two possible keys:</dt><dd><dl class="simple">
<dt>eq_sets: A dictionary of indices mapping to sets of indices, each key maps to</dt><dd><p>indices of all equivalent atoms. The keys are guaranteed to be not equivalent.</p>
</dd>
<dt>sym_ops: Twofold nested dictionary. operations[i][j] gives the symmetry</dt><dd><p>operation that maps atom i unto j.</p>
</dd>
</dl>
</dd>
</dl>
</p>
</dd>
<dt class="field-even">Return type<span class="colon">:</span></dt>
<dd class="field-even"><p>dict</p>
</dd>
</dl>
</dd></dl>

<dl class="py method">
<dt class="sig sig-object py" id="pymatgen.symmetry.analyzer.PointGroupAnalyzer.get_pointgroup">
<span class="sig-name descname"><span class="pre">get_pointgroup</span></span><span class="sig-paren">(</span><span class="sig-paren">)</span> <span class="sig-return"><span class="sig-return-icon">&#x2192;</span> <span class="sig-return-typehint"><a class="reference internal" href="#pymatgen.symmetry.analyzer.PointGroupOperations" title="pymatgen.symmetry.analyzer.PointGroupOperations"><span class="pre">PointGroupOperations</span></a></span></span><a class="reference external" href="https://github.com/materialsproject/pymatgen/blob/v2025.1.24/src/pymatgen/core/../symmetry/analyzer.py#L1369-L1371"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pymatgen.symmetry.analyzer.PointGroupAnalyzer.get_pointgroup" title="Link to this definition"></a></dt>
<dd><p>Get a PointGroup object for the molecule.</p>
</dd></dl>

<dl class="py method">
<dt class="sig sig-object py" id="pymatgen.symmetry.analyzer.PointGroupAnalyzer.get_rotational_symmetry_number">
<span class="sig-name descname"><span class="pre">get_rotational_symmetry_number</span></span><span class="sig-paren">(</span><span class="sig-paren">)</span> <span class="sig-return"><span class="sig-return-icon">&#x2192;</span> <span class="sig-return-typehint"><span class="pre">int</span></span></span><a class="reference external" href="https://github.com/materialsproject/pymatgen/blob/v2025.1.24/src/pymatgen/core/../symmetry/analyzer.py#L1381-L1398"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pymatgen.symmetry.analyzer.PointGroupAnalyzer.get_rotational_symmetry_number" title="Link to this definition"></a></dt>
<dd><p>Get rotational symmetry number.</p>
<dl class="field-list simple">
<dt class="field-odd">Returns<span class="colon">:</span></dt>
<dd class="field-odd"><p>Rotational symmetry number.</p>
</dd>
<dt class="field-even">Return type<span class="colon">:</span></dt>
<dd class="field-even"><p>int</p>
</dd>
</dl>
</dd></dl>

<dl class="py method">
<dt class="sig sig-object py" id="pymatgen.symmetry.analyzer.PointGroupAnalyzer.get_symmetry_operations">
<span class="sig-name descname"><span class="pre">get_symmetry_operations</span></span><span class="sig-paren">(</span><span class="sig-paren">)</span> <span class="sig-return"><span class="sig-return-icon">&#x2192;</span> <span class="sig-return-typehint"><span class="pre">Sequence</span><span class="p"><span class="pre">[</span></span><a class="reference internal" href="pymatgen.core.html#pymatgen.core.operations.SymmOp" title="pymatgen.core.operations.SymmOp"><span class="pre">SymmOp</span></a><span class="p"><span class="pre">]</span></span></span></span><a class="reference external" href="https://github.com/materialsproject/pymatgen/blob/v2025.1.24/src/pymatgen/core/../symmetry/analyzer.py#L1373-L1379"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pymatgen.symmetry.analyzer.PointGroupAnalyzer.get_symmetry_operations" title="Link to this definition"></a></dt>
<dd><p>Get symmetry operations.</p>
<dl class="field-list simple">
<dt class="field-odd">Returns<span class="colon">:</span></dt>
<dd class="field-odd"><p>symmetry operations in Cartesian coord.</p>
</dd>
<dt class="field-even">Return type<span class="colon">:</span></dt>
<dd class="field-even"><p>list[<a class="reference internal" href="pymatgen.core.html#pymatgen.core.operations.SymmOp" title="pymatgen.core.operations.SymmOp">SymmOp</a>]</p>
</dd>
</dl>
</dd></dl>

<dl class="py attribute">
<dt class="sig sig-object py" id="pymatgen.symmetry.analyzer.PointGroupAnalyzer.inversion_op">
<span class="sig-name descname"><span class="pre">inversion_op</span></span><em class="property"><span class="w"> </span><span class="p"><span class="pre">=</span></span><span class="w"> </span><span class="pre">SymmOp(self.affine_matrix=array([[-1.,</span> <span class="pre">-0.,</span> <span class="pre">-0.,</span>&#160; <span class="pre">0.],</span>&#160;&#160;&#160;&#160;&#160;&#160;&#160; <span class="pre">[-0.,</span> <span class="pre">-1.,</span> <span class="pre">-0.,</span>&#160; <span class="pre">0.],</span>&#160;&#160;&#160;&#160;&#160;&#160;&#160; <span class="pre">[-0.,</span> <span class="pre">-0.,</span> <span class="pre">-1.,</span>&#160; <span class="pre">0.],</span>&#160;&#160;&#160;&#160;&#160;&#160;&#160; <span class="pre">[-0.,</span> <span class="pre">-0.,</span> <span class="pre">-0.,</span>&#160; <span class="pre">1.]]))</span></em><a class="reference external" href="https://github.com/materialsproject/pymatgen/blob/v2025.1.24/src/pymatgen/symmetry/analyzer.py"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pymatgen.symmetry.analyzer.PointGroupAnalyzer.inversion_op" title="Link to this definition"></a></dt>
<dd></dd></dl>

<dl class="py method">
<dt class="sig sig-object py" id="pymatgen.symmetry.analyzer.PointGroupAnalyzer.is_valid_op">
<span class="sig-name descname"><span class="pre">is_valid_op</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">symm_op</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><a class="reference internal" href="pymatgen.core.html#pymatgen.core.operations.SymmOp" title="pymatgen.core.operations.SymmOp"><span class="pre">SymmOp</span></a></span></em><span class="sig-paren">)</span> <span class="sig-return"><span class="sig-return-icon">&#x2192;</span> <span class="sig-return-typehint"><span class="pre">bool</span></span></span><a class="reference external" href="https://github.com/materialsproject/pymatgen/blob/v2025.1.24/src/pymatgen/core/../symmetry/analyzer.py#L1400-L1416"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pymatgen.symmetry.analyzer.PointGroupAnalyzer.is_valid_op" title="Link to this definition"></a></dt>
<dd><p>Check if a particular symmetry operation is a valid symmetry operation for a
molecule, i.e., the operation maps all atoms to another equivalent atom.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
<dd class="field-odd"><p><strong>symm_op</strong> (<a class="reference internal" href="pymatgen.core.html#pymatgen.core.operations.SymmOp" title="pymatgen.core.operations.SymmOp"><em>SymmOp</em></a>) – Symmetry operation to test.</p>
</dd>
<dt class="field-even">Returns<span class="colon">:</span></dt>
<dd class="field-even"><p>True if SymmOp is valid for Molecule.</p>
</dd>
<dt class="field-odd">Return type<span class="colon">:</span></dt>
<dd class="field-odd"><p>bool</p>
</dd>
</dl>
</dd></dl>

<dl class="py method">
<dt class="sig sig-object py" id="pymatgen.symmetry.analyzer.PointGroupAnalyzer.symmetrize_molecule">
<span class="sig-name descname"><span class="pre">symmetrize_molecule</span></span><span class="sig-paren">(</span><span class="sig-paren">)</span> <span class="sig-return"><span class="sig-return-icon">&#x2192;</span> <span class="sig-return-typehint"><span class="pre">dict</span></span></span><a class="reference external" href="https://github.com/materialsproject/pymatgen/blob/v2025.1.24/src/pymatgen/core/../symmetry/analyzer.py#L1525-L1557"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pymatgen.symmetry.analyzer.PointGroupAnalyzer.symmetrize_molecule" title="Link to this definition"></a></dt>
<dd><p>Get a symmetrized molecule.</p>
<p>The equivalent atoms obtained via
<a class="reference internal" href="#pymatgen.symmetry.analyzer.PointGroupAnalyzer.get_equivalent_atoms" title="pymatgen.symmetry.analyzer.PointGroupAnalyzer.get_equivalent_atoms"><code class="xref py py-meth docutils literal notranslate"><span class="pre">get_equivalent_atoms()</span></code></a>
are rotated, mirrored… unto one position.
Then the average position is calculated.
The average position is rotated, mirrored… back with the inverse
of the previous symmetry operations, which gives the
symmetrized molecule</p>
<dl class="field-list simple">
<dt class="field-odd">Returns<span class="colon">:</span></dt>
<dd class="field-odd"><p><dl>
<dt>with three possible keys:</dt><dd><p>sym_mol: A symmetrized molecule instance.
eq_sets: A dictionary of indices mapping to sets of indices, each key maps to indices</p>
<blockquote>
<div><p>of all equivalent atoms. The keys are guaranteed to be not equivalent.</p>
</div></blockquote>
<dl class="simple">
<dt>sym_ops: Twofold nested dictionary. operations[i][j] gives the symmetry operation</dt><dd><p>that maps atom i unto j.</p>
</dd>
</dl>
</dd>
</dl>
</p>
</dd>
<dt class="field-even">Return type<span class="colon">:</span></dt>
<dd class="field-even"><p>dict</p>
</dd>
</dl>
</dd></dl>

</dd></dl>

<dl class="py class">
<dt class="sig sig-object py" id="pymatgen.symmetry.analyzer.PointGroupOperations">
<em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">PointGroupOperations</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">sch_symbol</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">str</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">operations</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">Sequence</span><span class="p"><span class="pre">[</span></span><a class="reference internal" href="pymatgen.core.html#pymatgen.core.operations.SymmOp" title="pymatgen.core.operations.SymmOp"><span class="pre">SymmOp</span></a><span class="p"><span class="pre">]</span></span></span></em>, <em class="sig-param"><span class="n"><span class="pre">tol</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">float</span></span><span class="w"> </span><span class="o"><span class="pre">=</span></span><span class="w"> </span><span class="default_value"><span class="pre">0.1</span></span></em><span class="sig-paren">)</span><a class="reference external" href="https://github.com/materialsproject/pymatgen/blob/v2025.1.24/src/pymatgen/core/../symmetry/analyzer.py#L1747-L1773"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pymatgen.symmetry.analyzer.PointGroupOperations" title="Link to this definition"></a></dt>
<dd><p>Bases: <code class="xref py py-class docutils literal notranslate"><span class="pre">list</span></code></p>
<p>Represents a point group, which is a sequence of symmetry operations.</p>
<dl class="py attribute">
<dt class="sig sig-object py" id="pymatgen.symmetry.analyzer.PointGroupOperations.sch_symbol">
<span class="sig-name descname"><span class="pre">sch_symbol</span></span><a class="reference external" href="https://github.com/materialsproject/pymatgen/blob/v2025.1.24/src/pymatgen/symmetry/analyzer.py"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pymatgen.symmetry.analyzer.PointGroupOperations.sch_symbol" title="Link to this definition"></a></dt>
<dd><p>Schoenflies symbol of the point group.</p>
<dl class="field-list simple">
<dt class="field-odd">Type<span class="colon">:</span></dt>
<dd class="field-odd"><p>str</p>
</dd>
</dl>
</dd></dl>

<dl class="field-list simple">
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>sch_symbol</strong> (<em>str</em>) – Schoenflies symbol of the point group.</p></li>
<li><p><strong>operations</strong> (<em>[</em><a class="reference internal" href="pymatgen.core.html#pymatgen.core.operations.SymmOp" title="pymatgen.core.operations.SymmOp"><em>SymmOp</em></a><em>]</em>) – Initial set of symmetry operations. It is
sufficient to provide only just enough operations to generate
the full set of symmetries.</p></li>
<li><p><strong>tol</strong> (<em>float</em>) – Tolerance to generate the full set of symmetry
operations.</p></li>
</ul>
</dd>
</dl>
</dd></dl>

<dl class="py class">
<dt class="sig sig-object py" id="pymatgen.symmetry.analyzer.SpacegroupAnalyzer">
<em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">SpacegroupAnalyzer</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">structure</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><a class="reference internal" href="pymatgen.core.html#pymatgen.core.structure.Structure" title="pymatgen.core.structure.Structure"><span class="pre">Structure</span></a></span></em>, <em class="sig-param"><span class="n"><span class="pre">symprec</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">float</span><span class="w"> </span><span class="p"><span class="pre">|</span></span><span class="w"> </span><span class="pre">None</span></span><span class="w"> </span><span class="o"><span class="pre">=</span></span><span class="w"> </span><span class="default_value"><span class="pre">0.01</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">angle_tolerance</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">float</span></span><span class="w"> </span><span class="o"><span class="pre">=</span></span><span class="w"> </span><span class="default_value"><span class="pre">5</span></span></em><span class="sig-paren">)</span><a class="reference external" href="https://github.com/materialsproject/pymatgen/blob/v2025.1.24/src/pymatgen/core/../symmetry/analyzer.py#L84-L1011"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pymatgen.symmetry.analyzer.SpacegroupAnalyzer" title="Link to this definition"></a></dt>
<dd><p>Bases: <code class="xref py py-class docutils literal notranslate"><span class="pre">object</span></code></p>
<p>Takes a pymatgen Structure object and a symprec.</p>
<p>Uses spglib to perform various symmetry finding operations.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>structure</strong> (<a class="reference internal" href="pymatgen.core.html#pymatgen.core.structure.Structure" title="pymatgen.core.structure.Structure"><em>Structure</em></a><em> | </em><a class="reference internal" href="pymatgen.core.html#pymatgen.core.structure.IStructure" title="pymatgen.core.structure.IStructure"><em>IStructure</em></a>) – Structure to find symmetry</p></li>
<li><p><strong>symprec</strong> (<em>float</em>) – Tolerance for symmetry finding. Defaults to 0.01,
which is fairly strict and works well for properly refined
structures with atoms in the proper symmetry coordinates. For
structures with slight deviations from their proper atomic
positions (e.g., structures relaxed with electronic structure
codes), a looser tolerance of 0.1 (the value used in Materials
Project) is often needed.</p></li>
<li><p><strong>angle_tolerance</strong> (<em>float</em>) – Angle tolerance for symmetry finding. Defaults to 5 degrees.</p></li>
</ul>
</dd>
</dl>
<dl class="py method">
<dt class="sig sig-object py" id="pymatgen.symmetry.analyzer.SpacegroupAnalyzer.find_primitive">
<span class="sig-name descname"><span class="pre">find_primitive</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">keep_site_properties</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">bool</span></span><span class="w"> </span><span class="o"><span class="pre">=</span></span><span class="w"> </span><span class="default_value"><span class="pre">False</span></span></em><span class="sig-paren">)</span> <span class="sig-return"><span class="sig-return-icon">&#x2192;</span> <span class="sig-return-typehint"><a class="reference internal" href="pymatgen.core.html#pymatgen.core.structure.Structure" title="pymatgen.core.structure.Structure"><span class="pre">Structure</span></a></span></span><a class="reference external" href="https://github.com/materialsproject/pymatgen/blob/v2025.1.24/src/pymatgen/core/../symmetry/analyzer.py#L390-L423"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pymatgen.symmetry.analyzer.SpacegroupAnalyzer.find_primitive" title="Link to this definition"></a></dt>
<dd><p>Find a primitive version of the unit cell.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
<dd class="field-odd"><p><strong>keep_site_properties</strong> (<em>bool</em>) – Whether to keep the input site properties (including
magnetic moments) on the sites that are still present after the refinement. Note:
This is disabled by default because the magnetic moments are not always directly
transferable between unit cell definitions. For instance, long-range magnetic
ordering or antiferromagnetic character may no longer be present (or exist in
the same way) in the returned structure. If keep_site_properties is True,
each site retains the same site property as in the original structure without
further adjustment.</p>
</dd>
<dt class="field-even">Returns<span class="colon">:</span></dt>
<dd class="field-even"><p>A primitive cell in the input cell is searched and returned
as a Structure object. If no primitive cell is found, None is
returned.</p>
</dd>
</dl>
</dd></dl>

<dl class="py method">
<dt class="sig sig-object py" id="pymatgen.symmetry.analyzer.SpacegroupAnalyzer.get_conventional_standard_structure">
<span class="sig-name descname"><span class="pre">get_conventional_standard_structure</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">international_monoclinic</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">bool</span></span><span class="w"> </span><span class="o"><span class="pre">=</span></span><span class="w"> </span><span class="default_value"><span class="pre">True</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">keep_site_properties</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">bool</span></span><span class="w"> </span><span class="o"><span class="pre">=</span></span><span class="w"> </span><span class="default_value"><span class="pre">False</span></span></em><span class="sig-paren">)</span> <span class="sig-return"><span class="sig-return-icon">&#x2192;</span> <span class="sig-return-typehint"><a class="reference internal" href="pymatgen.core.html#pymatgen.core.structure.Structure" title="pymatgen.core.structure.Structure"><span class="pre">Structure</span></a></span></span><a class="reference external" href="https://github.com/materialsproject/pymatgen/blob/v2025.1.24/src/pymatgen/core/../symmetry/analyzer.py#L607-L947"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pymatgen.symmetry.analyzer.SpacegroupAnalyzer.get_conventional_standard_structure" title="Link to this definition"></a></dt>
<dd><p>Get a structure with a conventional cell according to certain standards. The
standards are defined in Setyawan, W., &amp; Curtarolo, S. (2010). High-throughput
electronic band structure calculations: Challenges and tools. Computational
Materials Science, 49(2), 299-312. doi:10.1016/j.commatsci.2010.05.010 They
basically enforce as much as possible norm(a1)&lt;norm(a2)&lt;norm(a3). NB This is not
necessarily the same as the standard settings within the International Tables of
Crystallography, for which get_refined_structure should be used instead.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>international_monoclinic</strong> (<em>bool</em>) – Whether to convert to proper international convention
such that beta is the non-right angle.</p></li>
<li><p><strong>keep_site_properties</strong> (<em>bool</em>) – Whether to keep the input site properties (including
magnetic moments) on the sites that are still present after the refinement. Note:
This is disabled by default because the magnetic moments are not always directly
transferable between unit cell definitions. For instance, long-range magnetic
ordering or antiferromagnetic character may no longer be present (or exist in
the same way) in the returned structure. If keep_site_properties is True,
each site retains the same site property as in the original structure without
further adjustment.</p></li>
</ul>
</dd>
<dt class="field-even">Returns<span class="colon">:</span></dt>
<dd class="field-even"><p>The structure in a conventional standardized cell</p>
</dd>
</dl>
</dd></dl>

<dl class="py method">
<dt class="sig sig-object py" id="pymatgen.symmetry.analyzer.SpacegroupAnalyzer.get_conventional_to_primitive_transformation_matrix">
<span class="sig-name descname"><span class="pre">get_conventional_to_primitive_transformation_matrix</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">international_monoclinic</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">bool</span></span><span class="w"> </span><span class="o"><span class="pre">=</span></span><span class="w"> </span><span class="default_value"><span class="pre">True</span></span></em><span class="sig-paren">)</span> <span class="sig-return"><span class="sig-return-icon">&#x2192;</span> <span class="sig-return-typehint"><span class="pre">NDArray</span></span></span><a class="reference external" href="https://github.com/materialsproject/pymatgen/blob/v2025.1.24/src/pymatgen/core/../symmetry/analyzer.py#L478-L521"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pymatgen.symmetry.analyzer.SpacegroupAnalyzer.get_conventional_to_primitive_transformation_matrix" title="Link to this definition"></a></dt>
<dd><p>Get the transformation matrix to transform a conventional unit cell to a
primitive cell according to certain standards the standards are defined in
Setyawan, W., &amp; Curtarolo, S. (2010). High-throughput electronic band structure
calculations: Challenges and tools. Computational Materials Science, 49(2),
299-312. doi:10.1016/j.commatsci.2010.05.010.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
<dd class="field-odd"><p><strong>international_monoclinic</strong> (<em>bool</em>) – Whether to convert to proper international convention
such that beta is the non-right angle.</p>
</dd>
<dt class="field-even">Returns<span class="colon">:</span></dt>
<dd class="field-even"><p>Transformation matrix to go from conventional to primitive cell</p>
</dd>
</dl>
</dd></dl>

<dl class="py method">
<dt class="sig sig-object py" id="pymatgen.symmetry.analyzer.SpacegroupAnalyzer.get_crystal_system">
<span class="sig-name descname"><span class="pre">get_crystal_system</span></span><span class="sig-paren">(</span><span class="sig-paren">)</span> <span class="sig-return"><span class="sig-return-icon">&#x2192;</span> <span class="sig-return-typehint"><span class="pre">CrystalSystem</span></span></span><a class="reference external" href="https://github.com/materialsproject/pymatgen/blob/v2025.1.24/src/pymatgen/core/../symmetry/analyzer.py#L202-L230"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pymatgen.symmetry.analyzer.SpacegroupAnalyzer.get_crystal_system" title="Link to this definition"></a></dt>
<dd><p>Get the crystal system for the structure, e.g. (triclinic, orthorhombic,
cubic, etc.).</p>
<dl class="field-list simple">
<dt class="field-odd">Raises<span class="colon">:</span></dt>
<dd class="field-odd"><p><strong>ValueError</strong> – on invalid space group numbers &lt; 1 or &gt; 230.</p>
</dd>
<dt class="field-even">Returns<span class="colon">:</span></dt>
<dd class="field-even"><p>Crystal system for structure</p>
</dd>
<dt class="field-odd">Return type<span class="colon">:</span></dt>
<dd class="field-odd"><p>str</p>
</dd>
</dl>
</dd></dl>

<dl class="py method">
<dt class="sig sig-object py" id="pymatgen.symmetry.analyzer.SpacegroupAnalyzer.get_hall">
<span class="sig-name descname"><span class="pre">get_hall</span></span><span class="sig-paren">(</span><span class="sig-paren">)</span> <span class="sig-return"><span class="sig-return-icon">&#x2192;</span> <span class="sig-return-typehint"><span class="pre">str</span></span></span><a class="reference external" href="https://github.com/materialsproject/pymatgen/blob/v2025.1.24/src/pymatgen/core/../symmetry/analyzer.py#L182-L188"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pymatgen.symmetry.analyzer.SpacegroupAnalyzer.get_hall" title="Link to this definition"></a></dt>
<dd><p>Get Hall symbol for structure.</p>
<dl class="field-list simple">
<dt class="field-odd">Returns<span class="colon">:</span></dt>
<dd class="field-odd"><p>Hall symbol</p>
</dd>
<dt class="field-even">Return type<span class="colon">:</span></dt>
<dd class="field-even"><p>str</p>
</dd>
</dl>
</dd></dl>

<dl class="py method">
<dt class="sig sig-object py" id="pymatgen.symmetry.analyzer.SpacegroupAnalyzer.get_ir_reciprocal_mesh">
<span class="sig-name descname"><span class="pre">get_ir_reciprocal_mesh</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">mesh</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">tuple</span><span class="p"><span class="pre">[</span></span><span class="pre">int</span><span class="p"><span class="pre">,</span></span><span class="w"> </span><span class="pre">int</span><span class="p"><span class="pre">,</span></span><span class="w"> </span><span class="pre">int</span><span class="p"><span class="pre">]</span></span></span><span class="w"> </span><span class="o"><span class="pre">=</span></span><span class="w"> </span><span class="default_value"><span class="pre">(10,</span> <span class="pre">10,</span> <span class="pre">10)</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">is_shift</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">tuple</span><span class="p"><span class="pre">[</span></span><span class="pre">float</span><span class="p"><span class="pre">,</span></span><span class="w"> </span><span class="pre">float</span><span class="p"><span class="pre">,</span></span><span class="w"> </span><span class="pre">float</span><span class="p"><span class="pre">]</span></span></span><span class="w"> </span><span class="o"><span class="pre">=</span></span><span class="w"> </span><span class="default_value"><span class="pre">(0,</span> <span class="pre">0,</span> <span class="pre">0)</span></span></em><span class="sig-paren">)</span> <span class="sig-return"><span class="sig-return-icon">&#x2192;</span> <span class="sig-return-typehint"><span class="pre">list</span><span class="p"><span class="pre">[</span></span><span class="pre">tuple</span><span class="p"><span class="pre">[</span></span><a class="reference internal" href="pymatgen.electronic_structure.html#pymatgen.electronic_structure.bandstructure.Kpoint" title="pymatgen.electronic_structure.bandstructure.Kpoint"><span class="pre">Kpoint</span></a><span class="p"><span class="pre">,</span></span><span class="w"> </span><span class="pre">float</span><span class="p"><span class="pre">]</span></span><span class="p"><span class="pre">]</span></span></span></span><a class="reference external" href="https://github.com/materialsproject/pymatgen/blob/v2025.1.24/src/pymatgen/core/../symmetry/analyzer.py#L425-L450"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pymatgen.symmetry.analyzer.SpacegroupAnalyzer.get_ir_reciprocal_mesh" title="Link to this definition"></a></dt>
<dd><p>k-point mesh of the Brillouin zone generated taken into account symmetry.
The method returns the irreducible kpoints of the mesh and their weights.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>mesh</strong> (<em>3x1 array</em>) – The number of kpoint for the mesh needed in
each direction</p></li>
<li><p><strong>is_shift</strong> (<em>3x1 array</em>) – Whether to shift the kpoint grid. (1, 1,</p></li>
<li><p><strong>0.5</strong> (<em>1</em><em>) </em><em>means all points are shifted by</em>)</p></li>
<li><p><strong>0.5</strong></p></li>
<li><p><strong>0.5.</strong></p></li>
</ul>
</dd>
<dt class="field-even">Returns<span class="colon">:</span></dt>
<dd class="field-even"><p>A list of irreducible kpoints and their weights as a list of
tuples [(ir_kpoint, weight)], with ir_kpoint given
in fractional coordinates</p>
</dd>
</dl>
</dd></dl>

<dl class="py method">
<dt class="sig sig-object py" id="pymatgen.symmetry.analyzer.SpacegroupAnalyzer.get_ir_reciprocal_mesh_map">
<span class="sig-name descname"><span class="pre">get_ir_reciprocal_mesh_map</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">mesh</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">tuple</span><span class="p"><span class="pre">[</span></span><span class="pre">int</span><span class="p"><span class="pre">,</span></span><span class="w"> </span><span class="pre">int</span><span class="p"><span class="pre">,</span></span><span class="w"> </span><span class="pre">int</span><span class="p"><span class="pre">]</span></span></span><span class="w"> </span><span class="o"><span class="pre">=</span></span><span class="w"> </span><span class="default_value"><span class="pre">(10,</span> <span class="pre">10,</span> <span class="pre">10)</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">is_shift</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">tuple</span><span class="p"><span class="pre">[</span></span><span class="pre">float</span><span class="p"><span class="pre">,</span></span><span class="w"> </span><span class="pre">float</span><span class="p"><span class="pre">,</span></span><span class="w"> </span><span class="pre">float</span><span class="p"><span class="pre">]</span></span></span><span class="w"> </span><span class="o"><span class="pre">=</span></span><span class="w"> </span><span class="default_value"><span class="pre">(0,</span> <span class="pre">0,</span> <span class="pre">0)</span></span></em><span class="sig-paren">)</span> <span class="sig-return"><span class="sig-return-icon">&#x2192;</span> <span class="sig-return-typehint"><span class="pre">tuple</span><span class="p"><span class="pre">[</span></span><span class="pre">NDArray</span><span class="p"><span class="pre">,</span></span><span class="w"> </span><span class="pre">NDArray</span><span class="p"><span class="pre">]</span></span></span></span><a class="reference external" href="https://github.com/materialsproject/pymatgen/blob/v2025.1.24/src/pymatgen/core/../symmetry/analyzer.py#L452-L476"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pymatgen.symmetry.analyzer.SpacegroupAnalyzer.get_ir_reciprocal_mesh_map" title="Link to this definition"></a></dt>
<dd><p>Same as ‘get_ir_reciprocal_mesh’ but the full grid together with the mapping
that maps a reducible to an irreducible kpoint is returned.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>mesh</strong> (<em>3x1 array</em>) – The number of kpoint for the mesh needed in
each direction</p></li>
<li><p><strong>is_shift</strong> (<em>3x1 array</em>) – Whether to shift the kpoint grid. (1, 1,</p></li>
<li><p><strong>0.5</strong> (<em>1</em><em>) </em><em>means all points are shifted by</em>)</p></li>
<li><p><strong>0.5</strong></p></li>
<li><p><strong>0.5.</strong></p></li>
</ul>
</dd>
<dt class="field-even">Returns<span class="colon">:</span></dt>
<dd class="field-even"><p>A tuple containing two numpy.ndarray. The first is the mesh in
fractional coordinates and the second is an array of integers
that maps all the reducible kpoints from to irreducible ones.</p>
</dd>
</dl>
</dd></dl>

<dl class="py method">
<dt class="sig sig-object py" id="pymatgen.symmetry.analyzer.SpacegroupAnalyzer.get_kpoint_weights">
<span class="sig-name descname"><span class="pre">get_kpoint_weights</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">kpoints</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">Sequence</span><span class="p"><span class="pre">[</span></span><a class="reference internal" href="pymatgen.electronic_structure.html#pymatgen.electronic_structure.bandstructure.Kpoint" title="pymatgen.electronic_structure.bandstructure.Kpoint"><span class="pre">Kpoint</span></a><span class="p"><span class="pre">]</span></span></span></em>, <em class="sig-param"><span class="n"><span class="pre">atol</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">float</span></span><span class="w"> </span><span class="o"><span class="pre">=</span></span><span class="w"> </span><span class="default_value"><span class="pre">1e-05</span></span></em><span class="sig-paren">)</span> <span class="sig-return"><span class="sig-return-icon">&#x2192;</span> <span class="sig-return-typehint"><span class="pre">list</span><span class="p"><span class="pre">[</span></span><span class="pre">float</span><span class="p"><span class="pre">]</span></span></span></span><a class="reference external" href="https://github.com/materialsproject/pymatgen/blob/v2025.1.24/src/pymatgen/core/../symmetry/analyzer.py#L949-L993"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pymatgen.symmetry.analyzer.SpacegroupAnalyzer.get_kpoint_weights" title="Link to this definition"></a></dt>
<dd><p>Calculate the weights for a list of kpoints.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>kpoints</strong> (<em>Sequence</em>) – Sequence of kpoints. np.arrays is fine. Note
that the code does not check that the list of kpoints
provided does not contain duplicates.</p></li>
<li><p><strong>atol</strong> (<em>float</em>) – Tolerance for fractional coordinates comparisons.</p></li>
</ul>
</dd>
<dt class="field-even">Returns<span class="colon">:</span></dt>
<dd class="field-even"><p>List of weights, in the SAME order as kpoints.</p>
</dd>
</dl>
</dd></dl>

<dl class="py method">
<dt class="sig sig-object py" id="pymatgen.symmetry.analyzer.SpacegroupAnalyzer.get_lattice_type">
<span class="sig-name descname"><span class="pre">get_lattice_type</span></span><span class="sig-paren">(</span><span class="sig-paren">)</span> <span class="sig-return"><span class="sig-return-icon">&#x2192;</span> <span class="sig-return-typehint"><span class="pre">LatticeType</span></span></span><a class="reference external" href="https://github.com/materialsproject/pymatgen/blob/v2025.1.24/src/pymatgen/core/../symmetry/analyzer.py#L232-L247"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pymatgen.symmetry.analyzer.SpacegroupAnalyzer.get_lattice_type" title="Link to this definition"></a></dt>
<dd><p>Get the lattice for the structure, e.g. (triclinic, orthorhombic, cubic,
etc.).This is the same as the crystal system with the exception of the
hexagonal/rhombohedral lattice.</p>
<dl class="field-list simple">
<dt class="field-odd">Raises<span class="colon">:</span></dt>
<dd class="field-odd"><p><strong>ValueError</strong> – on invalid space group numbers &lt; 1 or &gt; 230.</p>
</dd>
<dt class="field-even">Returns<span class="colon">:</span></dt>
<dd class="field-even"><p>Lattice type for structure</p>
</dd>
<dt class="field-odd">Return type<span class="colon">:</span></dt>
<dd class="field-odd"><p>str</p>
</dd>
</dl>
</dd></dl>

<dl class="py method">
<dt class="sig sig-object py" id="pymatgen.symmetry.analyzer.SpacegroupAnalyzer.get_point_group_operations">
<span class="sig-name descname"><span class="pre">get_point_group_operations</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">cartesian</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">bool</span></span><span class="w"> </span><span class="o"><span class="pre">=</span></span><span class="w"> </span><span class="default_value"><span class="pre">False</span></span></em><span class="sig-paren">)</span> <span class="sig-return"><span class="sig-return-icon">&#x2192;</span> <span class="sig-return-typehint"><span class="pre">list</span><span class="p"><span class="pre">[</span></span><a class="reference internal" href="pymatgen.core.html#pymatgen.core.operations.SymmOp" title="pymatgen.core.operations.SymmOp"><span class="pre">SymmOp</span></a><span class="p"><span class="pre">]</span></span></span></span><a class="reference external" href="https://github.com/materialsproject/pymatgen/blob/v2025.1.24/src/pymatgen/core/../symmetry/analyzer.py#L319-L344"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pymatgen.symmetry.analyzer.SpacegroupAnalyzer.get_point_group_operations" title="Link to this definition"></a></dt>
<dd><p>Return symmetry operations as a list of SymmOp objects. By default returns
fractional coord symm ops. But Cartesian can be returned too.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
<dd class="field-odd"><p><strong>cartesian</strong> (<em>bool</em>) – Whether to return SymmOps as Cartesian or
direct coordinate operations.</p>
</dd>
<dt class="field-even">Returns<span class="colon">:</span></dt>
<dd class="field-even"><p>Point group symmetry operations.</p>
</dd>
<dt class="field-odd">Return type<span class="colon">:</span></dt>
<dd class="field-odd"><p>list[<a class="reference internal" href="pymatgen.core.html#pymatgen.core.operations.SymmOp" title="pymatgen.core.operations.SymmOp">SymmOp</a>]</p>
</dd>
</dl>
</dd></dl>

<dl class="py method">
<dt class="sig sig-object py" id="pymatgen.symmetry.analyzer.SpacegroupAnalyzer.get_point_group_symbol">
<span class="sig-name descname"><span class="pre">get_point_group_symbol</span></span><span class="sig-paren">(</span><span class="sig-paren">)</span> <span class="sig-return"><span class="sig-return-icon">&#x2192;</span> <span class="sig-return-typehint"><span class="pre">str</span></span></span><a class="reference external" href="https://github.com/materialsproject/pymatgen/blob/v2025.1.24/src/pymatgen/core/../symmetry/analyzer.py#L190-L200"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pymatgen.symmetry.analyzer.SpacegroupAnalyzer.get_point_group_symbol" title="Link to this definition"></a></dt>
<dd><p>Get the point group associated with the structure.</p>
<dl class="field-list simple">
<dt class="field-odd">Returns<span class="colon">:</span></dt>
<dd class="field-odd"><p>Point group for structure.</p>
</dd>
<dt class="field-even">Return type<span class="colon">:</span></dt>
<dd class="field-even"><p>Pointgroup</p>
</dd>
</dl>
</dd></dl>

<dl class="py method">
<dt class="sig sig-object py" id="pymatgen.symmetry.analyzer.SpacegroupAnalyzer.get_primitive_standard_structure">
<span class="sig-name descname"><span class="pre">get_primitive_standard_structure</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">international_monoclinic</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">bool</span></span><span class="w"> </span><span class="o"><span class="pre">=</span></span><span class="w"> </span><span class="default_value"><span class="pre">True</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">keep_site_properties</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">bool</span></span><span class="w"> </span><span class="o"><span class="pre">=</span></span><span class="w"> </span><span class="default_value"><span class="pre">False</span></span></em><span class="sig-paren">)</span> <span class="sig-return"><span class="sig-return-icon">&#x2192;</span> <span class="sig-return-typehint"><a class="reference internal" href="pymatgen.core.html#pymatgen.core.structure.Structure" title="pymatgen.core.structure.Structure"><span class="pre">Structure</span></a></span></span><a class="reference external" href="https://github.com/materialsproject/pymatgen/blob/v2025.1.24/src/pymatgen/core/../symmetry/analyzer.py#L523-L605"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pymatgen.symmetry.analyzer.SpacegroupAnalyzer.get_primitive_standard_structure" title="Link to this definition"></a></dt>
<dd><p>Get a structure with a primitive cell according to certain standards. The
standards are defined in Setyawan, W., &amp; Curtarolo, S. (2010). High-throughput
electronic band structure calculations: Challenges and tools. Computational
Materials Science, 49(2), 299-312. doi:10.1016/j.commatsci.2010.05.010.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>international_monoclinic</strong> (<em>bool</em>) – Whether to convert to proper international convention
such that beta is the non-right angle.</p></li>
<li><p><strong>keep_site_properties</strong> (<em>bool</em>) – Whether to keep the input site properties (including
magnetic moments) on the sites that are still present after the refinement. Note:
This is disabled by default because the magnetic moments are not always directly
transferable between unit cell definitions. For instance, long-range magnetic
ordering or antiferromagnetic character may no longer be present (or exist in
the same way) in the returned structure. If keep_site_properties is True,
each site retains the same site property as in the original structure without
further adjustment.</p></li>
</ul>
</dd>
<dt class="field-even">Returns<span class="colon">:</span></dt>
<dd class="field-even"><p>The structure in a primitive standardized cell</p>
</dd>
</dl>
</dd></dl>

<dl class="py method">
<dt class="sig sig-object py" id="pymatgen.symmetry.analyzer.SpacegroupAnalyzer.get_refined_structure">
<span class="sig-name descname"><span class="pre">get_refined_structure</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">keep_site_properties</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">bool</span></span><span class="w"> </span><span class="o"><span class="pre">=</span></span><span class="w"> </span><span class="default_value"><span class="pre">False</span></span></em><span class="sig-paren">)</span> <span class="sig-return"><span class="sig-return-icon">&#x2192;</span> <span class="sig-return-typehint"><a class="reference internal" href="pymatgen.core.html#pymatgen.core.structure.Structure" title="pymatgen.core.structure.Structure"><span class="pre">Structure</span></a></span></span><a class="reference external" href="https://github.com/materialsproject/pymatgen/blob/v2025.1.24/src/pymatgen/core/../symmetry/analyzer.py#L361-L388"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pymatgen.symmetry.analyzer.SpacegroupAnalyzer.get_refined_structure" title="Link to this definition"></a></dt>
<dd><p>Get the refined structure based on detected symmetry. The refined structure is
a <em>conventional</em> cell setting with atoms moved to the expected symmetry positions.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
<dd class="field-odd"><p><strong>keep_site_properties</strong> (<em>bool</em>) – Whether to keep the input site properties (including
magnetic moments) on the sites that are still present after the refinement. Note:
This is disabled by default because the magnetic moments are not always directly
transferable between unit cell definitions. For instance, long-range magnetic
ordering or antiferromagnetic character may no longer be present (or exist in
the same way) in the returned structure. If keep_site_properties is True,
each site retains the same site property as in the original structure without
further adjustment.</p>
</dd>
<dt class="field-even">Returns<span class="colon">:</span></dt>
<dd class="field-even"><p>Refined structure.</p>
</dd>
</dl>
</dd></dl>

<dl class="py method">
<dt class="sig sig-object py" id="pymatgen.symmetry.analyzer.SpacegroupAnalyzer.get_space_group_number">
<span class="sig-name descname"><span class="pre">get_space_group_number</span></span><span class="sig-paren">(</span><span class="sig-paren">)</span> <span class="sig-return"><span class="sig-return-icon">&#x2192;</span> <span class="sig-return-typehint"><span class="pre">int</span></span></span><a class="reference external" href="https://github.com/materialsproject/pymatgen/blob/v2025.1.24/src/pymatgen/core/../symmetry/analyzer.py#L162-L168"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pymatgen.symmetry.analyzer.SpacegroupAnalyzer.get_space_group_number" title="Link to this definition"></a></dt>
<dd><p>Get the international spacegroup number (e.g., 62) for structure.</p>
<dl class="field-list simple">
<dt class="field-odd">Returns<span class="colon">:</span></dt>
<dd class="field-odd"><p>International spacegroup number for structure.</p>
</dd>
<dt class="field-even">Return type<span class="colon">:</span></dt>
<dd class="field-even"><p>int</p>
</dd>
</dl>
</dd></dl>

<dl class="py method">
<dt class="sig sig-object py" id="pymatgen.symmetry.analyzer.SpacegroupAnalyzer.get_space_group_operations">
<span class="sig-name descname"><span class="pre">get_space_group_operations</span></span><span class="sig-paren">(</span><span class="sig-paren">)</span> <span class="sig-return"><span class="sig-return-icon">&#x2192;</span> <span class="sig-return-typehint"><a class="reference internal" href="#pymatgen.symmetry.analyzer.SpacegroupOperations" title="pymatgen.symmetry.analyzer.SpacegroupOperations"><span class="pre">SpacegroupOperations</span></a></span></span><a class="reference external" href="https://github.com/materialsproject/pymatgen/blob/v2025.1.24/src/pymatgen/core/../symmetry/analyzer.py#L170-L180"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pymatgen.symmetry.analyzer.SpacegroupAnalyzer.get_space_group_operations" title="Link to this definition"></a></dt>
<dd><p>Get the SpacegroupOperations for the Structure.</p>
<dl class="field-list simple">
<dt class="field-odd">Returns<span class="colon">:</span></dt>
<dd class="field-odd"><p>SpacegroupOperations object.</p>
</dd>
</dl>
</dd></dl>

<dl class="py method">
<dt class="sig sig-object py" id="pymatgen.symmetry.analyzer.SpacegroupAnalyzer.get_space_group_symbol">
<span class="sig-name descname"><span class="pre">get_space_group_symbol</span></span><span class="sig-paren">(</span><span class="sig-paren">)</span> <span class="sig-return"><span class="sig-return-icon">&#x2192;</span> <span class="sig-return-typehint"><span class="pre">str</span></span></span><a class="reference external" href="https://github.com/materialsproject/pymatgen/blob/v2025.1.24/src/pymatgen/core/../symmetry/analyzer.py#L154-L160"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pymatgen.symmetry.analyzer.SpacegroupAnalyzer.get_space_group_symbol" title="Link to this definition"></a></dt>
<dd><p>Get the spacegroup symbol (e.g., Pnma) for structure.</p>
<dl class="field-list simple">
<dt class="field-odd">Returns<span class="colon">:</span></dt>
<dd class="field-odd"><p>Spacegroup symbol for structure.</p>
</dd>
<dt class="field-even">Return type<span class="colon">:</span></dt>
<dd class="field-even"><p>str</p>
</dd>
</dl>
</dd></dl>

<dl class="py method">
<dt class="sig sig-object py" id="pymatgen.symmetry.analyzer.SpacegroupAnalyzer.get_symmetrized_structure">
<span class="sig-name descname"><span class="pre">get_symmetrized_structure</span></span><span class="sig-paren">(</span><span class="sig-paren">)</span> <span class="sig-return"><span class="sig-return-icon">&#x2192;</span> <span class="sig-return-typehint"><a class="reference internal" href="#pymatgen.symmetry.structure.SymmetrizedStructure" title="pymatgen.symmetry.structure.SymmetrizedStructure"><span class="pre">SymmetrizedStructure</span></a></span></span><a class="reference external" href="https://github.com/materialsproject/pymatgen/blob/v2025.1.24/src/pymatgen/core/../symmetry/analyzer.py#L346-L359"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pymatgen.symmetry.analyzer.SpacegroupAnalyzer.get_symmetrized_structure" title="Link to this definition"></a></dt>
<dd><p>Get a symmetrized structure. A symmetrized structure is one where the sites
have been grouped into symmetrically equivalent groups.</p>
<dl class="field-list simple">
<dt class="field-odd">Returns<span class="colon">:</span></dt>
<dd class="field-odd"><p>pymatgen.symmetry.structure.SymmetrizedStructure object.</p>
</dd>
</dl>
</dd></dl>

<dl class="py method">
<dt class="sig sig-object py" id="pymatgen.symmetry.analyzer.SpacegroupAnalyzer.get_symmetry_dataset">
<span class="sig-name descname"><span class="pre">get_symmetry_dataset</span></span><span class="sig-paren">(</span><span class="sig-paren">)</span> <span class="sig-return"><span class="sig-return-icon">&#x2192;</span> <span class="sig-return-typehint"><span class="pre">SpglibDataset</span></span></span><a class="reference external" href="https://github.com/materialsproject/pymatgen/blob/v2025.1.24/src/pymatgen/core/../symmetry/analyzer.py#L249-L265"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pymatgen.symmetry.analyzer.SpacegroupAnalyzer.get_symmetry_dataset" title="Link to this definition"></a></dt>
<dd><p>Get the symmetry dataset as a SpglibDataset.</p>
<dl class="field-list simple">
<dt class="field-odd">Returns<span class="colon">:</span></dt>
<dd class="field-odd"><p><dl>
<dt>With the following properties:</dt><dd><p>number: International space group number
international: International symbol
hall: Hall symbol
transformation_matrix: Transformation matrix from lattice of</p>
<blockquote>
<div><p>input cell to Bravais lattice L^bravais = L^original * Tmat
origin shift: Origin shift in the setting of “Bravais lattice”
rotations, translations: Rotation matrices and translation
vectors. Space group operations are obtained by
[(r,t) for r, t in zip(rotations, translations)]</p>
</div></blockquote>
<p>wyckoffs: Wyckoff letters</p>
</dd>
</dl>
</p>
</dd>
<dt class="field-even">Return type<span class="colon">:</span></dt>
<dd class="field-even"><p>frozen dict</p>
</dd>
</dl>
</dd></dl>

<dl class="py method">
<dt class="sig sig-object py" id="pymatgen.symmetry.analyzer.SpacegroupAnalyzer.get_symmetry_operations">
<span class="sig-name descname"><span class="pre">get_symmetry_operations</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">cartesian</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">bool</span></span><span class="w"> </span><span class="o"><span class="pre">=</span></span><span class="w"> </span><span class="default_value"><span class="pre">False</span></span></em><span class="sig-paren">)</span> <span class="sig-return"><span class="sig-return-icon">&#x2192;</span> <span class="sig-return-typehint"><span class="pre">list</span><span class="p"><span class="pre">[</span></span><a class="reference internal" href="pymatgen.core.html#pymatgen.core.operations.SymmOp" title="pymatgen.core.operations.SymmOp"><span class="pre">SymmOp</span></a><span class="p"><span class="pre">]</span></span></span></span><a class="reference external" href="https://github.com/materialsproject/pymatgen/blob/v2025.1.24/src/pymatgen/core/../symmetry/analyzer.py#L300-L317"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pymatgen.symmetry.analyzer.SpacegroupAnalyzer.get_symmetry_operations" title="Link to this definition"></a></dt>
<dd><p>Return symmetry operations as a list of SymmOp objects. By default returns
fractional coord sym_ops. But Cartesian can be returned too.</p>
<dl class="field-list simple">
<dt class="field-odd">Returns<span class="colon">:</span></dt>
<dd class="field-odd"><p>symmetry operations.</p>
</dd>
<dt class="field-even">Return type<span class="colon">:</span></dt>
<dd class="field-even"><p>list[<a class="reference internal" href="pymatgen.core.html#pymatgen.core.operations.SymmOp" title="pymatgen.core.operations.SymmOp">SymmOp</a>]</p>
</dd>
</dl>
</dd></dl>

<dl class="py method">
<dt class="sig sig-object py" id="pymatgen.symmetry.analyzer.SpacegroupAnalyzer.is_laue">
<span class="sig-name descname"><span class="pre">is_laue</span></span><span class="sig-paren">(</span><span class="sig-paren">)</span> <span class="sig-return"><span class="sig-return-icon">&#x2192;</span> <span class="sig-return-typehint"><span class="pre">bool</span></span></span><a class="reference external" href="https://github.com/materialsproject/pymatgen/blob/v2025.1.24/src/pymatgen/core/../symmetry/analyzer.py#L995-L1011"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pymatgen.symmetry.analyzer.SpacegroupAnalyzer.is_laue" title="Link to this definition"></a></dt>
<dd><p>Check if the point group of the structure has Laue symmetry (centrosymmetry).</p>
</dd></dl>

</dd></dl>

<dl class="py class">
<dt class="sig sig-object py" id="pymatgen.symmetry.analyzer.SpacegroupOperations">
<em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">SpacegroupOperations</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">int_symbol</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">str</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">int_number</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">int</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">symmops</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">Sequence</span><span class="p"><span class="pre">[</span></span><a class="reference internal" href="pymatgen.core.html#pymatgen.core.operations.SymmOp" title="pymatgen.core.operations.SymmOp"><span class="pre">SymmOp</span></a><span class="p"><span class="pre">]</span></span></span></em><span class="sig-paren">)</span><a class="reference external" href="https://github.com/materialsproject/pymatgen/blob/v2025.1.24/src/pymatgen/core/../symmetry/analyzer.py#L1687-L1744"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pymatgen.symmetry.analyzer.SpacegroupOperations" title="Link to this definition"></a></dt>
<dd><p>Bases: <code class="xref py py-class docutils literal notranslate"><span class="pre">list</span></code></p>
<p>Represents a space group, which is a collection of symmetry operations.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>int_symbol</strong> (<em>str</em>) – International symbol of the spacegroup.</p></li>
<li><p><strong>int_number</strong> (<em>int</em>) – International number of the spacegroup.</p></li>
<li><p><strong>symmops</strong> (<em>[</em><a class="reference internal" href="pymatgen.core.html#pymatgen.core.operations.SymmOp" title="pymatgen.core.operations.SymmOp"><em>SymmOp</em></a><em>]</em>) – Symmetry operations associated with the
spacegroup.</p></li>
</ul>
</dd>
</dl>
<dl class="py method">
<dt class="sig sig-object py" id="pymatgen.symmetry.analyzer.SpacegroupOperations.are_symmetrically_equivalent">
<span class="sig-name descname"><span class="pre">are_symmetrically_equivalent</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">sites1</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">set</span><span class="p"><span class="pre">[</span></span><a class="reference internal" href="pymatgen.core.html#pymatgen.core.sites.PeriodicSite" title="pymatgen.core.sites.PeriodicSite"><span class="pre">PeriodicSite</span></a><span class="p"><span class="pre">]</span></span></span></em>, <em class="sig-param"><span class="n"><span class="pre">sites2</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">set</span><span class="p"><span class="pre">[</span></span><a class="reference internal" href="pymatgen.core.html#pymatgen.core.sites.PeriodicSite" title="pymatgen.core.sites.PeriodicSite"><span class="pre">PeriodicSite</span></a><span class="p"><span class="pre">]</span></span></span></em>, <em class="sig-param"><span class="n"><span class="pre">symm_prec</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">float</span></span><span class="w"> </span><span class="o"><span class="pre">=</span></span><span class="w"> </span><span class="default_value"><span class="pre">0.001</span></span></em><span class="sig-paren">)</span> <span class="sig-return"><span class="sig-return-icon">&#x2192;</span> <span class="sig-return-typehint"><span class="pre">bool</span></span></span><a class="reference external" href="https://github.com/materialsproject/pymatgen/blob/v2025.1.24/src/pymatgen/core/../symmetry/analyzer.py#L1710-L1744"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pymatgen.symmetry.analyzer.SpacegroupOperations.are_symmetrically_equivalent" title="Link to this definition"></a></dt>
<dd><p>Given two sets of PeriodicSites, test if they are actually symmetrically
equivalent under this space group. Useful, for example, if you want to test if
selecting atoms 1 and 2 out of a set of 4 atoms are symmetrically the same as
selecting atoms 3 and 4, etc.</p>
<p>One use is in PartialRemoveSpecie transformation to return only
symmetrically distinct arrangements of atoms.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>sites1</strong> (<em>[</em><a class="reference internal" href="pymatgen.core.html#pymatgen.core.sites.PeriodicSite" title="pymatgen.core.sites.PeriodicSite"><em>PeriodicSite</em></a><em>]</em>) – 1st set of sites</p></li>
<li><p><strong>sites2</strong> (<em>[</em><a class="reference internal" href="pymatgen.core.html#pymatgen.core.sites.PeriodicSite" title="pymatgen.core.sites.PeriodicSite"><em>PeriodicSite</em></a><em>]</em>) – 2nd set of sites</p></li>
<li><p><strong>symm_prec</strong> (<em>float</em>) – Tolerance in atomic distance to test if atoms
are symmetrically similar.</p></li>
</ul>
</dd>
<dt class="field-even">Returns<span class="colon">:</span></dt>
<dd class="field-even"><p>True if the two sets of sites are symmetrically equivalent.</p>
</dd>
<dt class="field-odd">Return type<span class="colon">:</span></dt>
<dd class="field-odd"><p>bool</p>
</dd>
</dl>
</dd></dl>

</dd></dl>

<dl class="py exception">
<dt class="sig sig-object py" id="pymatgen.symmetry.analyzer.SymmetryUndeterminedError">
<em class="property"><span class="pre">exception</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">SymmetryUndeterminedError</span></span><a class="reference external" href="https://github.com/materialsproject/pymatgen/blob/v2025.1.24/src/pymatgen/core/../symmetry/analyzer.py#L66-L70"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pymatgen.symmetry.analyzer.SymmetryUndeterminedError" title="Link to this definition"></a></dt>
<dd><p>Bases: <code class="xref py py-class docutils literal notranslate"><span class="pre">ValueError</span></code></p>
<p>An Exception for when symmetry cannot be determined. This might happen
when, for example, atoms are very close together.</p>
</dd></dl>

<dl class="py function">
<dt class="sig sig-object py" id="pymatgen.symmetry.analyzer.cluster_sites">
<span class="sig-name descname"><span class="pre">cluster_sites</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">mol</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><a class="reference internal" href="pymatgen.core.html#pymatgen.core.structure.Molecule" title="pymatgen.core.structure.Molecule"><span class="pre">Molecule</span></a></span></em>, <em class="sig-param"><span class="n"><span class="pre">tol</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">float</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">give_only_index</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">bool</span></span><span class="w"> </span><span class="o"><span class="pre">=</span></span><span class="w"> </span><span class="default_value"><span class="pre">False</span></span></em><span class="sig-paren">)</span> <span class="sig-return"><span class="sig-return-icon">&#x2192;</span> <span class="sig-return-typehint"><span class="pre">tuple</span><span class="p"><span class="pre">[</span></span><a class="reference internal" href="pymatgen.core.html#pymatgen.core.sites.Site" title="pymatgen.core.sites.Site"><span class="pre">Site</span></a><span class="w"> </span><span class="p"><span class="pre">|</span></span><span class="w"> </span><span class="pre">None</span><span class="p"><span class="pre">,</span></span><span class="w"> </span><span class="pre">dict</span><span class="p"><span class="pre">]</span></span></span></span><a class="reference external" href="https://github.com/materialsproject/pymatgen/blob/v2025.1.24/src/pymatgen/core/../symmetry/analyzer.py#L1602-L1638"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pymatgen.symmetry.analyzer.cluster_sites" title="Link to this definition"></a></dt>
<dd><p>Cluster sites based on distance and species type.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>mol</strong> (<a class="reference internal" href="pymatgen.core.html#pymatgen.core.structure.Molecule" title="pymatgen.core.structure.Molecule"><em>Molecule</em></a>) – Molecule <strong>with origin at center of mass</strong>.</p></li>
<li><p><strong>tol</strong> (<em>float</em>) – Tolerance to use.</p></li>
<li><p><strong>give_only_index</strong> (<em>bool</em>) – Whether to return only the index of the
origin site, instead of the site itself. Defaults to False.</p></li>
</ul>
</dd>
<dt class="field-even">Returns<span class="colon">:</span></dt>
<dd class="field-even"><p><dl class="simple">
<dt>origin_site is a site at the center</dt><dd><p>of mass (None if there are no origin atoms). clustered_sites is a
dict of {(avg_dist, species_and_occu): [list of sites]}</p>
</dd>
</dl>
</p>
</dd>
<dt class="field-odd">Return type<span class="colon">:</span></dt>
<dd class="field-odd"><p>tuple[<a class="reference internal" href="pymatgen.core.html#pymatgen.core.sites.Site" title="pymatgen.core.sites.Site">Site</a> | None, dict]</p>
</dd>
</dl>
</dd></dl>

<dl class="py function">
<dt class="sig sig-object py" id="pymatgen.symmetry.analyzer.generate_full_symmops">
<span class="sig-name descname"><span class="pre">generate_full_symmops</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">symmops</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">Sequence</span><span class="p"><span class="pre">[</span></span><a class="reference internal" href="pymatgen.core.html#pymatgen.core.operations.SymmOp" title="pymatgen.core.operations.SymmOp"><span class="pre">SymmOp</span></a><span class="p"><span class="pre">]</span></span></span></em>, <em class="sig-param"><span class="n"><span class="pre">tol</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">float</span></span></em><span class="sig-paren">)</span> <span class="sig-return"><span class="sig-return-icon">&#x2192;</span> <span class="sig-return-typehint"><span class="pre">Sequence</span><span class="p"><span class="pre">[</span></span><a class="reference internal" href="pymatgen.core.html#pymatgen.core.operations.SymmOp" title="pymatgen.core.operations.SymmOp"><span class="pre">SymmOp</span></a><span class="p"><span class="pre">]</span></span></span></span><a class="reference external" href="https://github.com/materialsproject/pymatgen/blob/v2025.1.24/src/pymatgen/core/../symmetry/analyzer.py#L1641-L1684"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pymatgen.symmetry.analyzer.generate_full_symmops" title="Link to this definition"></a></dt>
<dd><p>Recursive algorithm to permute through all possible combinations of the initially
supplied symmetry operations to arrive at a complete set of operations mapping a
single atom to all other equivalent atoms in the point group. This assumes that the
initial number already uniquely identifies all operations.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>symmops</strong> (<em>list</em><em>[</em><a class="reference internal" href="pymatgen.core.html#pymatgen.core.operations.SymmOp" title="pymatgen.core.operations.SymmOp"><em>SymmOp</em></a><em>]</em>) – Initial set of symmetry operations.</p></li>
<li><p><strong>tol</strong> (<em>float</em>) – Tolerance for detecting symmetry.</p></li>
</ul>
</dd>
<dt class="field-even">Returns<span class="colon">:</span></dt>
<dd class="field-even"><p>Full set of symmetry operations.</p>
</dd>
<dt class="field-odd">Return type<span class="colon">:</span></dt>
<dd class="field-odd"><p>list[<a class="reference internal" href="pymatgen.core.html#pymatgen.core.operations.SymmOp" title="pymatgen.core.operations.SymmOp">SymmOp</a>]</p>
</dd>
</dl>
</dd></dl>

<dl class="py function">
<dt class="sig sig-object py" id="pymatgen.symmetry.analyzer.iterative_symmetrize">
<span class="sig-name descname"><span class="pre">iterative_symmetrize</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">mol</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><a class="reference internal" href="pymatgen.core.html#pymatgen.core.structure.Molecule" title="pymatgen.core.structure.Molecule"><span class="pre">Molecule</span></a></span></em>, <em class="sig-param"><span class="n"><span class="pre">max_n</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">int</span></span><span class="w"> </span><span class="o"><span class="pre">=</span></span><span class="w"> </span><span class="default_value"><span class="pre">10</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">tolerance</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">float</span></span><span class="w"> </span><span class="o"><span class="pre">=</span></span><span class="w"> </span><span class="default_value"><span class="pre">0.3</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">epsilon</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">float</span></span><span class="w"> </span><span class="o"><span class="pre">=</span></span><span class="w"> </span><span class="default_value"><span class="pre">0.01</span></span></em><span class="sig-paren">)</span> <span class="sig-return"><span class="sig-return-icon">&#x2192;</span> <span class="sig-return-typehint"><span class="pre">dict</span><span class="p"><span class="pre">[</span></span><span class="pre">Literal</span><span class="p"><span class="pre">[</span></span><span class="s"><span class="pre">'sym_mol'</span></span><span class="p"><span class="pre">,</span></span><span class="w"> </span><span class="s"><span class="pre">'eq_sets'</span></span><span class="p"><span class="pre">,</span></span><span class="w"> </span><span class="s"><span class="pre">'sym_ops'</span></span><span class="p"><span class="pre">]</span></span><span class="p"><span class="pre">,</span></span><span class="w"> </span><a class="reference internal" href="pymatgen.core.html#pymatgen.core.structure.Molecule" title="pymatgen.core.structure.Molecule"><span class="pre">Molecule</span></a><span class="w"> </span><span class="p"><span class="pre">|</span></span><span class="w"> </span><span class="pre">dict</span><span class="p"><span class="pre">]</span></span></span></span><a class="reference external" href="https://github.com/materialsproject/pymatgen/blob/v2025.1.24/src/pymatgen/core/../symmetry/analyzer.py#L1560-L1599"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pymatgen.symmetry.analyzer.iterative_symmetrize" title="Link to this definition"></a></dt>
<dd><p>Get a symmetrized molecule.</p>
<p>The equivalent atoms obtained via <cite>PointGroupAnalyzer.get_equivalent_atoms</cite>
are rotated, mirrored… unto one position.
Then the average position is calculated, which is rotated, mirrored…
back with the inverse of the previous symmetry operations, giving the
symmetrized molecule.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>mol</strong> (<a class="reference internal" href="pymatgen.core.html#pymatgen.core.structure.Molecule" title="pymatgen.core.structure.Molecule"><em>Molecule</em></a>) – A pymatgen Molecule instance.</p></li>
<li><p><strong>max_n</strong> (<em>int</em>) – Maximum number of iterations.</p></li>
<li><p><strong>tolerance</strong> (<em>float</em>) – Tolerance for detecting symmetry with PointGroupAnalyzer.</p></li>
<li><p><strong>epsilon</strong> (<em>float</em>) – If the element-wise absolute difference of two
subsequently symmetrized structures is smaller epsilon,
the iteration stops before max_n is reached.</p></li>
</ul>
</dd>
<dt class="field-even">Returns<span class="colon">:</span></dt>
<dd class="field-even"><p><p>sym_mol: A symmetrized Molecule instance.
eq_sets: A dictionary of indices mapping to sets of indices, each key maps to indices</p>
<blockquote>
<div><p>of all equivalent atoms. The keys are guaranteed to be not equivalent.</p>
</div></blockquote>
<dl class="simple">
<dt>sym_ops: Two-fold nested dictionary. operations[i][j] gives the symmetry operation</dt><dd><p>that maps atom i unto j.</p>
</dd>
</dl>
</p>
</dd>
<dt class="field-odd">Return type<span class="colon">:</span></dt>
<dd class="field-odd"><p>dict with three keys</p>
</dd>
</dl>
</dd></dl>

</section>
<section id="module-pymatgen.symmetry.bandstructure">
<span id="pymatgen-symmetry-bandstructure-module"></span><h2>pymatgen.symmetry.bandstructure module<a class="headerlink" href="#module-pymatgen.symmetry.bandstructure" title="Link to this heading"></a></h2>
<p>A class for interacting with KPath classes to
generate high-symmetry k-paths using different conventions.</p>
<dl class="py class">
<dt class="sig sig-object py" id="pymatgen.symmetry.bandstructure.HighSymmKpath">
<em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">HighSymmKpath</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">structure</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">has_magmoms</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">False</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">magmom_axis</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">path_type</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">'setyawan_curtarolo'</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">symprec</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">0.01</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">angle_tolerance</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">5</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">atol</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">1e-05</span></span></em><span class="sig-paren">)</span><a class="reference external" href="https://github.com/materialsproject/pymatgen/blob/v2025.1.24/src/pymatgen/core/../symmetry/bandstructure.py#L27-L397"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pymatgen.symmetry.bandstructure.HighSymmKpath" title="Link to this definition"></a></dt>
<dd><p>Bases: <a class="reference internal" href="#pymatgen.symmetry.kpath.KPathBase" title="pymatgen.symmetry.kpath.KPathBase"><code class="xref py py-class docutils literal notranslate"><span class="pre">KPathBase</span></code></a></p>
<p>This class generates path along high symmetry lines in the
Brillouin zone according to different conventions.
The class is designed to be used with a specific primitive
cell setting. The definitions for the primitive cell
used can be found in: Computational Materials Science,
49(2), 299-312. doi:10.1016/j.commatsci.2010.05.010.
The space group analyzer can be used to produce the correct
primitive structure
(method get_primitive_standard_structure(international_monoclinic=False)).
Ensure input structure is correct before ‘get_kpoints()’ method is used.
See individual KPath classes for details on specific conventions.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>structure</strong> (<a class="reference internal" href="pymatgen.core.html#pymatgen.core.structure.Structure" title="pymatgen.core.structure.Structure"><em>Structure</em></a>) – Structure object</p></li>
<li><p><strong>has_magmoms</strong> (<em>bool</em>) – Whether the input structure contains
magnetic moments as site properties with the key ‘magmom.’
Values may be in the form of 3-component vectors given in
the basis of the input lattice vectors, in
which case the spin axis will default to a_3, the third
real-space lattice vector (this triggers a warning).</p></li>
<li><p><strong>magmom_axis</strong> (<em>list</em><em> or </em><em>numpy array</em>) – 3-component vector specifying
direction along which magnetic moments given as scalars
should point. If all magnetic moments are provided as
vectors then this argument is not used.</p></li>
<li><p><strong>path_type</strong> (<em>str</em>) – Chooses which convention to use to generate
the high symmetry path. Options are: ‘setyawan_curtarolo’, ‘hinuma’,
‘latimer_munro’ for the Setyawan &amp; Curtarolo, Hinuma et al., and
Latimer &amp; Munro conventions. Choosing ‘all’ will generate one path
with points from all three conventions. Equivalent labels between
each will also be generated. Order will always be Latimer &amp; Munro,
Setyawan &amp; Curtarolo, and Hinuma et al. Lengths for each of the paths
will also be generated and output as a list. Note for ‘all’ the user
will have to alter the labels on their own for plotting.</p></li>
<li><p><strong>symprec</strong> (<em>float</em>) – Tolerance for symmetry finding</p></li>
<li><p><strong>angle_tolerance</strong> (<em>float</em>) – Angle tolerance for symmetry finding.</p></li>
<li><p><strong>atol</strong> (<em>float</em>) – Absolute tolerance used to determine symmetric
equivalence of points and lines on the BZ.</p></li>
</ul>
</dd>
</dl>
<dl class="py property">
<dt class="sig sig-object py" id="pymatgen.symmetry.bandstructure.HighSymmKpath.equiv_labels">
<em class="property"><span class="pre">property</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">equiv_labels</span></span><a class="reference external" href="https://github.com/materialsproject/pymatgen/blob/v2025.1.24/src/pymatgen/symmetry/bandstructure.py"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pymatgen.symmetry.bandstructure.HighSymmKpath.equiv_labels" title="Link to this definition"></a></dt>
<dd><p>The correspondence between the kpoint symbols in the Latimer and
Munro convention, Setyawan and Curtarolo, and Hinuma
conventions respectively. Only generated when path_type = ‘all’.</p>
</dd></dl>

<dl class="py method">
<dt class="sig sig-object py" id="pymatgen.symmetry.bandstructure.HighSymmKpath.get_continuous_path">
<em class="property"><span class="pre">static</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">get_continuous_path</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">bandstructure</span></span></em><span class="sig-paren">)</span><a class="reference external" href="https://github.com/materialsproject/pymatgen/blob/v2025.1.24/src/pymatgen/core/../symmetry/bandstructure.py#L291-L397"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pymatgen.symmetry.bandstructure.HighSymmKpath.get_continuous_path" title="Link to this definition"></a></dt>
<dd><p>Obtain a continuous version of an inputted path using graph theory.
This routine will attempt to add connections between nodes of
odd-degree to ensure a Eulerian path can be formed. Initial
k-path must be able to be converted to a connected graph. See
npj Comput Mater 6, 112 (2020). 10.1038/s41524-020-00383-7
for more details.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
<dd class="field-odd"><p><strong>bandstructure</strong> (<em>BandstructureSymmLine</em>) – BandstructureSymmLine object.</p>
</dd>
<dt class="field-even">Returns<span class="colon">:</span></dt>
<dd class="field-even"><p>New BandstructureSymmLine object with continuous path.</p>
</dd>
<dt class="field-odd">Return type<span class="colon">:</span></dt>
<dd class="field-odd"><p>bandstructure (BandstructureSymmLine)</p>
</dd>
</dl>
</dd></dl>

<dl class="py property">
<dt class="sig sig-object py" id="pymatgen.symmetry.bandstructure.HighSymmKpath.label_index">
<em class="property"><span class="pre">property</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">label_index</span></span><a class="reference external" href="https://github.com/materialsproject/pymatgen/blob/v2025.1.24/src/pymatgen/symmetry/bandstructure.py"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pymatgen.symmetry.bandstructure.HighSymmKpath.label_index" title="Link to this definition"></a></dt>
<dd><p>The correspondence between numbers and kpoint symbols for the
combined kpath generated when path_type = ‘all’. None otherwise.</p>
</dd></dl>

<dl class="py property">
<dt class="sig sig-object py" id="pymatgen.symmetry.bandstructure.HighSymmKpath.path_lengths">
<em class="property"><span class="pre">property</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">path_lengths</span></span><a class="reference external" href="https://github.com/materialsproject/pymatgen/blob/v2025.1.24/src/pymatgen/symmetry/bandstructure.py"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pymatgen.symmetry.bandstructure.HighSymmKpath.path_lengths" title="Link to this definition"></a></dt>
<dd><p>List of lengths of the Latimer and Munro, Setyawan and Curtarolo, and Hinuma
conventions in the combined HighSymmKpath object when path_type = ‘all’ respectively.
None otherwise.</p>
</dd></dl>

<dl class="py property">
<dt class="sig sig-object py" id="pymatgen.symmetry.bandstructure.HighSymmKpath.path_type">
<em class="property"><span class="pre">property</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">path_type</span></span><a class="reference external" href="https://github.com/materialsproject/pymatgen/blob/v2025.1.24/src/pymatgen/symmetry/bandstructure.py"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pymatgen.symmetry.bandstructure.HighSymmKpath.path_type" title="Link to this definition"></a></dt>
<dd><p>The type of kpath chosen.</p>
</dd></dl>

</dd></dl>

</section>
<section id="module-pymatgen.symmetry.groups">
<span id="pymatgen-symmetry-groups-module"></span><h2>pymatgen.symmetry.groups module<a class="headerlink" href="#module-pymatgen.symmetry.groups" title="Link to this heading"></a></h2>
<p>Defines SymmetryGroup parent class and PointGroup and SpaceGroup classes.
Shyue Ping Ong thanks Marc De Graef for his generous sharing of his
SpaceGroup data as published in his textbook “Structure of Materials”.</p>
<dl class="py class">
<dt class="sig sig-object py" id="pymatgen.symmetry.groups.PointGroup">
<em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">PointGroup</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="o"><span class="pre">**</span></span><span class="n"><span class="pre">kwargs</span></span></em><span class="sig-paren">)</span><a class="reference external" href="https://github.com/materialsproject/pymatgen/blob/v2025.1.24/src/pymatgen/core/../symmetry/groups.py#L140-L291"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pymatgen.symmetry.groups.PointGroup" title="Link to this definition"></a></dt>
<dd><p>Bases: <a class="reference internal" href="#pymatgen.symmetry.groups.SymmetryGroup" title="pymatgen.symmetry.groups.SymmetryGroup"><code class="xref py py-class docutils literal notranslate"><span class="pre">SymmetryGroup</span></code></a></p>
<p>A Point Group, with generators and symmetry operations.</p>
<dl class="py attribute">
<dt class="sig sig-object py" id="pymatgen.symmetry.groups.PointGroup.symbol">
<span class="sig-name descname"><span class="pre">symbol</span></span><a class="reference external" href="https://github.com/materialsproject/pymatgen/blob/v2025.1.24/src/pymatgen/symmetry/groups.py"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pymatgen.symmetry.groups.PointGroup.symbol" title="Link to this definition"></a></dt>
<dd><p>Full International or Hermann-Mauguin Symbol.</p>
<dl class="field-list simple">
<dt class="field-odd">Type<span class="colon">:</span></dt>
<dd class="field-odd"><p>str</p>
</dd>
</dl>
</dd></dl>

<dl class="py attribute">
<dt class="sig sig-object py" id="pymatgen.symmetry.groups.PointGroup.generators">
<span class="sig-name descname"><span class="pre">generators</span></span><a class="reference external" href="https://github.com/materialsproject/pymatgen/blob/v2025.1.24/src/pymatgen/symmetry/groups.py"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pymatgen.symmetry.groups.PointGroup.generators" title="Link to this definition"></a></dt>
<dd><p>List of generator matrices. Note that 3x3 matrices are used for Point Groups.</p>
<dl class="field-list simple">
<dt class="field-odd">Type<span class="colon">:</span></dt>
<dd class="field-odd"><p>list</p>
</dd>
</dl>
</dd></dl>

<dl class="py attribute">
<dt class="sig sig-object py" id="pymatgen.symmetry.groups.PointGroup.symmetry_ops">
<span class="sig-name descname"><span class="pre">symmetry_ops</span></span><a class="reference external" href="https://github.com/materialsproject/pymatgen/blob/v2025.1.24/src/pymatgen/symmetry/groups.py"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pymatgen.symmetry.groups.PointGroup.symmetry_ops" title="Link to this definition"></a></dt>
<dd><p>Full set of symmetry operations as matrices.</p>
<dl class="field-list simple">
<dt class="field-odd">Type<span class="colon">:</span></dt>
<dd class="field-odd"><p>list</p>
</dd>
</dl>
</dd></dl>

<p>Initialize a Point Group from its international symbol.
Please note that only the 32 crystal classes are supported right now.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>int_symbol</strong> (<em>str</em>) – International or Hermann-Mauguin Symbol. Please note that the PointGroup object</p></li>
<li><p><strong>group</strong> (<em>may have a different setting than specified in the int_symbol as only one setting per point</em>)</p></li>
<li><p><strong>now.</strong> (<em>is available right</em>)</p></li>
</ul>
</dd>
</dl>
<dl class="py method">
<dt class="sig sig-object py" id="pymatgen.symmetry.groups.PointGroup.from_space_group">
<em class="property"><span class="pre">classmethod</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">from_space_group</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">sg_symbol</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">str</span></span></em><span class="sig-paren">)</span> <span class="sig-return"><span class="sig-return-icon">&#x2192;</span> <span class="sig-return-typehint"><a class="reference internal" href="#pymatgen.symmetry.groups.PointGroup" title="pymatgen.symmetry.groups.PointGroup"><span class="pre">PointGroup</span></a></span></span><a class="reference external" href="https://github.com/materialsproject/pymatgen/blob/v2025.1.24/src/pymatgen/core/../symmetry/groups.py#L252-L291"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pymatgen.symmetry.groups.PointGroup.from_space_group" title="Link to this definition"></a></dt>
<dd><p>Instantiate one of the 32 crystal classes from a space group symbol in
Hermann Mauguin notation (int symbol or full symbol).
Please note that the axes of space group and crystal class may be different.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
<dd class="field-odd"><p><strong>sg_symbol</strong> – space group symbol in Hermann Mauguin notation.</p>
</dd>
<dt class="field-even">Raises<span class="colon">:</span></dt>
<dd class="field-even"><p><strong>AssertionError if a valid crystal class cannot be created</strong> – </p>
</dd>
<dt class="field-odd">Returns<span class="colon">:</span></dt>
<dd class="field-odd"><p>crystal class in Hermann-Mauguin notation.</p>
</dd>
</dl>
</dd></dl>

<dl class="py method">
<dt class="sig sig-object py" id="pymatgen.symmetry.groups.PointGroup.get_orbit">
<span class="sig-name descname"><span class="pre">get_orbit</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">p</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">ArrayLike</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">tol</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">float</span></span><span class="w"> </span><span class="o"><span class="pre">=</span></span><span class="w"> </span><span class="default_value"><span class="pre">1e-05</span></span></em><span class="sig-paren">)</span> <span class="sig-return"><span class="sig-return-icon">&#x2192;</span> <span class="sig-return-typehint"><span class="pre">list</span><span class="p"><span class="pre">[</span></span><span class="pre">np.ndarray</span><span class="p"><span class="pre">]</span></span></span></span><a class="reference external" href="https://github.com/materialsproject/pymatgen/blob/v2025.1.24/src/pymatgen/core/../symmetry/groups.py#L194-L211"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pymatgen.symmetry.groups.PointGroup.get_orbit" title="Link to this definition"></a></dt>
<dd><p>Get the orbit for a point.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>p</strong> – Point as a 3x1 array.</p></li>
<li><p><strong>tol</strong> – Tolerance for determining if sites are the same. 1e-5 should
be sufficient for most purposes. Set to 0 for exact matching
(and also needed for symbolic orbits).</p></li>
</ul>
</dd>
<dt class="field-even">Returns<span class="colon">:</span></dt>
<dd class="field-even"><p>Orbit for point.</p>
</dd>
<dt class="field-odd">Return type<span class="colon">:</span></dt>
<dd class="field-odd"><p>list[array]</p>
</dd>
</dl>
</dd></dl>

<dl class="py method">
<dt class="sig sig-object py" id="pymatgen.symmetry.groups.PointGroup.is_subgroup">
<span class="sig-name descname"><span class="pre">is_subgroup</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">supergroup</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><a class="reference internal" href="#pymatgen.symmetry.groups.PointGroup" title="pymatgen.symmetry.groups.PointGroup"><span class="pre">PointGroup</span></a></span></em><span class="sig-paren">)</span> <span class="sig-return"><span class="sig-return-icon">&#x2192;</span> <span class="sig-return-typehint"><span class="pre">bool</span></span></span><a class="reference external" href="https://github.com/materialsproject/pymatgen/blob/v2025.1.24/src/pymatgen/core/../symmetry/groups.py#L213-L238"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pymatgen.symmetry.groups.PointGroup.is_subgroup" title="Link to this definition"></a></dt>
<dd><dl class="simple">
<dt>True if this group is a subgroup of the supplied group.</dt><dd><p>Modification of SymmetryGroup method with a few more constraints.</p>
</dd>
</dl>
<dl class="field-list simple">
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
<dd class="field-odd"><p><strong>supergroup</strong> (<em>pointGroup</em>) – Supergroup to test.</p>
</dd>
<dt class="field-even">Returns<span class="colon">:</span></dt>
<dd class="field-even"><p>True if this group is a subgroup of the supplied group.</p>
</dd>
<dt class="field-odd">Return type<span class="colon">:</span></dt>
<dd class="field-odd"><p>bool</p>
</dd>
</dl>
</dd></dl>

<dl class="py method">
<dt class="sig sig-object py" id="pymatgen.symmetry.groups.PointGroup.is_supergroup">
<span class="sig-name descname"><span class="pre">is_supergroup</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">subgroup</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><a class="reference internal" href="#pymatgen.symmetry.groups.PointGroup" title="pymatgen.symmetry.groups.PointGroup"><span class="pre">PointGroup</span></a></span></em><span class="sig-paren">)</span> <span class="sig-return"><span class="sig-return-icon">&#x2192;</span> <span class="sig-return-typehint"><span class="pre">bool</span></span></span><a class="reference external" href="https://github.com/materialsproject/pymatgen/blob/v2025.1.24/src/pymatgen/core/../symmetry/groups.py#L240-L250"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pymatgen.symmetry.groups.PointGroup.is_supergroup" title="Link to this definition"></a></dt>
<dd><dl class="simple">
<dt>True if this group is a subgroup of the supplied group.</dt><dd><p>Modification of SymmetryGroup method with a few more constraints.</p>
</dd>
</dl>
<dl class="field-list simple">
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
<dd class="field-odd"><p><strong>subgroup</strong> (<a class="reference internal" href="#pymatgen.symmetry.groups.PointGroup" title="pymatgen.symmetry.groups.PointGroup"><em>PointGroup</em></a>) – Subgroup to test.</p>
</dd>
<dt class="field-even">Returns<span class="colon">:</span></dt>
<dd class="field-even"><p>True if this group is a supergroup of the supplied group.</p>
</dd>
<dt class="field-odd">Return type<span class="colon">:</span></dt>
<dd class="field-odd"><p>bool</p>
</dd>
</dl>
</dd></dl>

<dl class="py property">
<dt class="sig sig-object py" id="id0">
<em class="property"><span class="pre">property</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">symmetry_ops</span></span><em class="property"><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="pre">set</span><span class="p"><span class="pre">[</span></span><a class="reference internal" href="pymatgen.core.html#pymatgen.core.operations.SymmOp" title="pymatgen.core.operations.SymmOp"><span class="pre">SymmOp</span></a><span class="p"><span class="pre">]</span></span></em><a class="reference external" href="https://github.com/materialsproject/pymatgen/blob/v2025.1.24/src/pymatgen/symmetry/groups.py"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#id0" title="Link to this definition"></a></dt>
<dd><p>Returns:
List of symmetry operations associated with the group.</p>
</dd></dl>

</dd></dl>

<dl class="py class">
<dt class="sig sig-object py" id="pymatgen.symmetry.groups.SpaceGroup">
<em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">SpaceGroup</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="o"><span class="pre">**</span></span><span class="n"><span class="pre">kwargs</span></span></em><span class="sig-paren">)</span><a class="reference external" href="https://github.com/materialsproject/pymatgen/blob/v2025.1.24/src/pymatgen/core/../symmetry/groups.py#L294-L699"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pymatgen.symmetry.groups.SpaceGroup" title="Link to this definition"></a></dt>
<dd><p>Bases: <a class="reference internal" href="#pymatgen.symmetry.groups.SymmetryGroup" title="pymatgen.symmetry.groups.SymmetryGroup"><code class="xref py py-class docutils literal notranslate"><span class="pre">SymmetryGroup</span></code></a></p>
<p>A SpaceGroup.</p>
<dl class="py attribute">
<dt class="sig sig-object py" id="pymatgen.symmetry.groups.SpaceGroup.symbol">
<span class="sig-name descname"><span class="pre">symbol</span></span><a class="reference external" href="https://github.com/materialsproject/pymatgen/blob/v2025.1.24/src/pymatgen/symmetry/groups.py"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pymatgen.symmetry.groups.SpaceGroup.symbol" title="Link to this definition"></a></dt>
<dd><p>Full International or Hermann-Mauguin Symbol.</p>
<dl class="field-list simple">
<dt class="field-odd">Type<span class="colon">:</span></dt>
<dd class="field-odd"><p>str</p>
</dd>
</dl>
</dd></dl>

<dl class="py attribute">
<dt class="sig sig-object py" id="pymatgen.symmetry.groups.SpaceGroup.int_number">
<span class="sig-name descname"><span class="pre">int_number</span></span><a class="reference external" href="https://github.com/materialsproject/pymatgen/blob/v2025.1.24/src/pymatgen/symmetry/groups.py"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pymatgen.symmetry.groups.SpaceGroup.int_number" title="Link to this definition"></a></dt>
<dd><p>International number.</p>
<dl class="field-list simple">
<dt class="field-odd">Type<span class="colon">:</span></dt>
<dd class="field-odd"><p>int</p>
</dd>
</dl>
</dd></dl>

<dl class="py attribute">
<dt class="sig sig-object py" id="pymatgen.symmetry.groups.SpaceGroup.generators">
<span class="sig-name descname"><span class="pre">generators</span></span><a class="reference external" href="https://github.com/materialsproject/pymatgen/blob/v2025.1.24/src/pymatgen/symmetry/groups.py"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pymatgen.symmetry.groups.SpaceGroup.generators" title="Link to this definition"></a></dt>
<dd><p>List of generator matrices. Note that 4x4 matrices are used for Space Groups.</p>
<dl class="field-list simple">
<dt class="field-odd">Type<span class="colon">:</span></dt>
<dd class="field-odd"><p>list</p>
</dd>
</dl>
</dd></dl>

<dl class="py attribute">
<dt class="sig sig-object py" id="pymatgen.symmetry.groups.SpaceGroup.order">
<span class="sig-name descname"><span class="pre">order</span></span><a class="reference external" href="https://github.com/materialsproject/pymatgen/blob/v2025.1.24/src/pymatgen/symmetry/groups.py"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pymatgen.symmetry.groups.SpaceGroup.order" title="Link to this definition"></a></dt>
<dd><p>Order of Space Group.</p>
<dl class="field-list simple">
<dt class="field-odd">Type<span class="colon">:</span></dt>
<dd class="field-odd"><p>int</p>
</dd>
</dl>
</dd></dl>

<p>Initialize a Space Group from its full or abbreviated international
symbol. Only standard settings are supported.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>int_symbol</strong> (<em>str</em>) – Full International (e.g., “P2/m2/m2/m”) or
Hermann-Mauguin Symbol (“Pmmm”) or abbreviated symbol. The
notation is a LaTeX-like string, with screw axes being
represented by an underscore. For example, “P6_3/mmc”.
Alternative settings can be accessed by adding a “:identifier”.
For example, the hexagonal setting for rhombohedral cells can be
accessed by adding a “:H”, e.g. “R-3m:H”. To find out all
possible settings for a spacegroup, use the get_settings()
classmethod. Alternative origin choices can be indicated by a
translation vector, e.g. ‘Fm-3m(a-1/4,b-1/4,c-1/4)’.</p></li>
<li><p><strong>hexagonal</strong> (<em>bool</em>) – For rhombohedral groups, whether to handle as in
hexagonal setting (default) or rhombohedral setting.
If the int_symbol of a rhombohedral spacegroup is given with the
setting (“(:)H”/”(:)R”), this parameter is overwritten accordingly
(please note that the setting is not contained in the symbol
attribute anymore).</p></li>
</ul>
</dd>
</dl>
<dl class="py attribute">
<dt class="sig sig-object py" id="pymatgen.symmetry.groups.SpaceGroup.SG_SYMBOLS">
<span class="sig-name descname"><span class="pre">SG_SYMBOLS</span></span><em class="property"><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="pre">ClassVar</span><span class="p"><span class="pre">[</span></span><span class="pre">set</span><span class="p"><span class="pre">[</span></span><span class="pre">str</span><span class="p"><span class="pre">]</span></span><span class="p"><span class="pre">]</span></span></em><em class="property"><span class="w"> </span><span class="p"><span class="pre">=</span></span><span class="w"> </span><span class="pre">{'A-1',</span> <span class="pre">'A112',</span> <span class="pre">'A112/a',</span> <span class="pre">'A112/m',</span> <span class="pre">'A112/n',</span> <span class="pre">'A11a',</span> <span class="pre">'A11m',</span> <span class="pre">'A11n',</span> <span class="pre">'A12/a1',</span> <span class="pre">'A12/m1',</span> <span class="pre">'A12/n1',</span> <span class="pre">'A121',</span> <span class="pre">'A1a1',</span> <span class="pre">'A1m1',</span> <span class="pre">'A1n1',</span> <span class="pre">'A2122',</span> <span class="pre">'A21am',</span> <span class="pre">'A21ma',</span> <span class="pre">'A222',</span> <span class="pre">'A2aa',</span> <span class="pre">'A2mm',</span> <span class="pre">'Aba2',</span> <span class="pre">'Abaa',</span> <span class="pre">'Abaa:2',</span> <span class="pre">'Abm2',</span> <span class="pre">'Abmm',</span> <span class="pre">'Acaa',</span> <span class="pre">'Acaa:2',</span> <span class="pre">'Acmm',</span> <span class="pre">'Ae2a',</span> <span class="pre">'Ae2m',</span> <span class="pre">'Aea2',</span> <span class="pre">'Aea2(-a,c+1/4,b-1/4)',</span> <span class="pre">'Aea2(a,b+1/4,c-1/4)',</span> <span class="pre">'Aea2(b,-a+1/4,c-1/4)',</span> <span class="pre">'Aea2(b,c+1/4,a-1/4)',</span> <span class="pre">'Aeaa',</span> <span class="pre">'Aeaa:1',</span> <span class="pre">'Aeam',</span> <span class="pre">'Aem2',</span> <span class="pre">'Aem2(-a,c+1/4,b-1/4)',</span> <span class="pre">'Aem2(a,b+1/4,c-1/4)',</span> <span class="pre">'Aem2(b,-a+1/4,c-1/4)',</span> <span class="pre">'Aem2(b,c+1/4,a-1/4)',</span> <span class="pre">'Aema',</span> <span class="pre">'Am2a',</span> <span class="pre">'Am2m',</span> <span class="pre">'Ama2',</span> <span class="pre">'Ama2(-a+1/4,c+1/4,b-1/4)',</span> <span class="pre">'Ama2(-a,c+1/4,b-1/4)',</span> <span class="pre">'Ama2(a+1/4,b+1/4,c-1/4)',</span> <span class="pre">'Ama2(a,b+1/4,c-1/4)',</span> <span class="pre">'Ama2(b+1/4,-a+1/4,c-1/4)',</span> <span class="pre">'Ama2(b+1/4,c+1/4,a-1/4)',</span> <span class="pre">'Ama2(b,-a+1/4,c-1/4)',</span> <span class="pre">'Ama2(b,c+1/4,a-1/4)',</span> <span class="pre">'Amaa',</span> <span class="pre">'Amam',</span> <span class="pre">'Amm2',</span> <span class="pre">'Amm2(-a,c+1/4,b-1/4)',</span> <span class="pre">'Amm2(a,b+1/4,c-1/4)',</span> <span class="pre">'Amm2(b,-a+1/4,c-1/4)',</span> <span class="pre">'Amm2(b,c+1/4,a-1/4)',</span> <span class="pre">'Amma',</span> <span class="pre">'Ammm',</span> <span class="pre">'B-1',</span> <span class="pre">'B112',</span> <span class="pre">'B112/b',</span> <span class="pre">'B112/m',</span> <span class="pre">'B112/n',</span> <span class="pre">'B11b',</span> <span class="pre">'B11m',</span> <span class="pre">'B11n',</span> <span class="pre">'B121/m1',</span> <span class="pre">'B1211',</span> <span class="pre">'B2/b11',</span> <span class="pre">'B2/m11',</span> <span class="pre">'B2/n11',</span> <span class="pre">'B211',</span> <span class="pre">'B2212',</span> <span class="pre">'B222',</span> <span class="pre">'B2eb',</span> <span class="pre">'B2em',</span> <span class="pre">'B2mb',</span> <span class="pre">'B2mm',</span> <span class="pre">'Bb11',</span> <span class="pre">'Bb21m',</span> <span class="pre">'Bb2b',</span> <span class="pre">'Bbab',</span> <span class="pre">'Bbab:2',</span> <span class="pre">'Bbcb',</span> <span class="pre">'Bbcb:2',</span> <span class="pre">'Bbe2',</span> <span class="pre">'Bbeb',</span> <span class="pre">'Bbeb:1',</span> <span class="pre">'Bbem',</span> <span class="pre">'Bbm2',</span> <span class="pre">'Bbmb',</span> <span class="pre">'Bbmm',</span> <span class="pre">'Bm11',</span> <span class="pre">'Bm21b',</span> <span class="pre">'Bm2m',</span> <span class="pre">'Bmam',</span> <span class="pre">'Bmcm',</span> <span class="pre">'Bme2',</span> <span class="pre">'Bmeb',</span> <span class="pre">'Bmm2',</span> <span class="pre">'Bmmb',</span> <span class="pre">'Bmmm',</span> <span class="pre">'Bn11',</span> <span class="pre">'C-1',</span> <span class="pre">'C1',</span> <span class="pre">'C12/c1',</span> <span class="pre">'C12/m1',</span> <span class="pre">'C12/m1(-a-1/4,c+1/4,b)',</span> <span class="pre">'C12/m1(a+2*c,a,b)',</span> <span class="pre">'C12/m1(a+2*c-1/4,a+1/4,b)',</span> <span class="pre">'C12/m1(a+c-1/4,b+1/4,c)',</span> <span class="pre">'C12/m1(a,b,a+2*c)',</span> <span class="pre">'C12/m1(a-1/4,b+1/4,a+2*c)',</span> <span class="pre">'C12/m1(a-1/4,b+1/4,c)',</span> <span class="pre">'C12/m1(b,a+2*c,a)',</span> <span class="pre">'C12/m1(b-1/4,-a+1/4,c)',</span> <span class="pre">'C12/m1(b-1/4,a+2*c+1/4,a)',</span> <span class="pre">'C12/m1(b-1/4,c+1/4,a)',</span> <span class="pre">'C12/m1(b-1/4,c+1/4,a+c)',</span> <span class="pre">'C12/m1(c-1/4,a+1/4,b)',</span> <span class="pre">'C12/m1(c-1/4,a+c+1/4,b)',</span> <span class="pre">'C12/m1(c-1/4,b+1/4,-a)',</span> <span class="pre">'C12/n1',</span> <span class="pre">'C121',</span> <span class="pre">'C121(-a-1/4,c-1/4,b)',</span> <span class="pre">'C121(a+2*c,a,b)',</span> <span class="pre">'C121(a+2*c-1/4,a-1/4,b)',</span> <span class="pre">'C121(a+c-1/4,b-1/4,c)',</span> <span class="pre">'C121(a,b,a+2*c)',</span> <span class="pre">'C121(a-1/4,b-1/4,a+2*c)',</span> <span class="pre">'C121(a-1/4,b-1/4,c)',</span> <span class="pre">'C121(c-1/4,a+c-1/4,b)',</span> <span class="pre">'C121(c-1/4,a-1/4,b)',</span> <span class="pre">'C121(c-1/4,b-1/4,-a)',</span> <span class="pre">'C1c1',</span> <span class="pre">'C1c1(2*a+c,b,c)',</span> <span class="pre">'C1m1',</span> <span class="pre">'C1m1(-a-1/4,c-1/4,b)',</span> <span class="pre">'C1m1(a+2*c,a,b)',</span> <span class="pre">'C1m1(a+2*c-1/4,a-1/4,b)',</span> <span class="pre">'C1m1(a+c-1/4,b-1/4,c)',</span> <span class="pre">'C1m1(a,b,a+2*c)',</span> <span class="pre">'C1m1(a-1/4,b-1/4,a+2*c)',</span> <span class="pre">'C1m1(a-1/4,b-1/4,c)',</span> <span class="pre">'C1m1(b,a+2*c,a)',</span> <span class="pre">'C1m1(b-1/4,-a-1/4,c)',</span> <span class="pre">'C1m1(b-1/4,a+2*c-1/4,a)',</span> <span class="pre">'C1m1(b-1/4,c-1/4,a)',</span> <span class="pre">'C1m1(b-1/4,c-1/4,a+c)',</span> <span class="pre">'C1m1(c-1/4,a+c-1/4,b)',</span> <span class="pre">'C1m1(c-1/4,a-1/4,b)',</span> <span class="pre">'C1m1(c-1/4,b-1/4,-a)',</span> <span class="pre">'C1n1',</span> <span class="pre">'C2/c11',</span> <span class="pre">'C2/m11',</span> <span class="pre">'C2/n11',</span> <span class="pre">'C211',</span> <span class="pre">'C222',</span> <span class="pre">'C2221',</span> <span class="pre">'C222_1',</span> <span class="pre">'C2cm',</span> <span class="pre">'C2eb',</span> <span class="pre">'C2me',</span> <span class="pre">'C2mm',</span> <span class="pre">'Cc11',</span> <span class="pre">'Cc2e',</span> <span class="pre">'Cc2m',</span> <span class="pre">'Ccc2',</span> <span class="pre">'Ccc2(a-1/4,b-1/4,c)',</span> <span class="pre">'Ccc2(b-1/4,c-1/4,a)',</span> <span class="pre">'Ccca',</span> <span class="pre">'Ccca:2',</span> <span class="pre">'Cccb',</span> <span class="pre">'Cccb:2',</span> <span class="pre">'Ccce',</span> <span class="pre">'Ccce:1',</span> <span class="pre">'Cccm',</span> <span class="pre">'Cccm(a,b,c-1/4)',</span> <span class="pre">'Cccm(a-1/4,b-1/4,c)',</span> <span class="pre">'Cccm(b,c,a-1/4)',</span> <span class="pre">'Cccm(b-1/4,c-1/4,a)',</span> <span class="pre">'Cccm(c,a,b-1/4)',</span> <span class="pre">'Cccm(c-1/4,a-1/4,b)',</span> <span class="pre">'Ccm21',</span> <span class="pre">'Ccme',</span> <span class="pre">'Ccmm',</span> <span class="pre">'Cm11',</span> <span class="pre">'Cm2e',</span> <span class="pre">'Cm2m',</span> <span class="pre">'Cmc21',</span> <span class="pre">'Cmc21(-a,c+1/4,b)',</span> <span class="pre">'Cmc21(-a-1/4,c-1/4,b)',</span> <span class="pre">'Cmc21(a,b+1/4,c)',</span> <span class="pre">'Cmc21(a-1/4,b-1/4,c)',</span> <span class="pre">'Cmc21(b,-a+1/4,c)',</span> <span class="pre">'Cmc21(b,c+1/4,a)',</span> <span class="pre">'Cmc21(b-1/4,-a-1/4,c)',</span> <span class="pre">'Cmc21(b-1/4,c-1/4,a)',</span> <span class="pre">'Cmc2_1',</span> <span class="pre">'Cmce',</span> <span class="pre">'Cmce(-a-1/4,c-1/4,b)',</span> <span class="pre">'Cmce(a-1/4,b-1/4,c)',</span> <span class="pre">'Cmce(b-1/4,-a-1/4,c)',</span> <span class="pre">'Cmce(b-1/4,c-1/4,a)',</span> <span class="pre">'Cmce(c-1/4,a-1/4,b)',</span> <span class="pre">'Cmce(c-1/4,b-1/4,-a)',</span> <span class="pre">'Cmcm',</span> <span class="pre">'Cmcm(-a+1/2,c-1/4,b+1/4)',</span> <span class="pre">'Cmcm(-a-1/4,c-1/4,b)',</span> <span class="pre">'Cmcm(a+1/2,b-1/4,c+1/4)',</span> <span class="pre">'Cmcm(a-1/4,b-1/4,c)',</span> <span class="pre">'Cmcm(b+1/2,-a-1/4,c+1/4)',</span> <span class="pre">'Cmcm(b+1/2,c-1/4,a+1/4)',</span> <span class="pre">'Cmcm(b-1/4,-a-1/4,c)',</span> <span class="pre">'Cmcm(b-1/4,c-1/4,a)',</span> <span class="pre">'Cmcm(c+1/2,a-1/4,b+1/4)',</span> <span class="pre">'Cmcm(c+1/2,b-1/4,-a+1/4)',</span> <span class="pre">'Cmcm(c-1/4,a-1/4,b)',</span> <span class="pre">'Cmcm(c-1/4,b-1/4,-a)',</span> <span class="pre">'Cmm2',</span> <span class="pre">'Cmm2(2*c,a,b)',</span> <span class="pre">'Cmm2(a-1/4,b-1/4,c)',</span> <span class="pre">'Cmm2(b-1/4,c-1/4,a)',</span> <span class="pre">'Cmma',</span> <span class="pre">'Cmmb',</span> <span class="pre">'Cmme',</span> <span class="pre">'Cmmm',</span> <span class="pre">'Cmmm(a-1/4,b-1/4,c)',</span> <span class="pre">'Cmmm(b-1/4,c-1/4,a)',</span> <span class="pre">'Cmmm(c-1/4,a-1/4,b)',</span> <span class="pre">'Cn11',</span> <span class="pre">'F-43c',</span> <span class="pre">'F-43m',</span> <span class="pre">'F222',</span> <span class="pre">'F23',</span> <span class="pre">'F2dd',</span> <span class="pre">'F2mm',</span> <span class="pre">'F4132',</span> <span class="pre">'F432',</span> <span class="pre">'F4_132',</span> <span class="pre">'Fd-3',</span> <span class="pre">'Fd-3:1',</span> <span class="pre">'Fd-3:2',</span> <span class="pre">'Fd-3c',</span> <span class="pre">'Fd-3c:1',</span> <span class="pre">'Fd-3c:2',</span> <span class="pre">'Fd-3m',</span> <span class="pre">'Fd-3m:1',</span> <span class="pre">'Fd-3m:2',</span> <span class="pre">'Fd2d',</span> <span class="pre">'Fdd2',</span> <span class="pre">'Fddd',</span> <span class="pre">'Fddd:1',</span> <span class="pre">'Fddd:2',</span> <span class="pre">'Fm-3',</span> <span class="pre">'Fm-3(a-1/4,b-1/4,c-1/4)',</span> <span class="pre">'Fm-3c',</span> <span class="pre">'Fm-3c(a+1/4,b+1/4,c+1/4)',</span> <span class="pre">'Fm-3m',</span> <span class="pre">'Fm-3m(a-1/4,b-1/4,c-1/4)',</span> <span class="pre">'Fm2m',</span> <span class="pre">'Fmm2',</span> <span class="pre">'Fmm2(a+1/4,b+1/4,c+1/2)',</span> <span class="pre">'Fmm2(a+1/4,b,c+1/4)',</span> <span class="pre">'Fmm2(a,b-1/4,c-1/4)',</span> <span class="pre">'Fmm2(b+1/4,c+1/4,a+1/2)',</span> <span class="pre">'Fmm2(b+1/4,c,a+1/4)',</span> <span class="pre">'Fmm2(b,c-1/4,a-1/4)',</span> <span class="pre">'Fmmm',</span> <span class="pre">'Fmmm(a+1/2,b+1/4,c+1/4)',</span> <span class="pre">'Fmmm(a+1/4,b+1/4,c)',</span> <span class="pre">'Fmmm(a-1/4,b+1/2,c+1/4)',</span> <span class="pre">'Fmmm(a-1/4,b-1/4,c-1/4)',</span> <span class="pre">'I-1',</span> <span class="pre">'I-4',</span> <span class="pre">'I-42d',</span> <span class="pre">'I-42m',</span> <span class="pre">'I-43d',</span> <span class="pre">'I-43m',</span> <span class="pre">'I-4c2',</span> <span class="pre">'I-4m2',</span> <span class="pre">'I112',</span> <span class="pre">'I112/a',</span> <span class="pre">'I112/b',</span> <span class="pre">'I112/m',</span> <span class="pre">'I11a',</span> <span class="pre">'I11b',</span> <span class="pre">'I11m',</span> <span class="pre">'I12/a1',</span> <span class="pre">'I12/c1',</span> <span class="pre">'I12/m1',</span> <span class="pre">'I121',</span> <span class="pre">'I1a1',</span> <span class="pre">'I1c1',</span> <span class="pre">'I1m1',</span> <span class="pre">'I2/b11',</span> <span class="pre">'I2/c11',</span> <span class="pre">'I2/m11',</span> <span class="pre">'I211',</span> <span class="pre">'I212121',</span> <span class="pre">'I213',</span> <span class="pre">'I222',</span> <span class="pre">'I23',</span> <span class="pre">'I2_12_12_1',</span> <span class="pre">'I2_13',</span> <span class="pre">'I2cb',</span> <span class="pre">'I2cm',</span> <span class="pre">'I2mb',</span> <span class="pre">'I2mm',</span> <span class="pre">'I4',</span> <span class="pre">'I4/m',</span> <span class="pre">'I4/m(a+1/2,b,c)',</span> <span class="pre">'I4/m(a+1/2,b,c-1/4)',</span> <span class="pre">'I4/m(a+b+1/2,-a+b,c)',</span> <span class="pre">'I4/m(a+b+1/2,-a+b,c-1/4)',</span> <span class="pre">'I4/m(a+b,-a+b,c)',</span> <span class="pre">'I4/m(a-1/4,b-1/4,c+1/4)',</span> <span class="pre">'I4/mcm',</span> <span class="pre">'I4/mcm(a+1/2,b,c)',</span> <span class="pre">'I4/mcm(a+1/2,b,c+1/4)',</span> <span class="pre">'I4/mcm(a+1/4,b-1/4,c+1/4)',</span> <span class="pre">'I4/mcm(a+b+1/2,-a+b,c)',</span> <span class="pre">'I4/mcm(a+b+1/2,-a+b,c+1/4)',</span> <span class="pre">'I4/mcm(a+b,-a+b,c)',</span> <span class="pre">'I4/mcm(a+b,-a+b,c+1/4)',</span> <span class="pre">'I4/mcm(a,b,c+1/4)',</span> <span class="pre">'I4/mcm(a-1/4,b-1/4,c+1/4)',</span> <span class="pre">'I4/mmm',</span> <span class="pre">'I4/mmm(a+1/2,b,c)',</span> <span class="pre">'I4/mmm(a+1/2,b,c-1/4)',</span> <span class="pre">'I4/mmm(a+1/4,b-1/4,c+1/4)',</span> <span class="pre">'I4/mmm(a+b+1/2,-a+b,c)',</span> <span class="pre">'I4/mmm(a+b+1/2,-a+b,c-1/4)',</span> <span class="pre">'I4/mmm(a+b,-a+b,c)',</span> <span class="pre">'I4/mmm(a-1/4,b-1/4,c+1/4)',</span> <span class="pre">'I41',</span> <span class="pre">'I41/a',</span> <span class="pre">'I41/a:1',</span> <span class="pre">'I41/a:2',</span> <span class="pre">'I41/acd',</span> <span class="pre">'I41/acd:1',</span> <span class="pre">'I41/acd:2',</span> <span class="pre">'I41/amd',</span> <span class="pre">'I41/amd:1',</span> <span class="pre">'I41/amd:2',</span> <span class="pre">'I4122',</span> <span class="pre">'I4132',</span> <span class="pre">'I41cd',</span> <span class="pre">'I41md',</span> <span class="pre">'I422',</span> <span class="pre">'I432',</span> <span class="pre">'I4_1',</span> <span class="pre">'I4_1/a',</span> <span class="pre">'I4_1/acd',</span> <span class="pre">'I4_1/amd',</span> <span class="pre">'I4_122',</span> <span class="pre">'I4_132',</span> <span class="pre">'I4_1cd',</span> <span class="pre">'I4_1md',</span> <span class="pre">'I4cm',</span> <span class="pre">'I4mm',</span> <span class="pre">'Ia-3',</span> <span class="pre">'Ia-3d',</span> <span class="pre">'Ib11',</span> <span class="pre">'Iba2',</span> <span class="pre">'Iba2(a-1/4,b-1/4,c+1/4)',</span> <span class="pre">'Iba2(b-1/4,c-1/4,a+1/4)',</span> <span class="pre">'Ibam',</span> <span class="pre">'Ibam(a+1/4,b-1/4,c+1/4)',</span> <span class="pre">'Ibam(a,b,c+1/4)',</span> <span class="pre">'Ibam(b+1/4,c-1/4,a+1/4)',</span> <span class="pre">'Ibam(b,c,a+1/4)',</span> <span class="pre">'Ibam(c+1/4,a-1/4,b+1/4)',</span> <span class="pre">'Ibam(c,a,b+1/4)',</span> <span class="pre">'Ibca',</span> <span class="pre">'Ibm2',</span> <span class="pre">'Ibmm',</span> <span class="pre">'Ic11',</span> <span class="pre">'Ic2a',</span> <span class="pre">'Ic2m',</span> <span class="pre">'Icab',</span> <span class="pre">'Icma',</span> <span class="pre">'Icmm',</span> <span class="pre">'Im-3',</span> <span class="pre">'Im-3(a-1/4,b-1/4,c-1/4)',</span> <span class="pre">'Im-3m',</span> <span class="pre">'Im-3m(a-1/4,b-1/4,c-1/4)',</span> <span class="pre">'Im11',</span> <span class="pre">'Im2a',</span> <span class="pre">'Im2m',</span> <span class="pre">'Ima2',</span> <span class="pre">'Ima2(-a-1/4,c-1/4,b+1/4)',</span> <span class="pre">'Ima2(a-1/4,b-1/4,c+1/4)',</span> <span class="pre">'Ima2(b-1/4,-a-1/4,c+1/4)',</span> <span class="pre">'Ima2(b-1/4,c-1/4,a+1/4)',</span> <span class="pre">'Imam',</span> <span class="pre">'Imcb',</span> <span class="pre">'Imcm',</span> <span class="pre">'Imm2',</span> <span class="pre">'Imm2(a,b-1/4,c)',</span> <span class="pre">'Imm2(a-1/4,b,c+1/4)',</span> <span class="pre">'Imm2(b,c-1/4,a)',</span> <span class="pre">'Imm2(b-1/4,c,a+1/4)',</span> <span class="pre">'Imma',</span> <span class="pre">'Immb',</span> <span class="pre">'Immm',</span> <span class="pre">'Immm(a+1/4,b-1/4,c+1/4)',</span> <span class="pre">'Immm(a,b,c-1/4)',</span> <span class="pre">'Immm(a,b-1/4,c)',</span> <span class="pre">'Immm(a-1/4,b,c)',</span> <span class="pre">'P-1',</span> <span class="pre">'P-1(-a+b+c,a-b+c,a+b-c)',</span> <span class="pre">'P-3',</span> <span class="pre">'P-31c',</span> <span class="pre">'P-31m',</span> <span class="pre">'P-3c1',</span> <span class="pre">'P-3m1',</span> <span class="pre">'P-4',</span> <span class="pre">'P-421c',</span> <span class="pre">'P-421m',</span> <span class="pre">'P-42_1c',</span> <span class="pre">'P-42_1m',</span> <span class="pre">'P-42c',</span> <span class="pre">'P-42m',</span> <span class="pre">'P-43m',</span> <span class="pre">'P-43n',</span> <span class="pre">'P-4b2',</span> <span class="pre">'P-4c2',</span> <span class="pre">'P-4m2',</span> <span class="pre">'P-4n2',</span> <span class="pre">'P-6',</span> <span class="pre">'P-62c',</span> <span class="pre">'P-62m',</span> <span class="pre">'P-6c2',</span> <span class="pre">'P-6m2',</span> <span class="pre">'P1',</span> <span class="pre">'P1(-a+b+c,a-b+c,a+b-c)',</span> <span class="pre">'P1(-a+c,-b,a+c)',</span> <span class="pre">'P1(-a,-b+c,b+c)',</span> <span class="pre">'P1(b+c,a+c,a+b)',</span> <span class="pre">'P112',</span> <span class="pre">'P112/a',</span> <span class="pre">'P112/b',</span> <span class="pre">'P112/m',</span> <span class="pre">'P112/n',</span> <span class="pre">'P1121',</span> <span class="pre">'P1121/a',</span> <span class="pre">'P1121/b',</span> <span class="pre">'P1121/m',</span> <span class="pre">'P1121/n',</span> <span class="pre">'P11a',</span> <span class="pre">'P11b',</span> <span class="pre">'P11m',</span> <span class="pre">'P11n',</span> <span class="pre">'P12/a1',</span> <span class="pre">'P12/c1',</span> <span class="pre">'P12/c1(2*a+c,b,c)',</span> <span class="pre">'P12/c1(a,2*b,c)',</span> <span class="pre">'P12/c1(b,c,2*a+c)',</span> <span class="pre">'P12/c1(c,2*a+c,b)',</span> <span class="pre">'P12/m1',</span> <span class="pre">'P12/m1(2*a+c,b,c)',</span> <span class="pre">'P12/m1(b,c,2*a+c)',</span> <span class="pre">'P12/m1(c,2*a+c,b)',</span> <span class="pre">'P12/n1',</span> <span class="pre">'P121',</span> <span class="pre">'P121(2*a+c,b,c)',</span> <span class="pre">'P121(c,2*a+c,b)',</span> <span class="pre">'P121/a1',</span> <span class="pre">'P121/c1',</span> <span class="pre">'P121/c1(2*a+c,b,c)',</span> <span class="pre">'P121/c1(2*c,2*a+c,b)',</span> <span class="pre">'P121/c1(b,c,2*a+c)',</span> <span class="pre">'P121/c1(c,2*a+c,b)',</span> <span class="pre">'P121/m1',</span> <span class="pre">'P121/m1(b,c,2*a+c)',</span> <span class="pre">'P121/m1(c,2*a+c,b)',</span> <span class="pre">'P121/n1',</span> <span class="pre">'P1211',</span> <span class="pre">'P1211(a-1/4,b,c)',</span> <span class="pre">'P1211(c,2*a+c,b)',</span> <span class="pre">'P12_1/c1',</span> <span class="pre">'P12_1/m1',</span> <span class="pre">'P12_11',</span> <span class="pre">'P1a1',</span> <span class="pre">'P1c1',</span> <span class="pre">'P1c1(2*a+c,b,c)',</span> <span class="pre">'P1c1(b,c,2*a+c)',</span> <span class="pre">'P1c1(c,2*a+c,b)',</span> <span class="pre">'P1m1',</span> <span class="pre">'P1m1(2*a+c,b,c)',</span> <span class="pre">'P1m1(b,c,2*a+c)',</span> <span class="pre">'P1m1(c,2*a+c,b)',</span> <span class="pre">'P1n1',</span> <span class="pre">'P2/b11',</span> <span class="pre">'P2/c11',</span> <span class="pre">'P2/m11',</span> <span class="pre">'P2/n11',</span> <span class="pre">'P21/b11',</span> <span class="pre">'P21/c11',</span> <span class="pre">'P21/m11',</span> <span class="pre">'P21/n11',</span> <span class="pre">'P211',</span> <span class="pre">'P2111',</span> <span class="pre">'P21212',</span> <span class="pre">'P212121',</span> <span class="pre">'P212121(originshiftx,y,z+1/4)',</span> <span class="pre">'P2122',</span> <span class="pre">'P21221',</span> <span class="pre">'P213',</span> <span class="pre">'P21ab',</span> <span class="pre">'P21am',</span> <span class="pre">'P21ca',</span> <span class="pre">'P21cn',</span> <span class="pre">'P21ma',</span> <span class="pre">'P21mn',</span> <span class="pre">'P21nb',</span> <span class="pre">'P21nm',</span> <span class="pre">'P2212',</span> <span class="pre">'P22121',</span> <span class="pre">'P222',</span> <span class="pre">'P2221',</span> <span class="pre">'P222_1',</span> <span class="pre">'P23',</span> <span class="pre">'P2_12_12',</span> <span class="pre">'P2_12_12_1',</span> <span class="pre">'P2_13',</span> <span class="pre">'P2aa',</span> <span class="pre">'P2an',</span> <span class="pre">'P2cb',</span> <span class="pre">'P2cm',</span> <span class="pre">'P2mb',</span> <span class="pre">'P2mm',</span> <span class="pre">'P2na',</span> <span class="pre">'P2nn',</span> <span class="pre">'P3',</span> <span class="pre">'P31',</span> <span class="pre">'P3112',</span> <span class="pre">'P312',</span> <span class="pre">'P3121',</span> <span class="pre">'P31c',</span> <span class="pre">'P31m',</span> <span class="pre">'P32',</span> <span class="pre">'P321',</span> <span class="pre">'P3212',</span> <span class="pre">'P3221',</span> <span class="pre">'P3_1',</span> <span class="pre">'P3_112',</span> <span class="pre">'P3_121',</span> <span class="pre">'P3_2',</span> <span class="pre">'P3_212',</span> <span class="pre">'P3_221',</span> <span class="pre">'P3c1',</span> <span class="pre">'P3m1',</span> <span class="pre">'P4',</span> <span class="pre">'P4/m',</span> <span class="pre">'P4/m(a+b,-a+b+1/2,c)',</span> <span class="pre">'P4/m(a+b,-a+b,c)',</span> <span class="pre">'P4/mbm',</span> <span class="pre">'P4/mcc',</span> <span class="pre">'P4/mcc(a+b,-a+b+1/2,c)',</span> <span class="pre">'P4/mcc(a+b,-a+b,c)',</span> <span class="pre">'P4/mcc(a+b,-a+b,c+1/4)',</span> <span class="pre">'P4/mmm',</span> <span class="pre">'P4/mmm(a+b,-a+b+1/2,c)',</span> <span class="pre">'P4/mmm(a+b,-a+b,c)',</span> <span class="pre">'P4/mnc',</span> <span class="pre">'P4/n',</span> <span class="pre">'P4/n:1',</span> <span class="pre">'P4/n:2',</span> <span class="pre">'P4/nbm',</span> <span class="pre">'P4/nbm:1',</span> <span class="pre">'P4/nbm:2',</span> <span class="pre">'P4/ncc',</span> <span class="pre">'P4/ncc:1',</span> <span class="pre">'P4/ncc:2',</span> <span class="pre">'P4/nmm',</span> <span class="pre">'P4/nmm:1',</span> <span class="pre">'P4/nmm:2',</span> <span class="pre">'P4/nnc',</span> <span class="pre">'P4/nnc:1',</span> <span class="pre">'P4/nnc:2',</span> <span class="pre">'P41',</span> <span class="pre">'P41212',</span> <span class="pre">'P4122',</span> <span class="pre">'P4132',</span> <span class="pre">'P42',</span> <span class="pre">'P42/m',</span> <span class="pre">'P42/m(a+b,-a+b+1/2,c)',</span> <span class="pre">'P42/m(a+b,-a+b,c)',</span> <span class="pre">'P42/m(a+b,-a+b,c-1/4)',</span> <span class="pre">'P42/mbc',</span> <span class="pre">'P42/mcm',</span> <span class="pre">'P42/mcm(a+b,-a+b+1/2,c)',</span> <span class="pre">'P42/mcm(a+b,-a+b,c)',</span> <span class="pre">'P42/mcm(a+b,-a+b,c+1/4)',</span> <span class="pre">'P42/mmc',</span> <span class="pre">'P42/mmc(a+b,-a+b+1/2,c)',</span> <span class="pre">'P42/mmc(a+b,-a+b,c)',</span> <span class="pre">'P42/mmc(a+b,-a+b,c-1/4)',</span> <span class="pre">'P42/mnm',</span> <span class="pre">'P42/n',</span> <span class="pre">'P42/n:1',</span> <span class="pre">'P42/n:2',</span> <span class="pre">'P42/nbc',</span> <span class="pre">'P42/nbc:1',</span> <span class="pre">'P42/nbc:2',</span> <span class="pre">'P42/ncm',</span> <span class="pre">'P42/ncm:1',</span> <span class="pre">'P42/ncm:2',</span> <span class="pre">'P42/nmc',</span> <span class="pre">'P42/nmc:1',</span> <span class="pre">'P42/nmc:2',</span> <span class="pre">'P42/nnm',</span> <span class="pre">'P42/nnm:1',</span> <span class="pre">'P42/nnm:2',</span> <span class="pre">'P4212',</span> <span class="pre">'P422',</span> <span class="pre">'P42212',</span> <span class="pre">'P4222',</span> <span class="pre">'P4232',</span> <span class="pre">'P42_12',</span> <span class="pre">'P42bc',</span> <span class="pre">'P42cm',</span> <span class="pre">'P42mc',</span> <span class="pre">'P42nm',</span> <span class="pre">'P43',</span> <span class="pre">'P432',</span> <span class="pre">'P43212',</span> <span class="pre">'P4322',</span> <span class="pre">'P4332',</span> <span class="pre">'P4_1',</span> <span class="pre">'P4_122',</span> <span class="pre">'P4_12_12',</span> <span class="pre">'P4_132',</span> <span class="pre">'P4_2',</span> <span class="pre">'P4_2/m',</span> <span class="pre">'P4_2/mbc',</span> <span class="pre">'P4_2/mcm',</span> <span class="pre">'P4_2/mmc',</span> <span class="pre">'P4_2/mnm',</span> <span class="pre">'P4_2/n',</span> <span class="pre">'P4_2/nbc',</span> <span class="pre">'P4_2/ncm',</span> <span class="pre">'P4_2/nmc',</span> <span class="pre">'P4_2/nnm',</span> <span class="pre">'P4_222',</span> <span class="pre">'P4_22_12',</span> <span class="pre">'P4_232',</span> <span class="pre">'P4_2bc',</span> <span class="pre">'P4_2cm',</span> <span class="pre">'P4_2mc',</span> <span class="pre">'P4_2nm',</span> <span class="pre">'P4_3',</span> <span class="pre">'P4_322',</span> <span class="pre">'P4_32_12',</span> <span class="pre">'P4_332',</span> <span class="pre">'P4bm',</span> <span class="pre">'P4bm(a,b,2*c)',</span> <span class="pre">'P4cc',</span> <span class="pre">'P4mm',</span> <span class="pre">'P4nc',</span> <span class="pre">'P6',</span> <span class="pre">'P6/m',</span> <span class="pre">'P6/m(2*a,2*b,2*c)',</span> <span class="pre">'P6/m(2*a,2*b,c)',</span> <span class="pre">'P6/mcc',</span> <span class="pre">'P6/mcc(2*a,2*b,c)',</span> <span class="pre">'P6/mmm',</span> <span class="pre">'P6/mmm(2*a,2*b,2*c)',</span> <span class="pre">'P6/mmm(2*a,2*b,c)',</span> <span class="pre">'P61',</span> <span class="pre">'P6122',</span> <span class="pre">'P62',</span> <span class="pre">'P622',</span> <span class="pre">'P6222',</span> <span class="pre">'P63',</span> <span class="pre">'P63/m',</span> <span class="pre">'P63/m(2*a,2*b,c)',</span> <span class="pre">'P63/mcm',</span> <span class="pre">'P63/mcm(2*a,2*b,c)',</span> <span class="pre">'P63/mmc',</span> <span class="pre">'P63/mmc(2*a,2*b,c)',</span> <span class="pre">'P6322',</span> <span class="pre">'P63cm',</span> <span class="pre">'P63mc',</span> <span class="pre">'P64',</span> <span class="pre">'P6422',</span> <span class="pre">'P65',</span> <span class="pre">'P6522',</span> <span class="pre">'P6_1',</span> <span class="pre">'P6_122',</span> <span class="pre">'P6_2',</span> <span class="pre">'P6_222',</span> <span class="pre">'P6_3',</span> <span class="pre">'P6_3/m',</span> <span class="pre">'P6_3/mcm',</span> <span class="pre">'P6_3/mmc',</span> <span class="pre">'P6_322',</span> <span class="pre">'P6_3cm',</span> <span class="pre">'P6_3mc',</span> <span class="pre">'P6_4',</span> <span class="pre">'P6_422',</span> <span class="pre">'P6_5',</span> <span class="pre">'P6_522',</span> <span class="pre">'P6cc',</span> <span class="pre">'P6mm',</span> <span class="pre">'Pa-3',</span> <span class="pre">'Pb11',</span> <span class="pre">'Pb21a',</span> <span class="pre">'Pb21m',</span> <span class="pre">'Pb2b',</span> <span class="pre">'Pb2n',</span> <span class="pre">'Pba2',</span> <span class="pre">'Pbaa',</span> <span class="pre">'Pbab',</span> <span class="pre">'Pbam',</span> <span class="pre">'Pban',</span> <span class="pre">'Pban:1',</span> <span class="pre">'Pban:2',</span> <span class="pre">'Pbc21',</span> <span class="pre">'Pbca',</span> <span class="pre">'Pbcb',</span> <span class="pre">'Pbcm',</span> <span class="pre">'Pbcn',</span> <span class="pre">'Pbm2',</span> <span class="pre">'Pbma',</span> <span class="pre">'Pbmb',</span> <span class="pre">'Pbmm',</span> <span class="pre">'Pbmn',</span> <span class="pre">'Pbn21',</span> <span class="pre">'Pbna',</span> <span class="pre">'Pbnb',</span> <span class="pre">'Pbnm',</span> <span class="pre">'Pbnn',</span> <span class="pre">'Pc11',</span> <span class="pre">'Pc21b',</span> <span class="pre">'Pc21n',</span> <span class="pre">'Pc2a',</span> <span class="pre">'Pc2m',</span> <span class="pre">'Pca21',</span> <span class="pre">'Pca2_1',</span> <span class="pre">'Pcaa',</span> <span class="pre">'Pcab',</span> <span class="pre">'Pcam',</span> <span class="pre">'Pcan',</span> <span class="pre">'Pcc2',</span> <span class="pre">'Pcca',</span> <span class="pre">'Pccb',</span> <span class="pre">'Pccm',</span> <span class="pre">'Pccn',</span> <span class="pre">'Pcm21',</span> <span class="pre">'Pcma',</span> <span class="pre">'Pcmb',</span> <span class="pre">'Pcmm',</span> <span class="pre">'Pcmn',</span> <span class="pre">'Pcn2',</span> <span class="pre">'Pcna',</span> <span class="pre">'Pcna:1',</span> <span class="pre">'Pcna:2',</span> <span class="pre">'Pcnb',</span> <span class="pre">'Pcnm',</span> <span class="pre">'Pcnn',</span> <span class="pre">'Pm-3',</span> <span class="pre">'Pm-3m',</span> <span class="pre">'Pm-3n',</span> <span class="pre">'Pm11',</span> <span class="pre">'Pm21b',</span> <span class="pre">'Pm21n',</span> <span class="pre">'Pm2a',</span> <span class="pre">'Pm2m',</span> <span class="pre">'Pma2',</span> <span class="pre">'Pmaa',</span> <span class="pre">'Pmab',</span> <span class="pre">'Pmam',</span> <span class="pre">'Pman',</span> <span class="pre">'Pmc21',</span> <span class="pre">'Pmc21(2*a,b,c)',</span> <span class="pre">'Pmc2_1',</span> <span class="pre">'Pmca',</span> <span class="pre">'Pmcb',</span> <span class="pre">'Pmcm',</span> <span class="pre">'Pmcn',</span> <span class="pre">'Pmm2',</span> <span class="pre">'Pmma',</span> <span class="pre">'Pmma(2*b+1/4,c,a-1/3)',</span> <span class="pre">'Pmma(2*b,c,a)',</span> <span class="pre">'Pmmb',</span> <span class="pre">'Pmmm',</span> <span class="pre">'Pmmm(2*a,2*b,c)',</span> <span class="pre">'Pmmn',</span> <span class="pre">'Pmmn:1',</span> <span class="pre">'Pmmn:2',</span> <span class="pre">'Pmn21',</span> <span class="pre">'Pmn2_1',</span> <span class="pre">'Pmna',</span> <span class="pre">'Pmnb',</span> <span class="pre">'Pmnm',</span> <span class="pre">'Pmnm:1',</span> <span class="pre">'Pmnm:2',</span> <span class="pre">'Pmnn',</span> <span class="pre">'Pn-3',</span> <span class="pre">'Pn-3:1',</span> <span class="pre">'Pn-3:2',</span> <span class="pre">'Pn-3m',</span> <span class="pre">'Pn-3m:1',</span> <span class="pre">'Pn-3m:2',</span> <span class="pre">'Pn-3n',</span> <span class="pre">'Pn-3n:1',</span> <span class="pre">'Pn-3n:2',</span> <span class="pre">'Pn11',</span> <span class="pre">'Pn21a',</span> <span class="pre">'Pn21m',</span> <span class="pre">'Pn2b',</span> <span class="pre">'Pn2n',</span> <span class="pre">'Pna21',</span> <span class="pre">'Pna2_1',</span> <span class="pre">'Pnaa',</span> <span class="pre">'Pnab',</span> <span class="pre">'Pnam',</span> <span class="pre">'Pnan',</span> <span class="pre">'Pnc2',</span> <span class="pre">'Pnca',</span> <span class="pre">'Pncb',</span> <span class="pre">'Pncb:1',</span> <span class="pre">'Pncb:2',</span> <span class="pre">'Pncm',</span> <span class="pre">'Pncn',</span> <span class="pre">'Pnm21',</span> <span class="pre">'Pnma',</span> <span class="pre">'Pnma(c,a-1/4,b)',</span> <span class="pre">'Pnmb',</span> <span class="pre">'Pnmm',</span> <span class="pre">'Pnmm:1',</span> <span class="pre">'Pnmm:2',</span> <span class="pre">'Pnmn',</span> <span class="pre">'Pnn2',</span> <span class="pre">'Pnna',</span> <span class="pre">'Pnnb',</span> <span class="pre">'Pnnm',</span> <span class="pre">'Pnnn',</span> <span class="pre">'Pnnn:1',</span> <span class="pre">'Pnnn:2',</span> <span class="pre">'R-3',</span> <span class="pre">'R-3:H',</span> <span class="pre">'R-3:R',</span> <span class="pre">'R-3c',</span> <span class="pre">'R-3c:H',</span> <span class="pre">'R-3c:R',</span> <span class="pre">'R-3m',</span> <span class="pre">'R-3m:H',</span> <span class="pre">'R-3m:R',</span> <span class="pre">'R12/c1',</span> <span class="pre">'R3',</span> <span class="pre">'R32',</span> <span class="pre">'R32:H',</span> <span class="pre">'R32:R',</span> <span class="pre">'R3:H',</span> <span class="pre">'R3:R',</span> <span class="pre">'R3c',</span> <span class="pre">'R3c:H',</span> <span class="pre">'R3c:R',</span> <span class="pre">'R3m',</span> <span class="pre">'R3m:H',</span> <span class="pre">'R3m:R'}</span></em><a class="reference external" href="https://github.com/materialsproject/pymatgen/blob/v2025.1.24/src/pymatgen/symmetry/groups.py"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pymatgen.symmetry.groups.SpaceGroup.SG_SYMBOLS" title="Link to this definition"></a></dt>
<dd></dd></dl>

<dl class="py attribute">
<dt class="sig sig-object py" id="pymatgen.symmetry.groups.SpaceGroup.SYMM_OPS">
<span class="sig-name descname"><span class="pre">SYMM_OPS</span></span><em class="property"><span class="w"> </span><span class="p"><span class="pre">=</span></span><span class="w"> </span><span class="pre">[{'hall':</span> <span class="pre">'</span> <span class="pre">P</span> <span class="pre">1',</span> <span class="pre">'hermann_mauguin':</span> <span class="pre">'P1',</span> <span class="pre">'hermann_mauguin_u':</span> <span class="pre">'P1',</span> <span class="pre">'ncsym':</span> <span class="pre">['x,y,z'],</span> <span class="pre">'number':</span> <span class="pre">1,</span> <span class="pre">'point_group':</span> <span class="pre">'1',</span> <span class="pre">'schoenflies':</span> <span class="pre">'C1^1',</span> <span class="pre">'short_h_m':</span> <span class="pre">'P1',</span> <span class="pre">'symops':</span> <span class="pre">['x,y,z'],</span> <span class="pre">'universal_h_m':</span> <span class="pre">'P1'},</span> <span class="pre">{'hall':</span> <span class="pre">'-P</span> <span class="pre">1',</span> <span class="pre">'hermann_mauguin':</span> <span class="pre">'P-1',</span> <span class="pre">'hermann_mauguin_u':</span> <span class="pre">'P-1',</span> <span class="pre">'ncsym':</span> <span class="pre">['x,y,z',</span> <span class="pre">'-x,-y,-z'],</span> <span class="pre">'number':</span> <span class="pre">2,</span> <span class="pre">'point_group':</span> <span class="pre">'-1',</span> <span class="pre">'schoenflies':</span> <span class="pre">'Ci^1',</span> <span class="pre">'short_h_m':</span> <span class="pre">'P-1',</span> <span class="pre">'symops':</span> <span class="pre">['x,y,z',</span> <span class="pre">'-x,-y,-z'],</span> <span class="pre">'universal_h_m':</span> <span class="pre">'P-1'},</span> <span class="pre">{'hall':</span> <span class="pre">'</span> <span class="pre">P</span> <span class="pre">2y',</span> <span class="pre">'hermann_mauguin':</span> <span class="pre">'P121',</span> <span class="pre">'hermann_mauguin_u':</span> <span class="pre">'P121',</span> <span class="pre">'ncsym':</span> <span class="pre">['x,y,z',</span> <span class="pre">'-x,y,-z'],</span> <span class="pre">'number':</span> <span class="pre">3,</span> <span class="pre">'point_group':</span> <span class="pre">'2',</span> <span class="pre">'schoenflies':</span> <span class="pre">'C2^1',</span> <span class="pre">'short_h_m':</span> <span class="pre">'P2',</span> <span class="pre">'symops':</span> <span class="pre">['x,y,z',</span> <span class="pre">'-x,y,-z'],</span> <span class="pre">'universal_h_m':</span> <span class="pre">'P121'},</span> <span class="pre">{'hall':</span> <span class="pre">'</span> <span class="pre">P</span> <span class="pre">2',</span> <span class="pre">'hermann_mauguin':</span> <span class="pre">'P112',</span> <span class="pre">'hermann_mauguin_u':</span> <span class="pre">'P112',</span> <span class="pre">'ncsym':</span> <span class="pre">['x,y,z',</span> <span class="pre">'-x,-y,z'],</span> <span class="pre">'number':</span> <span class="pre">3,</span> <span class="pre">'point_group':</span> <span class="pre">'2',</span> <span class="pre">'schoenflies':</span> <span class="pre">'C2^1',</span> <span class="pre">'short_h_m':</span> <span class="pre">'P2',</span> <span class="pre">'symops':</span> <span class="pre">['x,y,z',</span> <span class="pre">'-x,-y,z'],</span> <span class="pre">'universal_h_m':</span> <span class="pre">'P112'},</span> <span class="pre">{'hall':</span> <span class="pre">'</span> <span class="pre">P</span> <span class="pre">2x',</span> <span class="pre">'hermann_mauguin':</span> <span class="pre">'P211',</span> <span class="pre">'hermann_mauguin_u':</span> <span class="pre">'P211',</span> <span class="pre">'ncsym':</span> <span class="pre">['x,y,z',</span> <span class="pre">'x,-y,-z'],</span> <span class="pre">'number':</span> <span class="pre">3,</span> <span class="pre">'point_group':</span> <span class="pre">'2',</span> <span class="pre">'schoenflies':</span> <span class="pre">'C2^1',</span> <span class="pre">'short_h_m':</span> <span class="pre">'P2',</span> <span class="pre">'symops':</span> <span class="pre">['x,y,z',</span> <span class="pre">'x,-y,-z'],</span> <span class="pre">'universal_h_m':</span> <span class="pre">'P211'},</span> <span class="pre">{'hall':</span> <span class="pre">'</span> <span class="pre">P</span> <span class="pre">2yb',</span> <span class="pre">'hermann_mauguin':</span> <span class="pre">'P1211',</span> <span class="pre">'hermann_mauguin_u':</span> <span class="pre">'P12_11',</span> <span class="pre">'ncsym':</span> <span class="pre">['x,y,z',</span> <span class="pre">'-x,y+1/2,-z'],</span> <span class="pre">'number':</span> <span class="pre">4,</span> <span class="pre">'point_group':</span> <span class="pre">'2',</span> <span class="pre">'schoenflies':</span> <span class="pre">'C2^2',</span> <span class="pre">'short_h_m':</span> <span class="pre">'P2_1',</span> <span class="pre">'symops':</span> <span class="pre">['x,y,z',</span> <span class="pre">'-x,y+1/2,-z'],</span> <span class="pre">'universal_h_m':</span> <span class="pre">'P1211'},</span> <span class="pre">{'hall':</span> <span class="pre">'</span> <span class="pre">P</span> <span class="pre">2c',</span> <span class="pre">'hermann_mauguin':</span> <span class="pre">'P1121',</span> <span class="pre">'hermann_mauguin_u':</span> <span class="pre">'P112_1',</span> <span class="pre">'ncsym':</span> <span class="pre">['x,y,z',</span> <span class="pre">'-x,-y,z+1/2'],</span> <span class="pre">'number':</span> <span class="pre">4,</span> <span class="pre">'point_group':</span> <span class="pre">'2',</span> <span class="pre">'schoenflies':</span> <span class="pre">'C2^2',</span> <span class="pre">'short_h_m':</span> <span class="pre">'P2_1',</span> <span class="pre">'symops':</span> <span class="pre">['x,y,z',</span> <span class="pre">'-x,-y,z+1/2'],</span> <span class="pre">'universal_h_m':</span> <span class="pre">'P1121'},</span> <span class="pre">{'hall':</span> <span class="pre">'</span> <span class="pre">P</span> <span class="pre">2xa',</span> <span class="pre">'hermann_mauguin':</span> <span class="pre">'P2111',</span> <span class="pre">'hermann_mauguin_u':</span> <span class="pre">'P2_111',</span> <span class="pre">'ncsym':</span> <span class="pre">['x,y,z',</span> <span class="pre">'x+1/2,-y,-z'],</span> <span class="pre">'number':</span> <span class="pre">4,</span> <span class="pre">'point_group':</span> <span class="pre">'2',</span> <span class="pre">'schoenflies':</span> <span class="pre">'C2^2',</span> <span class="pre">'short_h_m':</span> <span class="pre">'P2_1',</span> <span class="pre">'symops':</span> <span class="pre">['x,y,z',</span> <span class="pre">'x+1/2,-y,-z'],</span> <span class="pre">'universal_h_m':</span> <span class="pre">'P2111'},</span> <span class="pre">{'hall':</span> <span class="pre">'</span> <span class="pre">C</span> <span class="pre">2y',</span> <span class="pre">'hermann_mauguin':</span> <span class="pre">'C121',</span> <span class="pre">'hermann_mauguin_u':</span> <span class="pre">'C121',</span> <span class="pre">'ncsym':</span> <span class="pre">['x,y,z',</span> <span class="pre">'-x,y,-z'],</span> <span class="pre">'number':</span> <span class="pre">5,</span> <span class="pre">'point_group':</span> <span class="pre">'2',</span> <span class="pre">'schoenflies':</span> <span class="pre">'C2^3',</span> <span class="pre">'short_h_m':</span> <span class="pre">'C2',</span> <span class="pre">'symops':</span> <span class="pre">['x,y,z',</span> <span class="pre">'-x,y,-z',</span> <span class="pre">'x+1/2,y+1/2,z',</span> <span class="pre">'-x+1/2,y+1/2,-z'],</span> <span class="pre">'universal_h_m':</span> <span class="pre">'C121'},</span> <span class="pre">{'hall':</span> <span class="pre">'</span> <span class="pre">A</span> <span class="pre">2y',</span> <span class="pre">'hermann_mauguin':</span> <span class="pre">'A121',</span> <span class="pre">'hermann_mauguin_u':</span> <span class="pre">'A121',</span> <span class="pre">'ncsym':</span> <span class="pre">['x,y,z',</span> <span class="pre">'-x,y,-z'],</span> <span class="pre">'number':</span> <span class="pre">5,</span> <span class="pre">'point_group':</span> <span class="pre">'2',</span> <span class="pre">'schoenflies':</span> <span class="pre">'C2^3',</span> <span class="pre">'short_h_m':</span> <span class="pre">'A2',</span> <span class="pre">'symops':</span> <span class="pre">['x,y,z',</span> <span class="pre">'-x,y,-z',</span> <span class="pre">'x,y+1/2,z+1/2',</span> <span class="pre">'-x,y+1/2,-z+1/2'],</span> <span class="pre">'universal_h_m':</span> <span class="pre">'A121'},</span> <span class="pre">{'hall':</span> <span class="pre">'</span> <span class="pre">I</span> <span class="pre">2y',</span> <span class="pre">'hermann_mauguin':</span> <span class="pre">'I121',</span> <span class="pre">'hermann_mauguin_u':</span> <span class="pre">'I121',</span> <span class="pre">'ncsym':</span> <span class="pre">['x,y,z',</span> <span class="pre">'-x,y,-z'],</span> <span class="pre">'number':</span> <span class="pre">5,</span> <span class="pre">'point_group':</span> <span class="pre">'2',</span> <span class="pre">'schoenflies':</span> <span class="pre">'C2^3',</span> <span class="pre">'short_h_m':</span> <span class="pre">'I2',</span> <span class="pre">'symops':</span> <span class="pre">['x,y,z',</span> <span class="pre">'-x,y,-z',</span> <span class="pre">'x+1/2,y+1/2,z+1/2',</span> <span class="pre">'-x+1/2,y+1/2,-z+1/2'],</span> <span class="pre">'universal_h_m':</span> <span class="pre">'I121'},</span> <span class="pre">{'hall':</span> <span class="pre">'</span> <span class="pre">A</span> <span class="pre">2',</span> <span class="pre">'hermann_mauguin':</span> <span class="pre">'A112',</span> <span class="pre">'hermann_mauguin_u':</span> <span class="pre">'A112',</span> <span class="pre">'ncsym':</span> <span class="pre">['x,y,z',</span> <span class="pre">'-x,-y,z'],</span> <span class="pre">'number':</span> <span class="pre">5,</span> <span class="pre">'point_group':</span> <span class="pre">'2',</span> <span class="pre">'schoenflies':</span> <span class="pre">'C2^3',</span> <span class="pre">'short_h_m':</span> <span class="pre">'A2',</span> <span class="pre">'symops':</span> <span class="pre">['x,y,z',</span> <span class="pre">'-x,-y,z',</span> <span class="pre">'x,y+1/2,z+1/2',</span> <span class="pre">'-x,-y+1/2,z+1/2'],</span> <span class="pre">'universal_h_m':</span> <span class="pre">'A112'},</span> <span class="pre">{'hall':</span> <span class="pre">'</span> <span class="pre">B</span> <span class="pre">2',</span> <span class="pre">'hermann_mauguin':</span> <span class="pre">'B112',</span> <span class="pre">'hermann_mauguin_u':</span> <span class="pre">'B112',</span> <span class="pre">'ncsym':</span> <span 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<span class="pre">'Imm2',</span> <span class="pre">'symops':</span> <span class="pre">['x,y,z',</span> <span class="pre">'-x+1/2,-y,z',</span> <span class="pre">'-x+1/2,y,z',</span> <span class="pre">'x,-y,z',</span> <span class="pre">'x+1/2,y+1/2,z+1/2',</span> <span class="pre">'-x,-y+1/2,z+1/2',</span> <span class="pre">'-x,y+1/2,z+1/2',</span> <span class="pre">'x+1/2,-y+1/2,z+1/2'],</span> <span class="pre">'universal_h_m':</span> <span class="pre">'Imm2(a-1/4,b,c+1/4)'},</span> <span class="pre">{'hall':</span> <span class="pre">'</span> <span class="pre">C</span> <span class="pre">2c</span> <span class="pre">-2</span> <span class="pre">(y-1/4,z,x)',</span> <span class="pre">'hermann_mauguin':</span> <span class="pre">'Cmc21',</span> <span class="pre">'hermann_mauguin_u':</span> <span class="pre">'Cmc2_1',</span> <span class="pre">'ncsym':</span> <span class="pre">['x,y,z',</span> <span class="pre">'x,y,-z',</span> <span class="pre">'-x,y+1/2,z+1/2',</span> <span class="pre">'-x,y+1/2,-z+1/2'],</span> <span class="pre">'number':</span> <span class="pre">36,</span> <span class="pre">'point_group':</span> <span class="pre">'mm2',</span> <span class="pre">'schoenflies':</span> <span class="pre">'C2v^12',</span> <span class="pre">'short_h_m':</span> <span class="pre">'Cmc2_1',</span> <span class="pre">'symops':</span> <span class="pre">['x,y,z',</span> <span class="pre">'-x+1/2,y+1/2,-z',</span> <span class="pre">'x,y,-z',</span> <span class="pre">'-x+1/2,y+1/2,z',</span> <span class="pre">'x+1/2,y,z+1/2',</span> <span class="pre">'-x,y+1/2,-z+1/2',</span> <span class="pre">'x+1/2,y,-z+1/2',</span> <span class="pre">'-x,y+1/2,z+1/2'],</span> <span class="pre">'universal_h_m':</span> <span class="pre">'Cmc21(b,c+1/4,a)'},</span> <span class="pre">{'hall':</span> <span class="pre">'</span> <span class="pre">A</span> <span class="pre">2</span> <span class="pre">-2a</span> <span class="pre">(y-1/4,z+1/4,x-1/4)',</span> <span class="pre">'hermann_mauguin':</span> <span class="pre">'Ama2',</span> <span class="pre">'hermann_mauguin_u':</span> <span class="pre">'Ama2',</span> <span class="pre">'ncsym':</span> <span class="pre">['x,y,z',</span> <span class="pre">'x,y,-z',</span> <span class="pre">'-x,y+1/2,z+1/2',</span> <span class="pre">'-x,y+1/2,-z+1/2'],</span> <span class="pre">'number':</span> <span class="pre">40,</span> <span class="pre">'point_group':</span> <span class="pre">'mm2',</span> <span class="pre">'schoenflies':</span> <span class="pre">'C2v^16',</span> <span class="pre">'short_h_m':</span> <span class="pre">'Ama2',</span> <span class="pre">'symops':</span> <span class="pre">['x,y,z',</span> <span class="pre">'-x+1/2,y,-z+1/2',</span> <span class="pre">'x,y,-z',</span> <span class="pre">'-x+1/2,y,z+1/2',</span> <span class="pre">'x+1/2,y+1/2,z',</span> <span class="pre">'-x,y+1/2,-z+1/2',</span> <span class="pre">'x+1/2,y+1/2,-z',</span> <span class="pre">'-x,y+1/2,z+1/2'],</span> <span class="pre">'universal_h_m':</span> <span class="pre">'Ama2(b+1/4,c+1/4,a-1/4)'},</span> <span class="pre">{'hall':</span> <span class="pre">'</span> <span class="pre">I</span> <span class="pre">2</span> <span class="pre">-2</span> <span class="pre">(y+1/4,z,x)',</span> <span class="pre">'hermann_mauguin':</span> <span class="pre">'Imm2',</span> <span class="pre">'hermann_mauguin_u':</span> <span class="pre">'Imm2',</span> <span class="pre">'ncsym':</span> <span class="pre">['x,y,z',</span> <span class="pre">'x,y,-z',</span> <span class="pre">'-x,y+1/2,z+1/2',</span> <span class="pre">'-x,y+1/2,-z+1/2'],</span> <span class="pre">'number':</span> <span class="pre">44,</span> <span class="pre">'point_group':</span> <span class="pre">'mm2',</span> <span class="pre">'schoenflies':</span> <span class="pre">'C2v^20',</span> <span class="pre">'short_h_m':</span> <span class="pre">'Imm2',</span> <span class="pre">'symops':</span> <span class="pre">['x,y,z',</span> <span class="pre">'-x+1/2,y,-z',</span> <span class="pre">'x,y,-z',</span> <span class="pre">'-x+1/2,y,z',</span> <span class="pre">'x+1/2,y+1/2,z+1/2',</span> <span class="pre">'-x,y+1/2,-z+1/2',</span> <span class="pre">'x+1/2,y+1/2,-z+1/2',</span> <span class="pre">'-x,y+1/2,z+1/2'],</span> <span class="pre">'universal_h_m':</span> <span class="pre">'Imm2(b,c-1/4,a)'},</span> <span class="pre">{'hall':</span> <span class="pre">'</span> <span class="pre">A</span> <span class="pre">2</span> <span class="pre">-2a</span> <span class="pre">(-x+1/4,z+1/4,y-1/4)',</span> <span class="pre">'hermann_mauguin':</span> <span class="pre">'Ama2',</span> <span class="pre">'hermann_mauguin_u':</span> <span class="pre">'Ama2',</span> <span class="pre">'ncsym':</span> <span class="pre">['x,y,z',</span> <span class="pre">'x+1/2,y+1/2,-z',</span> <span class="pre">'-x,y,z',</span> <span class="pre">'-x+1/2,y+1/2,-z'],</span> <span class="pre">'number':</span> <span class="pre">40,</span> <span class="pre">'point_group':</span> <span class="pre">'mm2',</span> <span class="pre">'schoenflies':</span> <span class="pre">'C2v^16',</span> <span class="pre">'short_h_m':</span> <span class="pre">'Ama2',</span> <span class="pre">'symops':</span> <span class="pre">['x,y,z',</span> <span class="pre">'-x+1/2,y,-z+1/2',</span> <span class="pre">'-x,y,z',</span> <span class="pre">'x+1/2,y,-z+1/2',</span> <span class="pre">'x,y+1/2,z+1/2',</span> <span class="pre">'-x+1/2,y+1/2,-z',</span> <span class="pre">'-x,y+1/2,z+1/2',</span> <span class="pre">'x+1/2,y+1/2,-z'],</span> <span class="pre">'universal_h_m':</span> <span class="pre">'Ama2(-a+1/4,c+1/4,b-1/4)'},</span> <span class="pre">{'hall':</span> <span class="pre">'</span> <span class="pre">C</span> <span class="pre">2c</span> <span class="pre">-2</span> <span class="pre">(-x,z,y-1/4)',</span> <span class="pre">'hermann_mauguin':</span> <span class="pre">'Cmc21',</span> <span class="pre">'hermann_mauguin_u':</span> <span class="pre">'Cmc2_1',</span> <span class="pre">'ncsym':</span> <span class="pre">['x,y,z',</span> <span class="pre">'x+1/2,y+1/2,-z',</span> <span class="pre">'-x,y,z',</span> <span class="pre">'-x+1/2,y+1/2,-z'],</span> <span class="pre">'number':</span> <span class="pre">36,</span> <span class="pre">'point_group':</span> <span class="pre">'mm2',</span> <span class="pre">'schoenflies':</span> <span class="pre">'C2v^12',</span> <span class="pre">'short_h_m':</span> <span class="pre">'Cmc2_1',</span> <span class="pre">'symops':</span> <span class="pre">['x,y,z',</span> <span class="pre">'-x,y+1/2,-z+1/2',</span> <span class="pre">'-x,y,z',</span> <span class="pre">'x,y+1/2,-z+1/2',</span> <span class="pre">'x+1/2,y,z+1/2',</span> <span class="pre">'-x+1/2,y+1/2,-z',</span> <span class="pre">'-x+1/2,y,z+1/2',</span> <span class="pre">'x+1/2,y+1/2,-z'],</span> <span class="pre">'universal_h_m':</span> <span class="pre">'Cmc21(-a,c+1/4,b)'},</span> <span class="pre">{'hall':</span> <span class="pre">'</span> <span class="pre">I</span> <span class="pre">2</span> <span class="pre">-2</span> <span class="pre">(y,z-1/4,x+1/4)',</span> <span class="pre">'hermann_mauguin':</span> <span class="pre">'Imm2',</span> <span class="pre">'hermann_mauguin_u':</span> <span class="pre">'Imm2',</span> <span class="pre">'ncsym':</span> <span class="pre">['x,y,z',</span> <span class="pre">'x+1/2,y+1/2,-z',</span> <span class="pre">'-x,y,z',</span> <span class="pre">'-x+1/2,y+1/2,-z'],</span> <span class="pre">'number':</span> <span class="pre">44,</span> <span class="pre">'point_group':</span> <span class="pre">'mm2',</span> <span class="pre">'schoenflies':</span> <span class="pre">'C2v^20',</span> <span class="pre">'short_h_m':</span> <span class="pre">'Imm2',</span> <span class="pre">'symops':</span> <span class="pre">['x,y,z',</span> <span class="pre">'-x,y,-z+1/2',</span> <span class="pre">'x,y,-z+1/2',</span> <span class="pre">'-x,y,z',</span> <span class="pre">'x+1/2,y+1/2,z+1/2',</span> <span class="pre">'-x+1/2,y+1/2,-z',</span> <span class="pre">'x+1/2,y+1/2,-z',</span> <span class="pre">'-x+1/2,y+1/2,z+1/2'],</span> <span class="pre">'universal_h_m':</span> <span class="pre">'Imm2(b-1/4,c,a+1/4)'},</span> <span class="pre">{'hall':</span> <span class="pre">'</span> <span class="pre">A</span> <span class="pre">2</span> <span class="pre">-2a</span> <span class="pre">(x,y-1/4,z+1/4)',</span> <span class="pre">'hermann_mauguin':</span> <span class="pre">'Ama2',</span> <span class="pre">'hermann_mauguin_u':</span> <span class="pre">'Ama2',</span> <span class="pre">'ncsym':</span> <span class="pre">['x,y,z',</span> <span class="pre">'-x,-y,z+1/2',</span> <span class="pre">'-x+1/2,y+1/2,z+1/2',</span> <span class="pre">'x+1/2,-y+1/2,z'],</span> <span class="pre">'number':</span> <span class="pre">40,</span> <span class="pre">'point_group':</span> <span class="pre">'mm2',</span> <span class="pre">'schoenflies':</span> <span class="pre">'C2v^16',</span> <span class="pre">'short_h_m':</span> <span class="pre">'Ama2',</span> <span class="pre">'symops':</span> <span class="pre">['x,y,z',</span> <span class="pre">'-x,-y+1/2,z',</span> <span class="pre">'-x+1/2,y,z',</span> <span class="pre">'x+1/2,-y+1/2,z',</span> <span class="pre">'x,y+1/2,z+1/2',</span> <span class="pre">'-x,-y,z+1/2',</span> <span class="pre">'-x+1/2,y+1/2,z+1/2',</span> <span class="pre">'x+1/2,-y,z+1/2'],</span> <span class="pre">'universal_h_m':</span> <span class="pre">'Ama2(a,b+1/4,c-1/4)'},</span> <span class="pre">{'hall':</span> <span class="pre">'</span> <span class="pre">A</span> <span class="pre">2</span> <span class="pre">-2a</span> <span class="pre">(y-1/4,-x,z+1/4)',</span> <span class="pre">'hermann_mauguin':</span> <span class="pre">'Ama2',</span> <span class="pre">'hermann_mauguin_u':</span> <span class="pre">'Ama2',</span> <span class="pre">'ncsym':</span> <span class="pre">['x,y,z',</span> <span 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class="pre">-2a</span> <span class="pre">(y-1/4,z+1/4,x)',</span> <span class="pre">'hermann_mauguin':</span> <span class="pre">'Ama2',</span> <span class="pre">'hermann_mauguin_u':</span> <span class="pre">'Ama2',</span> <span class="pre">'ncsym':</span> <span class="pre">['x,y,z',</span> <span class="pre">'x+1/2,y+1/2,-z+1/2',</span> <span class="pre">'-x+1/2,y,z+1/2',</span> <span class="pre">'-x,y+1/2,-z'],</span> <span class="pre">'number':</span> <span class="pre">40,</span> <span class="pre">'point_group':</span> <span class="pre">'mm2',</span> <span class="pre">'schoenflies':</span> <span class="pre">'C2v^16',</span> <span class="pre">'short_h_m':</span> <span class="pre">'Ama2',</span> <span class="pre">'symops':</span> <span class="pre">['x,y,z',</span> <span class="pre">'-x+1/2,y,-z',</span> <span class="pre">'x,y,-z+1/2',</span> <span class="pre">'-x+1/2,y,z+1/2',</span> <span class="pre">'x+1/2,y+1/2,z',</span> <span class="pre">'-x,y+1/2,-z',</span> <span class="pre">'x+1/2,y+1/2,-z+1/2',</span> <span class="pre">'-x,y+1/2,z+1/2'],</span> <span class="pre">'universal_h_m':</span> <span class="pre">'Ama2(b,c+1/4,a-1/4)'},</span> <span class="pre">{'hall':</span> <span class="pre">'</span> <span class="pre">A</span> <span class="pre">2</span> <span class="pre">-2a</span> <span class="pre">(-x,z+1/4,y-1/4)',</span> <span class="pre">'hermann_mauguin':</span> <span class="pre">'Ama2',</span> <span class="pre">'hermann_mauguin_u':</span> <span class="pre">'Ama2',</span> <span class="pre">'ncsym':</span> <span class="pre">['x,y,z',</span> <span class="pre">'x+1/2,y,-z+1/2',</span> <span class="pre">'-x+1/2,y+1/2,z+1/2',</span> <span class="pre">'-x,y+1/2,-z'],</span> <span class="pre">'number':</span> <span class="pre">40,</span> <span class="pre">'point_group':</span> <span class="pre">'mm2',</span> <span class="pre">'schoenflies':</span> <span class="pre">'C2v^16',</span> <span class="pre">'short_h_m':</span> <span class="pre">'Ama2',</span> <span class="pre">'symops':</span> <span class="pre">['x,y,z',</span> <span class="pre">'-x,y,-z+1/2',</span> <span class="pre">'-x+1/2,y,z',</span> <span class="pre">'x+1/2,y,-z+1/2',</span> <span class="pre">'x,y+1/2,z+1/2',</span> <span class="pre">'-x,y+1/2,-z',</span> <span class="pre">'-x+1/2,y+1/2,z+1/2',</span> <span class="pre">'x+1/2,y+1/2,-z'],</span> <span class="pre">'universal_h_m':</span> <span class="pre">'Ama2(-a,c+1/4,b-1/4)'},</span> <span class="pre">{'hall':</span> <span class="pre">'-C</span> <span class="pre">2</span> <span class="pre">2c</span> <span class="pre">(z+1/4,x,y)',</span> <span class="pre">'hermann_mauguin':</span> <span class="pre">'Cccm',</span> <span class="pre">'hermann_mauguin_u':</span> <span class="pre">'Cccm',</span> <span class="pre">'ncsym':</span> <span class="pre">['x,y,z',</span> <span class="pre">'-x,-y,z',</span> <span class="pre">'x,-y,-z',</span> <span class="pre">'-x,y,-z',</span> <span 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class="pre">(1/2*z,x,y)',</span> <span class="pre">'hermann_mauguin':</span> <span class="pre">'Cmm2',</span> <span class="pre">'hermann_mauguin_u':</span> <span class="pre">'Cmm2',</span> <span class="pre">'ncsym':</span> <span class="pre">['x,y,z',</span> <span class="pre">'x,-y,z',</span> <span class="pre">'x,y,-z',</span> <span class="pre">'x,-y,-z'],</span> <span class="pre">'number':</span> <span class="pre">35,</span> <span class="pre">'point_group':</span> <span class="pre">'mm2',</span> <span class="pre">'schoenflies':</span> <span class="pre">'C2v^11',</span> <span class="pre">'short_h_m':</span> <span class="pre">'Cmm2',</span> <span class="pre">'symops':</span> <span class="pre">['x,y,z',</span> <span class="pre">'x,-y,z',</span> <span class="pre">'x,y,-z',</span> <span class="pre">'x,-y,-z',</span> <span class="pre">'x,y+1/2,z+1/2',</span> <span class="pre">'x,-y+1/2,z+1/2',</span> <span class="pre">'x,y+1/2,-z+1/2',</span> <span class="pre">'x,-y+1/2,-z+1/2',</span> <span class="pre">'x+1/2,y,z',</span> <span class="pre">'x+1/2,-y,z',</span> <span class="pre">'x+1/2,y,-z',</span> <span class="pre">'x+1/2,-y,-z',</span> <span class="pre">'x+1/2,y+1/2,z+1/2',</span> <span class="pre">'x+1/2,-y+1/2,z+1/2',</span> <span class="pre">'x+1/2,y+1/2,-z+1/2',</span> <span class="pre">'x+1/2,-y+1/2,-z+1/2'],</span> <span class="pre">'universal_h_m':</span> <span class="pre">'Cmm2(2*c,a,b)'},</span> <span class="pre">{'hall':</span> <span class="pre">'-P</span> <span class="pre">2ybc</span> <span class="pre">(-1/4*x+1/2*z,1/2*x,y)',</span> <span class="pre">'hermann_mauguin':</span> <span class="pre">'P121/c1',</span> <span class="pre">'hermann_mauguin_u':</span> <span class="pre">'P12_1/c1',</span> <span class="pre">'ncsym':</span> <span class="pre">['x,y,z',</span> <span class="pre">'-x+1/4,-y,z+1/2',</span> <span class="pre">'-x,-y,-z',</span> <span class="pre">'x-1/4,y,-z-1/2'],</span> <span class="pre">'number':</span> <span class="pre">14,</span> <span class="pre">'point_group':</span> <span class="pre">'2/m',</span> <span class="pre">'schoenflies':</span> <span class="pre">'C2h^5',</span> <span class="pre">'short_h_m':</span> <span class="pre">'P2_1/c',</span> <span class="pre">'symops':</span> <span class="pre">['x,y,z',</span> <span class="pre">'-x+1/4,-y,z+1/2',</span> <span class="pre">'-x,-y,-z',</span> <span class="pre">'x-1/4,y,-z-1/2',</span> <span class="pre">'x+3/4,y+1/2,z',</span> <span class="pre">'-x+1,-y+1/2,z+1/2',</span> <span class="pre">'-x+3/4,-y+1/2,-z',</span> <span class="pre">'x+1/2,y+1/2,-z-1/2',</span> <span class="pre">'x+1/4,y+1/2,z',</span> <span class="pre">'-x+1/2,-y+1/2,z+1/2',</span> <span class="pre">'-x+1/4,-y+1/2,-z',</span> <span class="pre">'x,y+1/2,-z-1/2',</span> <span class="pre">'x+1/2,y,z',</span> <span class="pre">'-x+3/4,-y,z+1/2',</span> <span class="pre">'-x+1/2,-y,-z',</span> <span class="pre">'x+1/4,y,-z-1/2'],</span> <span class="pre">'universal_h_m':</span> <span class="pre">'P121/c1(2*c,2*a+c,b)'},</span> <span class="pre">{'hall':</span> <span class="pre">'-P</span> <span class="pre">2a</span> <span class="pre">2a</span> <span class="pre">(1/2*y,z,x)',</span> <span class="pre">'hermann_mauguin':</span> <span class="pre">'Pmma',</span> <span class="pre">'hermann_mauguin_u':</span> <span class="pre">'Pmma',</span> <span class="pre">'ncsym':</span> <span class="pre">['x,y,z',</span> <span class="pre">'-x,y,z',</span> <span class="pre">'x,y,-z+1/2',</span> <span class="pre">'-x,y,-z+1/2',</span> <span class="pre">'-x,-y,-z',</span> <span class="pre">'x,-y,-z',</span> <span class="pre">'-x,-y,z-1/2',</span> <span class="pre">'x,-y,z-1/2'],</span> <span class="pre">'number':</span> <span class="pre">51,</span> <span class="pre">'point_group':</span> <span class="pre">'mmm',</span> <span class="pre">'schoenflies':</span> <span class="pre">'D2h^5',</span> <span class="pre">'short_h_m':</span> <span class="pre">'Pmma',</span> <span class="pre">'symops':</span> <span class="pre">['x,y,z',</span> <span class="pre">'-x,y,z',</span> <span class="pre">'x,y,-z+1/2',</span> <span class="pre">'-x,y,-z+1/2',</span> <span class="pre">'-x,-y,-z',</span> <span class="pre">'x,-y,-z',</span> <span class="pre">'-x,-y,z-1/2',</span> <span class="pre">'x,-y,z-1/2',</span> <span class="pre">'x+1/2,y,z',</span> <span class="pre">'-x+1/2,y,z',</span> <span class="pre">'x+1/2,y,-z+1/2',</span> <span class="pre">'-x+1/2,y,-z+1/2',</span> <span class="pre">'-x+1/2,-y,-z',</span> <span class="pre">'x+1/2,-y,-z',</span> <span class="pre">'-x+1/2,-y,z-1/2',</span> <span class="pre">'x+1/2,-y,z-1/2'],</span> <span class="pre">'universal_h_m':</span> <span class="pre">'Pmma(2*b,c,a)'},</span> <span class="pre">{'hall':</span> <span class="pre">'-P</span> <span class="pre">2a</span> <span class="pre">2a</span> <span class="pre">(1/2*y,z+1/3,x-1/4)',</span> <span class="pre">'hermann_mauguin':</span> <span class="pre">'Pmma',</span> <span class="pre">'hermann_mauguin_u':</span> <span class="pre">'Pmma',</span> <span class="pre">'ncsym':</span> <span class="pre">['x,y,z',</span> <span class="pre">'-x,y,z',</span> <span class="pre">'x,y,-z',</span> <span class="pre">'-x,y,-z',</span> <span class="pre">'x+1/2,y,z',</span> <span class="pre">'-x+1/2,y,z',</span> <span class="pre">'x+1/2,y,-z',</span> <span class="pre">'-x+1/2,y,-z'],</span> <span class="pre">'number':</span> <span class="pre">51,</span> <span class="pre">'point_group':</span> <span class="pre">'mmm',</span> <span class="pre">'schoenflies':</span> <span class="pre">'D2h^5',</span> <span class="pre">'short_h_m':</span> <span class="pre">'Pmma',</span> <span class="pre">'symops':</span> <span class="pre">['x,y,z',</span> <span class="pre">'-x,y,z',</span> <span class="pre">'x,y,-z',</span> <span class="pre">'-x,y,-z',</span> <span class="pre">'x+1/2,y,z',</span> <span class="pre">'-x+1/2,y,z',</span> <span class="pre">'x+1/2,y,-z',</span> <span class="pre">'-x+1/2,y,-z',</span> <span class="pre">'-x,-y+2/3,-z+1/2',</span> <span class="pre">'x,-y+2/3,-z+1/2',</span> <span class="pre">'-x,-y+2/3,z+1/2',</span> <span class="pre">'x,-y+2/3,z+1/2',</span> <span class="pre">'-x+1/2,-y+2/3,-z+1/2',</span> <span class="pre">'x+1/2,-y+2/3,-z+1/2',</span> <span class="pre">'-x+1/2,-y+2/3,z+1/2',</span> <span class="pre">'x+1/2,-y+2/3,z+1/2'],</span> <span class="pre">'universal_h_m':</span> <span class="pre">'Pmma(2*b+1/4,c,a-1/3)'},</span> <span class="pre">{'hall':</span> <span class="pre">'-P</span> <span class="pre">2yc</span> <span class="pre">(x,1/2*y,z)',</span> <span class="pre">'hermann_mauguin':</span> <span class="pre">'P12/c1',</span> <span class="pre">'hermann_mauguin_u':</span> <span class="pre">'P12/c1',</span> <span class="pre">'ncsym':</span> <span class="pre">['x,y,z',</span> <span class="pre">'-x,y,-z+1/2',</span> <span class="pre">'x,y+1/2,z',</span> <span class="pre">'-x,y+1/2,-z+1/2'],</span> <span class="pre">'number':</span> <span class="pre">13,</span> <span class="pre">'point_group':</span> <span class="pre">'2/m',</span> <span class="pre">'schoenflies':</span> <span class="pre">'C2h^4',</span> <span class="pre">'short_h_m':</span> <span class="pre">'P2/c',</span> <span class="pre">'symops':</span> <span class="pre">['x,y,z',</span> <span class="pre">'-x,y,-z+1/2',</span> <span class="pre">'x,y+1/2,z',</span> <span class="pre">'-x,y+1/2,-z+1/2',</span> <span class="pre">'-x,-y,-z',</span> <span class="pre">'x,-y,z+1/2',</span> <span class="pre">'-x,-y+1/2,-z',</span> <span class="pre">'x,-y+1/2,z+1/2'],</span> <span class="pre">'universal_h_m':</span> <span class="pre">'P12/c1(a,2*b,c)'},</span> <span class="pre">{'hall':</span> <span class="pre">'-P</span> <span class="pre">2</span> <span class="pre">2</span> <span class="pre">(1/2*x,1/2*y,z)',</span> <span class="pre">'hermann_mauguin':</span> <span class="pre">'Pmmm',</span> <span class="pre">'hermann_mauguin_u':</span> <span class="pre">'Pmmm',</span> <span class="pre">'ncsym':</span> <span class="pre">['x,y,z',</span> <span class="pre">'-x,y,z',</span> <span class="pre">'x,-y,z',</span> <span class="pre">'-x,-y,z',</span> <span class="pre">'x+1/2,y,z',</span> <span class="pre">'-x+1/2,y,z',</span> <span class="pre">'x+1/2,-y,z',</span> <span class="pre">'-x+1/2,-y,z'],</span> <span class="pre">'number':</span> <span class="pre">47,</span> <span class="pre">'point_group':</span> <span class="pre">'mmm',</span> <span class="pre">'schoenflies':</span> <span class="pre">'D2h^1',</span> <span class="pre">'short_h_m':</span> <span class="pre">'Pmmm',</span> <span class="pre">'symops':</span> <span class="pre">['x,y,z',</span> <span class="pre">'-x,y,z',</span> <span class="pre">'x,-y,z',</span> <span class="pre">'-x,-y,z',</span> <span class="pre">'x+1/2,y,z',</span> <span class="pre">'-x+1/2,y,z',</span> <span class="pre">'x+1/2,-y,z',</span> <span class="pre">'-x+1/2,-y,z',</span> <span class="pre">'x,y+1/2,z',</span> <span class="pre">'-x,y+1/2,z',</span> <span class="pre">'x,-y+1/2,z',</span> <span class="pre">'-x,-y+1/2,z',</span> <span class="pre">'x+1/2,y+1/2,z',</span> <span class="pre">'-x+1/2,y+1/2,z',</span> <span class="pre">'x+1/2,-y+1/2,z',</span> <span class="pre">'-x+1/2,-y+1/2,z',</span> <span class="pre">'-x,-y,-z',</span> <span class="pre">'x,-y,-z',</span> <span class="pre">'-x,y,-z',</span> <span class="pre">'x,y,-z',</span> <span class="pre">'-x+1/2,-y,-z',</span> <span class="pre">'x+1/2,-y,-z',</span> <span class="pre">'-x+1/2,y,-z',</span> <span class="pre">'x+1/2,y,-z',</span> <span class="pre">'-x,-y+1/2,-z',</span> <span class="pre">'x,-y+1/2,-z',</span> <span class="pre">'-x,y+1/2,-z',</span> <span class="pre">'x,y+1/2,-z',</span> <span class="pre">'-x+1/2,-y+1/2,-z',</span> <span class="pre">'x+1/2,-y+1/2,-z',</span> <span class="pre">'-x+1/2,y+1/2,-z',</span> <span class="pre">'x+1/2,y+1/2,-z'],</span> <span class="pre">'universal_h_m':</span> <span class="pre">'Pmmm(2*a,2*b,c)'},</span> <span class="pre">{'hall':</span> <span class="pre">'</span> <span class="pre">P</span> <span class="pre">2yb</span> <span class="pre">(x+1/4,y,z)',</span> <span class="pre">'hermann_mauguin':</span> <span class="pre">'P1211',</span> <span class="pre">'hermann_mauguin_u':</span> <span class="pre">'P12_11',</span> <span class="pre">'ncsym':</span> <span class="pre">['x,y,z',</span> <span class="pre">'-x+1/2,y+1/2,-z'],</span> <span class="pre">'number':</span> <span class="pre">4,</span> <span class="pre">'point_group':</span> <span class="pre">'2',</span> <span class="pre">'schoenflies':</span> <span class="pre">'C2^2',</span> <span class="pre">'short_h_m':</span> <span class="pre">'P2_1',</span> <span class="pre">'symops':</span> <span class="pre">['x,y,z',</span> <span class="pre">'-x+1/2,y+1/2,-z'],</span> <span class="pre">'universal_h_m':</span> <span class="pre">'P1211(a-1/4,b,c)'},</span> <span class="pre">{'hall':</span> <span class="pre">'-P</span> <span class="pre">2ac</span> <span class="pre">2n</span> <span class="pre">(z,x,y+1/4)',</span> <span class="pre">'hermann_mauguin':</span> <span class="pre">'Pnma',</span> <span class="pre">'hermann_mauguin_u':</span> <span class="pre">'Pnma',</span> <span class="pre">'ncsym':</span> <span class="pre">['x,y,z',</span> <span class="pre">'-x+1/2,y+1/2,-z',</span> <span class="pre">'-x,-y,z+1/2',</span> <span class="pre">'x+1/2,-y+1/2,-z+1/2',</span> <span class="pre">'-x,-y,-z+1/2',</span> <span class="pre">'x+1/2,-y+1/2,z+1/2',</span> <span class="pre">'x,y,-z',</span> <span class="pre">'-x+1/2,y+1/2,z'],</span> <span class="pre">'number':</span> <span class="pre">62,</span> <span class="pre">'point_group':</span> <span class="pre">'mmm',</span> <span class="pre">'schoenflies':</span> <span class="pre">'D2h^16',</span> <span class="pre">'short_h_m':</span> <span class="pre">'Pnma',</span> <span class="pre">'symops':</span> <span class="pre">['x,y,z',</span> <span class="pre">'-x+1/2,y+1/2,-z',</span> <span class="pre">'-x,-y,z+1/2',</span> <span class="pre">'x+1/2,-y+1/2,-z+1/2',</span> <span class="pre">'-x,-y,-z+1/2',</span> <span class="pre">'x+1/2,-y+1/2,z+1/2',</span> <span class="pre">'x,y,-z',</span> <span class="pre">'-x+1/2,y+1/2,z'],</span> <span class="pre">'universal_h_m':</span> <span class="pre">'Pnma(c,a-1/4,b)'}]</span></em><a class="reference external" href="https://github.com/materialsproject/pymatgen/blob/v2025.1.24/src/pymatgen/symmetry/groups.py"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pymatgen.symmetry.groups.SpaceGroup.SYMM_OPS" title="Link to this definition"></a></dt>
<dd></dd></dl>

<dl class="py attribute">
<dt class="sig sig-object py" id="pymatgen.symmetry.groups.SpaceGroup.abbrev_sg_mapping">
<span class="sig-name descname"><span class="pre">abbrev_sg_mapping</span></span><em class="property"><span class="w"> </span><span class="p"><span class="pre">=</span></span><span class="w"> </span><span class="pre">{'C2':</span> <span class="pre">'C121',</span> <span class="pre">'C2/c':</span> <span class="pre">'C12/c1',</span> <span class="pre">'C2/m':</span> <span class="pre">'C12/m1',</span> <span class="pre">'Cc':</span> <span class="pre">'C1c1',</span> <span class="pre">'Cm':</span> <span class="pre">'C1m1',</span> <span class="pre">'P2':</span> <span class="pre">'P121',</span> <span class="pre">'P2/c':</span> <span class="pre">'P12/c1',</span> <span class="pre">'P2/m':</span> <span class="pre">'P12/m1',</span> <span class="pre">'P2_1':</span> <span class="pre">'P12_11',</span> <span class="pre">'P2_1/c':</span> <span class="pre">'P12_1/c1',</span> <span class="pre">'P2_1/m':</span> <span class="pre">'P12_1/m1',</span> <span class="pre">'Pc':</span> <span class="pre">'P1c1',</span> <span class="pre">'Pm':</span> <span class="pre">'P1m1'}</span></em><a class="reference external" href="https://github.com/materialsproject/pymatgen/blob/v2025.1.24/src/pymatgen/symmetry/groups.py"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pymatgen.symmetry.groups.SpaceGroup.abbrev_sg_mapping" title="Link to this definition"></a></dt>
<dd></dd></dl>

<dl class="py property">
<dt class="sig sig-object py" id="pymatgen.symmetry.groups.SpaceGroup.crystal_system">
<em class="property"><span class="pre">property</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">crystal_system</span></span><em class="property"><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="pre">CrystalSystem</span></em><a class="reference external" href="https://github.com/materialsproject/pymatgen/blob/v2025.1.24/src/pymatgen/symmetry/groups.py"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pymatgen.symmetry.groups.SpaceGroup.crystal_system" title="Link to this definition"></a></dt>
<dd><p>Returns:
str: Crystal system of the space group, e.g. cubic, hexagonal, etc.</p>
</dd></dl>

<dl class="py method">
<dt class="sig sig-object py" id="pymatgen.symmetry.groups.SpaceGroup.from_int_number">
<em class="property"><span class="pre">classmethod</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">from_int_number</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">int_number</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">int</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">hexagonal</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">bool</span></span><span class="w"> </span><span class="o"><span class="pre">=</span></span><span class="w"> </span><span class="default_value"><span class="pre">True</span></span></em><span class="sig-paren">)</span> <span class="sig-return"><span class="sig-return-icon">&#x2192;</span> <span class="sig-return-typehint"><span class="pre">Self</span></span></span><a class="reference external" href="https://github.com/materialsproject/pymatgen/blob/v2025.1.24/src/pymatgen/core/../symmetry/groups.py#L663-L683"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pymatgen.symmetry.groups.SpaceGroup.from_int_number" title="Link to this definition"></a></dt>
<dd><p>Obtains a SpaceGroup from its international number.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>int_number</strong> (<em>int</em>) – International number.</p></li>
<li><p><strong>hexagonal</strong> (<em>bool</em>) – For rhombohedral groups, whether to return the
hexagonal setting (default) or rhombohedral setting.</p></li>
</ul>
</dd>
<dt class="field-even">Raises<span class="colon">:</span></dt>
<dd class="field-even"><p><strong>ValueError</strong> – If the international number is not valid, i.e. not between 1 and 230 inclusive.</p>
</dd>
<dt class="field-odd">Returns<span class="colon">:</span></dt>
<dd class="field-odd"><p>object with the given international number.</p>
</dd>
<dt class="field-even">Return type<span class="colon">:</span></dt>
<dd class="field-even"><p><a class="reference internal" href="#pymatgen.symmetry.groups.SpaceGroup" title="pymatgen.symmetry.groups.SpaceGroup">SpaceGroup</a></p>
</dd>
</dl>
</dd></dl>

<dl class="py attribute">
<dt class="sig sig-object py" id="pymatgen.symmetry.groups.SpaceGroup.full_sg_mapping">
<span class="sig-name descname"><span class="pre">full_sg_mapping</span></span><em class="property"><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="pre">ClassVar</span><span class="p"><span class="pre">[</span></span><span class="pre">dict</span><span class="p"><span class="pre">[</span></span><span class="pre">str</span><span class="p"><span class="pre">,</span></span><span class="w"> </span><span class="pre">str</span><span class="p"><span class="pre">]</span></span><span class="p"><span class="pre">]</span></span></em><em class="property"><span class="w"> </span><span class="p"><span class="pre">=</span></span><span class="w"> </span><span class="pre">{'Aea2':</span> <span class="pre">'Aea2',</span> <span class="pre">'Aem2':</span> <span class="pre">'Aem2',</span> <span class="pre">'Ama2':</span> <span class="pre">'Ama2',</span> <span class="pre">'Amm2':</span> <span class="pre">'Amm2',</span> <span class="pre">'C12/c1':</span> <span class="pre">'C12/c1',</span> <span class="pre">'C12/m1':</span> <span class="pre">'C12/m1',</span> <span class="pre">'C121':</span> <span class="pre">'C121',</span> <span class="pre">'C1c1':</span> <span class="pre">'C1c1',</span> <span class="pre">'C1m1':</span> <span class="pre">'C1m1',</span> <span class="pre">'C2/c2/c2/e':</span> <span class="pre">'Ccce',</span> <span class="pre">'C2/c2/c2/m':</span> <span class="pre">'Cccm',</span> <span class="pre">'C2/m2/c2_1/e':</span> <span class="pre">'Cmce',</span> <span class="pre">'C2/m2/c2_1/m':</span> <span class="pre">'Cmcm',</span> <span class="pre">'C2/m2/m2/e':</span> <span class="pre">'Cmme',</span> <span class="pre">'C2/m2/m2/m':</span> <span class="pre">'Cmmm',</span> <span class="pre">'C222':</span> <span class="pre">'C222',</span> <span class="pre">'C222_1':</span> <span class="pre">'C222_1',</span> <span class="pre">'Ccc2':</span> <span class="pre">'Ccc2',</span> <span class="pre">'Cmc2_1':</span> <span class="pre">'Cmc2_1',</span> <span class="pre">'Cmm2':</span> <span class="pre">'Cmm2',</span> <span class="pre">'F-43c':</span> <span class="pre">'F-43c',</span> <span class="pre">'F-43m':</span> <span class="pre">'F-43m',</span> <span class="pre">'F2/d-3':</span> <span class="pre">'Fd-3',</span> <span class="pre">'F2/d2/d2/d':</span> <span class="pre">'Fddd',</span> <span class="pre">'F2/m-3':</span> <span class="pre">'Fm-3',</span> <span class="pre">'F2/m2/m2/m':</span> <span class="pre">'Fmmm',</span> <span class="pre">'F222':</span> <span class="pre">'F222',</span> <span class="pre">'F23':</span> <span class="pre">'F23',</span> <span class="pre">'F4/m-32/c':</span> <span class="pre">'Fm-3c',</span> <span class="pre">'F4/m-32/m':</span> <span class="pre">'Fm-3m',</span> <span class="pre">'F432':</span> <span class="pre">'F432',</span> <span class="pre">'F4_1/d-32/c':</span> <span class="pre">'Fd-3c',</span> <span class="pre">'F4_1/d-32/m':</span> <span class="pre">'Fd-3m',</span> <span class="pre">'F4_132':</span> <span class="pre">'F4_132',</span> <span class="pre">'Fdd2':</span> <span class="pre">'Fdd2',</span> <span class="pre">'Fmm2':</span> <span class="pre">'Fmm2',</span> <span class="pre">'I-4':</span> <span class="pre">'I-4',</span> <span class="pre">'I-42d':</span> <span class="pre">'I-42d',</span> <span class="pre">'I-42m':</span> <span class="pre">'I-42m',</span> <span class="pre">'I-43d':</span> <span class="pre">'I-43d',</span> <span class="pre">'I-43m':</span> <span class="pre">'I-43m',</span> <span class="pre">'I-4c2':</span> <span class="pre">'I-4c2',</span> <span class="pre">'I-4m2':</span> <span class="pre">'I-4m2',</span> <span class="pre">'I2/b2/a2/m':</span> <span class="pre">'Ibam',</span> <span class="pre">'I2/m-3':</span> <span class="pre">'Im-3',</span> <span class="pre">'I2/m2/m2/m':</span> <span class="pre">'Immm',</span> <span class="pre">'I222':</span> <span class="pre">'I222',</span> <span class="pre">'I23':</span> <span class="pre">'I23',</span> <span class="pre">'I2_1/a-3':</span> <span class="pre">'Ia-3',</span> <span class="pre">'I2_1/b2_1/c2_1/a':</span> <span class="pre">'Ibca',</span> <span class="pre">'I2_1/m2_1/m2_1/a':</span> <span class="pre">'Imma',</span> <span class="pre">'I2_12_12_1':</span> <span class="pre">'I2_12_12_1',</span> <span class="pre">'I2_13':</span> <span class="pre">'I2_13',</span> <span class="pre">'I4':</span> <span class="pre">'I4',</span> <span class="pre">'I4/m':</span> <span class="pre">'I4/m',</span> <span class="pre">'I4/m-32/m':</span> <span class="pre">'Im-3m',</span> <span class="pre">'I4/m2/c2/m':</span> <span class="pre">'I4/mcm',</span> <span class="pre">'I4/m2/m2/m':</span> <span class="pre">'I4/mmm',</span> <span class="pre">'I422':</span> <span class="pre">'I422',</span> <span class="pre">'I432':</span> <span class="pre">'I432',</span> <span class="pre">'I4_1':</span> <span class="pre">'I4_1',</span> <span class="pre">'I4_1/a':</span> <span class="pre">'I4_1/a',</span> <span class="pre">'I4_1/a-32/d':</span> <span class="pre">'Ia-3d',</span> <span class="pre">'I4_1/a2/c2/d':</span> <span class="pre">'I4_1/acd',</span> <span class="pre">'I4_1/a2/m2/d':</span> <span class="pre">'I4_1/amd',</span> <span class="pre">'I4_122':</span> <span class="pre">'I4_122',</span> <span class="pre">'I4_132':</span> <span class="pre">'I4_132',</span> <span class="pre">'I4_1cd':</span> <span class="pre">'I4_1cd',</span> <span class="pre">'I4_1md':</span> <span class="pre">'I4_1md',</span> <span class="pre">'I4cm':</span> <span class="pre">'I4cm',</span> <span class="pre">'I4mm':</span> <span class="pre">'I4mm',</span> <span class="pre">'Iba2':</span> <span class="pre">'Iba2',</span> <span class="pre">'Ima2':</span> <span class="pre">'Ima2',</span> <span class="pre">'Imm2':</span> <span class="pre">'Imm2',</span> <span class="pre">'P-1':</span> <span class="pre">'P-1',</span> <span class="pre">'P-3':</span> <span class="pre">'P-3',</span> <span class="pre">'P-312/c':</span> <span class="pre">'P-31c',</span> <span class="pre">'P-312/m':</span> <span class="pre">'P-31m',</span> <span class="pre">'P-32/c1':</span> <span class="pre">'P-3c1',</span> <span class="pre">'P-32/m1':</span> <span class="pre">'P-3m1',</span> <span class="pre">'P-4':</span> <span class="pre">'P-4',</span> <span class="pre">'P-42_1c':</span> <span class="pre">'P-42_1c',</span> <span class="pre">'P-42_1m':</span> <span class="pre">'P-42_1m',</span> <span class="pre">'P-42c':</span> <span class="pre">'P-42c',</span> <span class="pre">'P-42m':</span> <span class="pre">'P-42m',</span> <span class="pre">'P-43m':</span> <span class="pre">'P-43m',</span> <span class="pre">'P-43n':</span> <span class="pre">'P-43n',</span> <span class="pre">'P-4b2':</span> <span class="pre">'P-4b2',</span> <span class="pre">'P-4c2':</span> <span class="pre">'P-4c2',</span> <span class="pre">'P-4m2':</span> <span class="pre">'P-4m2',</span> <span class="pre">'P-4n2':</span> <span class="pre">'P-4n2',</span> <span class="pre">'P-6':</span> <span class="pre">'P-6',</span> <span class="pre">'P-62c':</span> <span class="pre">'P-62c',</span> <span class="pre">'P-62m':</span> <span class="pre">'P-62m',</span> <span class="pre">'P-6c2':</span> <span class="pre">'P-6c2',</span> <span class="pre">'P-6m2':</span> <span class="pre">'P-6m2',</span> <span class="pre">'P1':</span> <span class="pre">'P1',</span> <span class="pre">'P12/c1':</span> <span class="pre">'P12/c1',</span> <span class="pre">'P12/m1':</span> <span class="pre">'P12/m1',</span> <span class="pre">'P121':</span> <span class="pre">'P121',</span> <span class="pre">'P12_1/c1':</span> <span class="pre">'P12_1/c1',</span> <span class="pre">'P12_1/m1':</span> <span class="pre">'P12_1/m1',</span> <span class="pre">'P12_11':</span> <span class="pre">'P12_11',</span> <span class="pre">'P1c1':</span> <span class="pre">'P1c1',</span> <span class="pre">'P1m1':</span> <span class="pre">'P1m1',</span> <span class="pre">'P2/b2/a2/n':</span> <span class="pre">'Pban',</span> <span class="pre">'P2/b2_1/c2_1/m':</span> <span class="pre">'Pbcm',</span> <span class="pre">'P2/c2/c2/m':</span> <span class="pre">'Pccm',</span> <span class="pre">'P2/m-3':</span> <span class="pre">'Pm-3',</span> <span class="pre">'P2/m2/m2/m':</span> <span class="pre">'Pmmm',</span> <span class="pre">'P2/m2/n2_1/a':</span> <span class="pre">'Pmna',</span> <span class="pre">'P2/n-3':</span> <span class="pre">'Pn-3',</span> <span class="pre">'P2/n2/n2/n':</span> <span class="pre">'Pnnn',</span> <span class="pre">'P2/n2_1/n2/a':</span> <span class="pre">'Pnna',</span> <span class="pre">'P222':</span> <span class="pre">'P222',</span> <span class="pre">'P222_1':</span> <span class="pre">'P222_1',</span> <span class="pre">'P23':</span> <span class="pre">'P23',</span> <span class="pre">'P2_1/a-3':</span> <span class="pre">'Pa-3',</span> <span class="pre">'P2_1/b2/c2_1/n':</span> <span class="pre">'Pbcn',</span> <span class="pre">'P2_1/b2_1/a2/m':</span> <span class="pre">'Pbam',</span> <span class="pre">'P2_1/b2_1/c2_1/a':</span> <span class="pre">'Pbca',</span> <span class="pre">'P2_1/c2/c2/a':</span> <span class="pre">'Pcca',</span> <span class="pre">'P2_1/c2_1/c2/n':</span> <span class="pre">'Pccn',</span> <span class="pre">'P2_1/m2/m2/a':</span> <span class="pre">'Pmma',</span> <span class="pre">'P2_1/m2_1/m2/n':</span> <span class="pre">'Pmmn',</span> <span class="pre">'P2_1/n2_1/m2_1/a':</span> <span class="pre">'Pnma',</span> <span class="pre">'P2_1/n2_1/n2/m':</span> <span class="pre">'Pnnm',</span> <span class="pre">'P2_12_12':</span> <span class="pre">'P2_12_12',</span> <span class="pre">'P2_12_12_1':</span> <span class="pre">'P2_12_12_1',</span> <span class="pre">'P2_13':</span> <span class="pre">'P2_13',</span> <span class="pre">'P3':</span> <span class="pre">'P3',</span> <span class="pre">'P312':</span> <span class="pre">'P312',</span> <span class="pre">'P31c':</span> <span class="pre">'P31c',</span> <span class="pre">'P31m':</span> <span class="pre">'P31m',</span> <span class="pre">'P321':</span> <span class="pre">'P321',</span> <span class="pre">'P3_1':</span> <span class="pre">'P3_1',</span> <span class="pre">'P3_112':</span> <span class="pre">'P3_112',</span> <span class="pre">'P3_121':</span> <span class="pre">'P3_121',</span> <span class="pre">'P3_2':</span> <span class="pre">'P3_2',</span> <span class="pre">'P3_212':</span> <span class="pre">'P3_212',</span> <span class="pre">'P3_221':</span> <span class="pre">'P3_221',</span> <span class="pre">'P3c1':</span> <span class="pre">'P3c1',</span> <span class="pre">'P3m1':</span> <span class="pre">'P3m1',</span> <span class="pre">'P4':</span> <span class="pre">'P4',</span> <span class="pre">'P4/m':</span> <span class="pre">'P4/m',</span> <span class="pre">'P4/m-32/m':</span> <span class="pre">'Pm-3m',</span> <span class="pre">'P4/m2/c2/c':</span> <span class="pre">'P4/mcc',</span> <span class="pre">'P4/m2/m2/m':</span> <span class="pre">'P4/mmm',</span> <span class="pre">'P4/m2_1/b2/m':</span> <span class="pre">'P4/mbm',</span> <span class="pre">'P4/m2_1/n2/c':</span> <span class="pre">'P4/mnc',</span> <span class="pre">'P4/n':</span> <span class="pre">'P4/n',</span> <span class="pre">'P4/n-32/n':</span> <span class="pre">'Pn-3n',</span> <span class="pre">'P4/n2/b2/m':</span> <span class="pre">'P4/nbm',</span> <span class="pre">'P4/n2/n2/c':</span> <span class="pre">'P4/nnc',</span> <span class="pre">'P4/n2_1/c2/c':</span> <span class="pre">'P4/ncc',</span> <span class="pre">'P4/n2_1/m2/m':</span> <span class="pre">'P4/nmm',</span> <span class="pre">'P422':</span> <span class="pre">'P422',</span> <span class="pre">'P42_12':</span> <span class="pre">'P42_12',</span> <span class="pre">'P432':</span> <span class="pre">'P432',</span> <span class="pre">'P4_1':</span> <span class="pre">'P4_1',</span> <span class="pre">'P4_122':</span> <span class="pre">'P4_122',</span> <span class="pre">'P4_12_12':</span> <span class="pre">'P4_12_12',</span> <span class="pre">'P4_132':</span> <span class="pre">'P4_132',</span> <span class="pre">'P4_2':</span> <span class="pre">'P4_2',</span> <span class="pre">'P4_2/m':</span> <span class="pre">'P4_2/m',</span> <span class="pre">'P4_2/m-32/n':</span> <span class="pre">'Pm-3n',</span> <span class="pre">'P4_2/m2/c2/m':</span> <span class="pre">'P4_2/mcm',</span> <span class="pre">'P4_2/m2/m2/c':</span> <span class="pre">'P4_2/mmc',</span> <span class="pre">'P4_2/m2_1/b2/c':</span> <span class="pre">'P4_2/mbc',</span> <span class="pre">'P4_2/m2_1/n2/m':</span> <span class="pre">'P4_2/mnm',</span> <span class="pre">'P4_2/n':</span> <span class="pre">'P4_2/n',</span> <span class="pre">'P4_2/n-32/m':</span> <span class="pre">'Pn-3m',</span> <span class="pre">'P4_2/n2/b2/c':</span> <span class="pre">'P4_2/nbc',</span> <span class="pre">'P4_2/n2/n2/m':</span> <span class="pre">'P4_2/nnm',</span> <span class="pre">'P4_2/n2_1/c2/m':</span> <span class="pre">'P4_2/ncm',</span> <span class="pre">'P4_2/n2_1/m2/c':</span> <span class="pre">'P4_2/nmc',</span> <span class="pre">'P4_222':</span> <span class="pre">'P4_222',</span> <span class="pre">'P4_22_12':</span> <span class="pre">'P4_22_12',</span> <span class="pre">'P4_232':</span> <span class="pre">'P4_232',</span> <span class="pre">'P4_2bc':</span> <span class="pre">'P4_2bc',</span> <span class="pre">'P4_2cm':</span> <span class="pre">'P4_2cm',</span> <span class="pre">'P4_2mc':</span> <span class="pre">'P4_2mc',</span> <span class="pre">'P4_2nm':</span> <span class="pre">'P4_2nm',</span> <span class="pre">'P4_3':</span> <span class="pre">'P4_3',</span> <span class="pre">'P4_322':</span> <span class="pre">'P4_322',</span> <span class="pre">'P4_32_12':</span> <span class="pre">'P4_32_12',</span> <span class="pre">'P4_332':</span> <span class="pre">'P4_332',</span> <span class="pre">'P4bm':</span> <span class="pre">'P4bm',</span> <span class="pre">'P4cc':</span> <span class="pre">'P4cc',</span> <span class="pre">'P4mm':</span> <span class="pre">'P4mm',</span> <span class="pre">'P4nc':</span> <span class="pre">'P4nc',</span> <span class="pre">'P6':</span> <span class="pre">'P6',</span> <span class="pre">'P6/m':</span> <span class="pre">'P6/m',</span> <span class="pre">'P6/m2/c2/c':</span> <span class="pre">'P6/mcc',</span> <span class="pre">'P6/m2/m2/m':</span> <span class="pre">'P6/mmm',</span> <span class="pre">'P622':</span> <span class="pre">'P622',</span> <span class="pre">'P6_1':</span> <span class="pre">'P6_1',</span> <span class="pre">'P6_122':</span> <span class="pre">'P6_122',</span> <span class="pre">'P6_2':</span> <span class="pre">'P6_2',</span> <span class="pre">'P6_222':</span> <span class="pre">'P6_222',</span> <span class="pre">'P6_3':</span> <span class="pre">'P6_3',</span> <span class="pre">'P6_3/m':</span> <span class="pre">'P6_3/m',</span> <span class="pre">'P6_3/m2/c2/m':</span> <span class="pre">'P6_3/mcm',</span> <span class="pre">'P6_3/m2/m2/c':</span> <span class="pre">'P6_3/mmc',</span> <span class="pre">'P6_322':</span> <span class="pre">'P6_322',</span> <span class="pre">'P6_3cm':</span> <span class="pre">'P6_3cm',</span> <span class="pre">'P6_3mc':</span> <span class="pre">'P6_3mc',</span> <span class="pre">'P6_4':</span> <span class="pre">'P6_4',</span> <span class="pre">'P6_422':</span> <span class="pre">'P6_422',</span> <span class="pre">'P6_5':</span> <span class="pre">'P6_5',</span> <span class="pre">'P6_522':</span> <span class="pre">'P6_522',</span> <span class="pre">'P6cc':</span> <span class="pre">'P6cc',</span> <span class="pre">'P6mm':</span> <span class="pre">'P6mm',</span> <span class="pre">'Pba2':</span> <span class="pre">'Pba2',</span> <span class="pre">'Pca2_1':</span> <span class="pre">'Pca2_1',</span> <span class="pre">'Pcc2':</span> <span class="pre">'Pcc2',</span> <span class="pre">'Pma2':</span> <span class="pre">'Pma2',</span> <span class="pre">'Pmc2_1':</span> <span class="pre">'Pmc2_1',</span> <span class="pre">'Pmm2':</span> <span class="pre">'Pmm2',</span> <span class="pre">'Pmn2_1':</span> <span class="pre">'Pmn2_1',</span> <span class="pre">'Pna2_1':</span> <span class="pre">'Pna2_1',</span> <span class="pre">'Pnc2':</span> <span class="pre">'Pnc2',</span> <span class="pre">'Pnn2':</span> <span class="pre">'Pnn2',</span> <span class="pre">'R-3':</span> <span class="pre">'R-3',</span> <span class="pre">'R-32/c':</span> <span class="pre">'R-3c',</span> <span class="pre">'R-32/m':</span> <span class="pre">'R-3m',</span> <span class="pre">'R3':</span> <span class="pre">'R3',</span> <span class="pre">'R32':</span> <span class="pre">'R32',</span> <span class="pre">'R3c':</span> <span class="pre">'R3c',</span> <span class="pre">'R3m':</span> <span class="pre">'R3m'}</span></em><a class="reference external" href="https://github.com/materialsproject/pymatgen/blob/v2025.1.24/src/pymatgen/symmetry/groups.py"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pymatgen.symmetry.groups.SpaceGroup.full_sg_mapping" title="Link to this definition"></a></dt>
<dd></dd></dl>

<dl class="py attribute">
<dt class="sig sig-object py" id="pymatgen.symmetry.groups.SpaceGroup.gen_matrices">
<span class="sig-name descname"><span class="pre">gen_matrices</span></span><em class="property"><span class="w"> </span><span class="p"><span class="pre">=</span></span><span class="w"> </span><span class="pre">{'a':</span> <span class="pre">[[1,</span> <span class="pre">0,</span> <span class="pre">0],</span> <span class="pre">[0,</span> <span class="pre">1,</span> <span class="pre">0],</span> <span class="pre">[0,</span> <span class="pre">0,</span> <span class="pre">1]],</span> <span class="pre">'b':</span> <span class="pre">[[-1,</span> <span class="pre">0,</span> <span class="pre">0],</span> <span class="pre">[0,</span> <span class="pre">-1,</span> <span class="pre">0],</span> <span class="pre">[0,</span> <span class="pre">0,</span> <span class="pre">1]],</span> <span class="pre">'c':</span> <span class="pre">[[-1,</span> <span class="pre">0,</span> <span class="pre">0],</span> <span class="pre">[0,</span> <span class="pre">1,</span> <span class="pre">0],</span> <span class="pre">[0,</span> <span class="pre">0,</span> <span class="pre">-1]],</span> <span class="pre">'d':</span> <span class="pre">[[0,</span> <span class="pre">0,</span> <span class="pre">1],</span> <span class="pre">[1,</span> <span class="pre">0,</span> <span class="pre">0],</span> <span class="pre">[0,</span> <span class="pre">1,</span> <span class="pre">0]],</span> <span class="pre">'e':</span> <span class="pre">[[0,</span> <span class="pre">1,</span> <span class="pre">0],</span> <span class="pre">[1,</span> <span class="pre">0,</span> <span class="pre">0],</span> <span class="pre">[0,</span> <span class="pre">0,</span> <span class="pre">-1]],</span> <span class="pre">'f':</span> <span class="pre">[[0,</span> <span class="pre">-1,</span> <span class="pre">0],</span> <span class="pre">[-1,</span> <span class="pre">0,</span> <span class="pre">0],</span> <span class="pre">[0,</span> <span class="pre">0,</span> <span class="pre">-1]],</span> <span class="pre">'g':</span> <span class="pre">[[0,</span> <span class="pre">-1,</span> <span class="pre">0],</span> <span class="pre">[1,</span> <span class="pre">0,</span> <span class="pre">0],</span> <span class="pre">[0,</span> <span class="pre">0,</span> <span class="pre">1]],</span> <span class="pre">'h':</span> <span class="pre">[[-1,</span> <span class="pre">0,</span> <span class="pre">0],</span> <span class="pre">[0,</span> <span class="pre">-1,</span> <span class="pre">0],</span> <span class="pre">[0,</span> <span class="pre">0,</span> <span class="pre">-1]],</span> <span class="pre">'i':</span> <span class="pre">[[1,</span> <span class="pre">0,</span> <span class="pre">0],</span> <span class="pre">[0,</span> <span class="pre">1,</span> <span class="pre">0],</span> <span class="pre">[0,</span> <span class="pre">0,</span> <span class="pre">-1]],</span> <span class="pre">'j':</span> <span class="pre">[[1,</span> <span class="pre">0,</span> <span class="pre">0],</span> <span class="pre">[0,</span> <span class="pre">-1,</span> <span class="pre">0],</span> <span class="pre">[0,</span> <span class="pre">0,</span> <span class="pre">1]],</span> <span class="pre">'k':</span> <span class="pre">[[0,</span> <span class="pre">-1,</span> <span class="pre">0],</span> <span class="pre">[-1,</span> <span class="pre">0,</span> <span class="pre">0],</span> <span class="pre">[0,</span> <span class="pre">0,</span> <span class="pre">1]],</span> <span class="pre">'l':</span> <span class="pre">[[0,</span> <span class="pre">1,</span> <span class="pre">0],</span> <span class="pre">[1,</span> <span class="pre">0,</span> <span class="pre">0],</span> <span class="pre">[0,</span> <span class="pre">0,</span> <span class="pre">1]],</span> <span class="pre">'m':</span> <span class="pre">[[0,</span> <span class="pre">1,</span> <span class="pre">0],</span> <span class="pre">[-1,</span> <span class="pre">0,</span> <span class="pre">0],</span> <span class="pre">[0,</span> <span class="pre">0,</span> <span class="pre">-1]],</span> <span class="pre">'n':</span> <span class="pre">[[0,</span> <span class="pre">-1,</span> <span class="pre">0],</span> <span class="pre">[1,</span> <span class="pre">-1,</span> <span class="pre">0],</span> <span class="pre">[0,</span> <span class="pre">0,</span> <span class="pre">1]]}</span></em><a class="reference external" href="https://github.com/materialsproject/pymatgen/blob/v2025.1.24/src/pymatgen/symmetry/groups.py"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pymatgen.symmetry.groups.SpaceGroup.gen_matrices" title="Link to this definition"></a></dt>
<dd></dd></dl>

<dl class="py method">
<dt class="sig sig-object py" id="pymatgen.symmetry.groups.SpaceGroup.get_orbit">
<span class="sig-name descname"><span class="pre">get_orbit</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">p</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">ArrayLike</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">tol</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">float</span></span><span class="w"> </span><span class="o"><span class="pre">=</span></span><span class="w"> </span><span class="default_value"><span class="pre">1e-05</span></span></em><span class="sig-paren">)</span> <span class="sig-return"><span class="sig-return-icon">&#x2192;</span> <span class="sig-return-typehint"><span class="pre">list</span><span class="p"><span class="pre">[</span></span><span class="pre">np.ndarray</span><span class="p"><span class="pre">]</span></span></span></span><a class="reference external" href="https://github.com/materialsproject/pymatgen/blob/v2025.1.24/src/pymatgen/core/../symmetry/groups.py#L489-L507"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pymatgen.symmetry.groups.SpaceGroup.get_orbit" title="Link to this definition"></a></dt>
<dd><p>Get the orbit for a point.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>p</strong> – Point as a 3x1 array.</p></li>
<li><p><strong>tol</strong> – Tolerance for determining if sites are the same. 1e-5 should
be sufficient for most purposes. Set to 0 for exact matching
(and also needed for symbolic orbits).</p></li>
</ul>
</dd>
<dt class="field-even">Returns<span class="colon">:</span></dt>
<dd class="field-even"><p>Orbit for point.</p>
</dd>
<dt class="field-odd">Return type<span class="colon">:</span></dt>
<dd class="field-odd"><p>list[array]</p>
</dd>
</dl>
</dd></dl>

<dl class="py method">
<dt class="sig sig-object py" id="pymatgen.symmetry.groups.SpaceGroup.get_orbit_and_generators">
<span class="sig-name descname"><span class="pre">get_orbit_and_generators</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">p</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">ArrayLike</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">tol</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">float</span></span><span class="w"> </span><span class="o"><span class="pre">=</span></span><span class="w"> </span><span class="default_value"><span class="pre">1e-05</span></span></em><span class="sig-paren">)</span> <span class="sig-return"><span class="sig-return-icon">&#x2192;</span> <span class="sig-return-typehint"><span class="pre">tuple</span><span class="p"><span class="pre">[</span></span><span class="pre">list</span><span class="p"><span class="pre">[</span></span><span class="pre">np.ndarray</span><span class="p"><span class="pre">]</span></span><span class="p"><span class="pre">,</span></span><span class="w"> </span><span class="pre">list</span><span class="p"><span class="pre">[</span></span><a class="reference internal" href="pymatgen.core.html#pymatgen.core.operations.SymmOp" title="pymatgen.core.operations.SymmOp"><span class="pre">SymmOp</span></a><span class="p"><span class="pre">]</span></span><span class="p"><span class="pre">]</span></span></span></span><a class="reference external" href="https://github.com/materialsproject/pymatgen/blob/v2025.1.24/src/pymatgen/core/../symmetry/groups.py#L509-L532"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pymatgen.symmetry.groups.SpaceGroup.get_orbit_and_generators" title="Link to this definition"></a></dt>
<dd><p>Get the orbit and its generators for a point.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>p</strong> – Point as a 3x1 array.</p></li>
<li><p><strong>tol</strong> – Tolerance for determining if sites are the same. 1e-5 should
be sufficient for most purposes. Set to 0 for exact matching
(and also needed for symbolic orbits).</p></li>
</ul>
</dd>
<dt class="field-even">Returns<span class="colon">:</span></dt>
<dd class="field-even"><p>Orbit and generators for point.</p>
</dd>
<dt class="field-odd">Return type<span class="colon">:</span></dt>
<dd class="field-odd"><p>tuple[list[np.ndarray], list[<a class="reference internal" href="pymatgen.core.html#pymatgen.core.operations.SymmOp" title="pymatgen.core.operations.SymmOp">SymmOp</a>]]</p>
</dd>
</dl>
</dd></dl>

<dl class="py method">
<dt class="sig sig-object py" id="pymatgen.symmetry.groups.SpaceGroup.get_settings">
<em class="property"><span class="pre">classmethod</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">get_settings</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">int_symbol</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">str</span></span></em><span class="sig-paren">)</span> <span class="sig-return"><span class="sig-return-icon">&#x2192;</span> <span class="sig-return-typehint"><span class="pre">set</span><span class="p"><span class="pre">[</span></span><span class="pre">str</span><span class="p"><span class="pre">]</span></span></span></span><a class="reference external" href="https://github.com/materialsproject/pymatgen/blob/v2025.1.24/src/pymatgen/core/../symmetry/groups.py#L441-L476"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pymatgen.symmetry.groups.SpaceGroup.get_settings" title="Link to this definition"></a></dt>
<dd><p>Get all the settings for a particular international symbol.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
<dd class="field-odd"><p><strong>int_symbol</strong> (<em>str</em>) – Full International (e.g., “P2/m2/m2/m”) or
Hermann-Mauguin Symbol (“Pmmm”) or abbreviated symbol. The
notation is a LaTeX-like string, with screw axes being
represented by an underscore. For example, “P6_3/mmc”.</p>
</dd>
<dt class="field-even">Returns<span class="colon">:</span></dt>
<dd class="field-even"><p>All possible settings for the given international symbol.</p>
</dd>
<dt class="field-odd">Return type<span class="colon">:</span></dt>
<dd class="field-odd"><p>set[str]</p>
</dd>
</dl>
</dd></dl>

<dl class="py method">
<dt class="sig sig-object py" id="pymatgen.symmetry.groups.SpaceGroup.is_compatible">
<span class="sig-name descname"><span class="pre">is_compatible</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">lattice</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><a class="reference internal" href="pymatgen.core.html#pymatgen.core.lattice.Lattice" title="pymatgen.core.lattice.Lattice"><span class="pre">Lattice</span></a></span></em>, <em class="sig-param"><span class="n"><span class="pre">tol</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">float</span></span><span class="w"> </span><span class="o"><span class="pre">=</span></span><span class="w"> </span><span class="default_value"><span class="pre">1e-05</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">angle_tol</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">float</span></span><span class="w"> </span><span class="o"><span class="pre">=</span></span><span class="w"> </span><span class="default_value"><span class="pre">5</span></span></em><span class="sig-paren">)</span> <span class="sig-return"><span class="sig-return-icon">&#x2192;</span> <span class="sig-return-typehint"><span class="pre">bool</span></span></span><a class="reference external" href="https://github.com/materialsproject/pymatgen/blob/v2025.1.24/src/pymatgen/core/../symmetry/groups.py#L534-L594"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pymatgen.symmetry.groups.SpaceGroup.is_compatible" title="Link to this definition"></a></dt>
<dd><p>Check whether a particular lattice is compatible with the
<em>conventional</em> unit cell.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>lattice</strong> (<a class="reference internal" href="pymatgen.core.html#pymatgen.core.lattice.Lattice" title="pymatgen.core.lattice.Lattice"><em>Lattice</em></a>) – A Lattice.</p></li>
<li><p><strong>tol</strong> (<em>float</em>) – The tolerance to check for equality of lengths.</p></li>
<li><p><strong>angle_tol</strong> (<em>float</em>) – The tolerance to check for equality of angles
in degrees.</p></li>
</ul>
</dd>
</dl>
</dd></dl>

<dl class="py method">
<dt class="sig sig-object py" id="pymatgen.symmetry.groups.SpaceGroup.is_subgroup">
<span class="sig-name descname"><span class="pre">is_subgroup</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">supergroup</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><a class="reference internal" href="#pymatgen.symmetry.groups.SymmetryGroup" title="pymatgen.symmetry.groups.SymmetryGroup"><span class="pre">SymmetryGroup</span></a></span></em><span class="sig-paren">)</span> <span class="sig-return"><span class="sig-return-icon">&#x2192;</span> <span class="sig-return-typehint"><span class="pre">bool</span></span></span><a class="reference external" href="https://github.com/materialsproject/pymatgen/blob/v2025.1.24/src/pymatgen/core/../symmetry/groups.py#L617-L650"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pymatgen.symmetry.groups.SpaceGroup.is_subgroup" title="Link to this definition"></a></dt>
<dd><p>Check if space group is a subgroup of the supplied symmetry group.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
<dd class="field-odd"><p><strong>supergroup</strong> (<em>Spacegroup</em>) – Supergroup to test.</p>
</dd>
<dt class="field-even">Returns<span class="colon">:</span></dt>
<dd class="field-even"><p>True if this space group is a subgroup of the supplied group.</p>
</dd>
<dt class="field-odd">Return type<span class="colon">:</span></dt>
<dd class="field-odd"><p>bool</p>
</dd>
</dl>
</dd></dl>

<dl class="py method">
<dt class="sig sig-object py" id="pymatgen.symmetry.groups.SpaceGroup.is_supergroup">
<span class="sig-name descname"><span class="pre">is_supergroup</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">subgroup</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><a class="reference internal" href="#pymatgen.symmetry.groups.SymmetryGroup" title="pymatgen.symmetry.groups.SymmetryGroup"><span class="pre">SymmetryGroup</span></a></span></em><span class="sig-paren">)</span> <span class="sig-return"><span class="sig-return-icon">&#x2192;</span> <span class="sig-return-typehint"><span class="pre">bool</span></span></span><a class="reference external" href="https://github.com/materialsproject/pymatgen/blob/v2025.1.24/src/pymatgen/core/../symmetry/groups.py#L652-L661"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pymatgen.symmetry.groups.SpaceGroup.is_supergroup" title="Link to this definition"></a></dt>
<dd><p>True if this space group is a supergroup of the supplied group.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
<dd class="field-odd"><p><strong>subgroup</strong> (<em>Spacegroup</em>) – Subgroup to test.</p>
</dd>
<dt class="field-even">Returns<span class="colon">:</span></dt>
<dd class="field-even"><p>True if this space group is a supergroup of the supplied group.</p>
</dd>
<dt class="field-odd">Return type<span class="colon">:</span></dt>
<dd class="field-odd"><p>bool</p>
</dd>
</dl>
</dd></dl>

<dl class="py attribute">
<dt class="sig sig-object py" id="pymatgen.symmetry.groups.SpaceGroup.op">
<span class="sig-name descname"><span class="pre">op</span></span><em class="property"><span class="w"> </span><span class="p"><span class="pre">=</span></span><span class="w"> </span><span class="pre">{'hall':</span> <span class="pre">'-P</span> <span class="pre">2ac</span> <span class="pre">2n</span> <span class="pre">(z,x,y+1/4)',</span> <span class="pre">'hermann_mauguin':</span> <span class="pre">'Pnma',</span> <span class="pre">'hermann_mauguin_u':</span> <span class="pre">'Pnma',</span> <span class="pre">'ncsym':</span> <span class="pre">['x,y,z',</span> <span class="pre">'-x+1/2,y+1/2,-z',</span> <span class="pre">'-x,-y,z+1/2',</span> <span class="pre">'x+1/2,-y+1/2,-z+1/2',</span> <span class="pre">'-x,-y,-z+1/2',</span> <span class="pre">'x+1/2,-y+1/2,z+1/2',</span> <span class="pre">'x,y,-z',</span> <span class="pre">'-x+1/2,y+1/2,z'],</span> <span class="pre">'number':</span> <span class="pre">62,</span> <span class="pre">'point_group':</span> <span class="pre">'mmm',</span> <span class="pre">'schoenflies':</span> <span class="pre">'D2h^16',</span> <span class="pre">'short_h_m':</span> <span class="pre">'Pnma',</span> <span class="pre">'symops':</span> <span class="pre">['x,y,z',</span> <span class="pre">'-x+1/2,y+1/2,-z',</span> <span class="pre">'-x,-y,z+1/2',</span> <span class="pre">'x+1/2,-y+1/2,-z+1/2',</span> <span class="pre">'-x,-y,-z+1/2',</span> <span class="pre">'x+1/2,-y+1/2,z+1/2',</span> <span class="pre">'x,y,-z',</span> <span class="pre">'-x+1/2,y+1/2,z'],</span> <span class="pre">'universal_h_m':</span> <span class="pre">'Pnma(c,a-1/4,b)'}</span></em><a class="reference external" href="https://github.com/materialsproject/pymatgen/blob/v2025.1.24/src/pymatgen/symmetry/groups.py"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pymatgen.symmetry.groups.SpaceGroup.op" title="Link to this definition"></a></dt>
<dd></dd></dl>

<dl class="py attribute">
<dt class="sig sig-object py" id="pymatgen.symmetry.groups.SpaceGroup.sg_encoding">
<span class="sig-name descname"><span class="pre">sg_encoding</span></span><em class="property"><span class="w"> </span><span class="p"><span class="pre">=</span></span><span class="w"> </span><span class="pre">{'Aba2':</span> <span class="pre">{'enc':</span> <span class="pre">'03aODDbOOOjDDO0',</span> <span class="pre">'full_symbol':</span> <span class="pre">'Aea2',</span> <span class="pre">'int_number':</span> <span class="pre">41,</span> <span class="pre">'order':</span> <span class="pre">8,</span> <span class="pre">'patterson_symmetry':</span> <span class="pre">'Ammm</span> <span class="pre">(Cmmm)',</span> <span class="pre">'point_group':</span> <span class="pre">'mm2'},</span> <span class="pre">'Abm2':</span> <span class="pre">{'enc':</span> <span class="pre">'03aODDbOOOjODO0',</span> <span class="pre">'full_symbol':</span> <span class="pre">'Aem2',</span> <span class="pre">'int_number':</span> <span class="pre">39,</span> <span class="pre">'order':</span> <span class="pre">8,</span> <span class="pre">'patterson_symmetry':</span> <span class="pre">'Ammm</span> <span class="pre">(Cmmm)',</span> <span class="pre">'point_group':</span> <span class="pre">'mm2'},</span> <span class="pre">'Aea2':</span> <span class="pre">{'enc':</span> <span class="pre">'03aODDbOOOjDDO0',</span> <span class="pre">'full_symbol':</span> <span class="pre">'Aea2',</span> <span class="pre">'int_number':</span> <span class="pre">41,</span> <span class="pre">'order':</span> <span class="pre">8,</span> <span class="pre">'patterson_symmetry':</span> <span class="pre">'Ammm</span> <span class="pre">(Cmmm)',</span> <span class="pre">'point_group':</span> <span class="pre">'mm2'},</span> <span class="pre">'Aem2':</span> <span class="pre">{'enc':</span> <span class="pre">'03aODDbOOOjODO0',</span> <span class="pre">'full_symbol':</span> <span class="pre">'Aem2',</span> <span class="pre">'int_number':</span> <span class="pre">39,</span> <span class="pre">'order':</span> <span class="pre">8,</span> <span class="pre">'patterson_symmetry':</span> <span class="pre">'Ammm</span> <span class="pre">(Cmmm)',</span> <span class="pre">'point_group':</span> <span class="pre">'mm2'},</span> <span class="pre">'Ama2':</span> <span class="pre">{'enc':</span> <span class="pre">'03aODDbOOOjDOO0',</span> <span class="pre">'full_symbol':</span> <span class="pre">'Ama2',</span> <span class="pre">'int_number':</span> <span class="pre">40,</span> <span class="pre">'order':</span> <span class="pre">8,</span> <span class="pre">'patterson_symmetry':</span> <span class="pre">'Ammm</span> <span class="pre">(Cmmm)',</span> <span class="pre">'point_group':</span> <span class="pre">'mm2'},</span> <span class="pre">'Amm2':</span> <span class="pre">{'enc':</span> <span class="pre">'03aODDbOOOjOOO0',</span> <span class="pre">'full_symbol':</span> <span class="pre">'Amm2',</span> <span class="pre">'int_number':</span> <span class="pre">38,</span> <span class="pre">'order':</span> <span class="pre">8,</span> <span class="pre">'patterson_symmetry':</span> <span class="pre">'Ammm</span> <span class="pre">(Cmmm)',</span> <span class="pre">'point_group':</span> <span class="pre">'mm2'},</span> <span class="pre">'C12/c1':</span> <span class="pre">{'enc':</span> <span class="pre">'12aDDOcOOD0',</span> <span class="pre">'full_symbol':</span> <span class="pre">'C12/c1',</span> <span class="pre">'int_number':</span> <span class="pre">15,</span> <span class="pre">'order':</span> <span class="pre">8,</span> <span class="pre">'patterson_symmetry':</span> <span class="pre">'C12/m1',</span> <span class="pre">'point_group':</span> <span class="pre">'2/m'},</span> <span class="pre">'C12/m1':</span> <span class="pre">{'enc':</span> <span class="pre">'12aDDOcOOO0',</span> <span class="pre">'full_symbol':</span> <span class="pre">'C12/m1',</span> <span class="pre">'int_number':</span> <span class="pre">12,</span> <span class="pre">'order':</span> <span class="pre">8,</span> <span class="pre">'patterson_symmetry':</span> <span class="pre">'C12/m1',</span> <span class="pre">'point_group':</span> <span class="pre">'2/m'},</span> <span class="pre">'C121':</span> <span class="pre">{'enc':</span> <span class="pre">'02aDDOcOOO0',</span> <span class="pre">'full_symbol':</span> <span class="pre">'C121',</span> <span class="pre">'int_number':</span> <span class="pre">5,</span> <span class="pre">'order':</span> <span class="pre">4,</span> <span class="pre">'patterson_symmetry':</span> <span class="pre">'C12/m1',</span> <span class="pre">'point_group':</span> <span class="pre">'2'},</span> <span class="pre">'C1c1':</span> <span class="pre">{'enc':</span> <span class="pre">'02aDDOjOOD0',</span> <span class="pre">'full_symbol':</span> <span class="pre">'C1c1',</span> <span class="pre">'int_number':</span> <span class="pre">9,</span> <span class="pre">'order':</span> <span class="pre">4,</span> <span class="pre">'patterson_symmetry':</span> <span class="pre">'C12/m1',</span> <span class="pre">'point_group':</span> <span class="pre">'m'},</span> <span class="pre">'C1m1':</span> <span class="pre">{'enc':</span> <span class="pre">'02aDDOjOOO0',</span> <span class="pre">'full_symbol':</span> <span class="pre">'C1m1',</span> <span class="pre">'int_number':</span> <span class="pre">8,</span> <span class="pre">'order':</span> <span class="pre">4,</span> <span class="pre">'patterson_symmetry':</span> <span class="pre">'C12/m1',</span> <span class="pre">'point_group':</span> <span class="pre">'m'},</span> <span class="pre">'C222':</span> <span class="pre">{'enc':</span> <span class="pre">'03aDDObOOOcOOO0',</span> <span class="pre">'full_symbol':</span> <span class="pre">'C222',</span> <span class="pre">'int_number':</span> <span class="pre">21,</span> <span class="pre">'order':</span> <span class="pre">8,</span> <span class="pre">'patterson_symmetry':</span> <span class="pre">'Cmmm',</span> <span class="pre">'point_group':</span> <span class="pre">'222'},</span> <span class="pre">'C222_1':</span> <span class="pre">{'enc':</span> <span class="pre">'03aDDObOODcOOD0',</span> <span class="pre">'full_symbol':</span> <span class="pre">'C222_1',</span> <span class="pre">'int_number':</span> <span class="pre">20,</span> <span class="pre">'order':</span> <span class="pre">8,</span> <span class="pre">'patterson_symmetry':</span> <span class="pre">'Cmmm',</span> <span class="pre">'point_group':</span> <span class="pre">'222'},</span> <span class="pre">'Ccc2':</span> <span class="pre">{'enc':</span> <span class="pre">'03aDDObOOOjOOD0',</span> <span class="pre">'full_symbol':</span> <span class="pre">'Ccc2',</span> <span class="pre">'int_number':</span> <span class="pre">37,</span> <span class="pre">'order':</span> <span class="pre">8,</span> <span class="pre">'patterson_symmetry':</span> <span class="pre">'Cmmm',</span> <span class="pre">'point_group':</span> <span class="pre">'mm2'},</span> <span class="pre">'Ccca':</span> <span class="pre">{'enc':</span> <span class="pre">'04aDDObDDOcOOOhODD1OBB',</span> <span class="pre">'full_symbol':</span> <span class="pre">'C2/c2/c2/e',</span> <span class="pre">'int_number':</span> <span class="pre">68,</span> <span class="pre">'order':</span> <span class="pre">16,</span> <span class="pre">'patterson_symmetry':</span> <span class="pre">'Cmmm',</span> <span class="pre">'point_group':</span> <span class="pre">'mmm'},</span> <span class="pre">'Ccce':</span> <span class="pre">{'enc':</span> <span class="pre">'04aDDObDDOcOOOhODD1OBB',</span> <span class="pre">'full_symbol':</span> <span class="pre">'C2/c2/c2/e',</span> <span class="pre">'int_number':</span> <span class="pre">68,</span> <span class="pre">'order':</span> <span class="pre">16,</span> <span class="pre">'patterson_symmetry':</span> <span class="pre">'Cmmm',</span> <span class="pre">'point_group':</span> <span class="pre">'mmm'},</span> <span class="pre">'Cccm':</span> <span class="pre">{'enc':</span> <span class="pre">'13aDDObOOOcOOD0',</span> <span class="pre">'full_symbol':</span> <span class="pre">'C2/c2/c2/m',</span> <span class="pre">'int_number':</span> <span class="pre">66,</span> <span class="pre">'order':</span> <span class="pre">16,</span> <span class="pre">'patterson_symmetry':</span> <span class="pre">'Cmmm',</span> <span class="pre">'point_group':</span> <span class="pre">'mmm'},</span> <span class="pre">'Cmc2_1':</span> <span class="pre">{'enc':</span> <span class="pre">'03aDDObOODjOOD0',</span> <span class="pre">'full_symbol':</span> <span class="pre">'Cmc2_1',</span> <span class="pre">'int_number':</span> <span class="pre">36,</span> <span class="pre">'order':</span> <span class="pre">8,</span> <span class="pre">'patterson_symmetry':</span> <span class="pre">'Cmmm',</span> <span class="pre">'point_group':</span> <span class="pre">'mm2'},</span> <span class="pre">'Cmce':</span> <span class="pre">{'enc':</span> <span class="pre">'13aDDObODDcODD0',</span> <span class="pre">'full_symbol':</span> <span class="pre">'C2/m2/c2_1/e',</span> <span class="pre">'int_number':</span> <span class="pre">64,</span> <span class="pre">'order':</span> <span class="pre">16,</span> <span class="pre">'patterson_symmetry':</span> <span class="pre">'Cmmm',</span> <span class="pre">'point_group':</span> <span class="pre">'mmm'},</span> <span class="pre">'Cmcm':</span> <span class="pre">{'enc':</span> <span class="pre">'13aDDObOODcOOD0',</span> <span class="pre">'full_symbol':</span> <span class="pre">'C2/m2/c2_1/m',</span> <span class="pre">'int_number':</span> <span class="pre">63,</span> <span class="pre">'order':</span> <span class="pre">16,</span> <span class="pre">'patterson_symmetry':</span> <span class="pre">'Cmmm',</span> <span class="pre">'point_group':</span> <span class="pre">'mmm'},</span> <span class="pre">'Cmm2':</span> <span class="pre">{'enc':</span> <span class="pre">'03aDDObOOOjOOO0',</span> <span class="pre">'full_symbol':</span> <span class="pre">'Cmm2',</span> <span class="pre">'int_number':</span> <span class="pre">35,</span> <span class="pre">'order':</span> <span class="pre">8,</span> <span class="pre">'patterson_symmetry':</span> <span class="pre">'Cmmm',</span> <span class="pre">'point_group':</span> <span class="pre">'mm2'},</span> <span class="pre">'Cmma':</span> <span class="pre">{'enc':</span> <span class="pre">'13aDDObODOcODO0',</span> <span class="pre">'full_symbol':</span> <span class="pre">'C2/m2/m2/e',</span> <span class="pre">'int_number':</span> <span class="pre">67,</span> <span class="pre">'order':</span> <span class="pre">16,</span> <span class="pre">'patterson_symmetry':</span> <span class="pre">'Cmmm',</span> <span class="pre">'point_group':</span> <span class="pre">'mmm'},</span> <span class="pre">'Cmme':</span> <span class="pre">{'enc':</span> <span class="pre">'13aDDObODOcODO0',</span> <span class="pre">'full_symbol':</span> <span class="pre">'C2/m2/m2/e',</span> <span class="pre">'int_number':</span> <span class="pre">67,</span> <span class="pre">'order':</span> <span class="pre">16,</span> <span class="pre">'patterson_symmetry':</span> <span class="pre">'Cmmm',</span> <span class="pre">'point_group':</span> <span class="pre">'mmm'},</span> <span class="pre">'Cmmm':</span> <span class="pre">{'enc':</span> <span class="pre">'13aDDObOOOcOOO0',</span> <span class="pre">'full_symbol':</span> <span class="pre">'C2/m2/m2/m',</span> <span class="pre">'int_number':</span> <span class="pre">65,</span> <span class="pre">'order':</span> <span class="pre">16,</span> <span class="pre">'patterson_symmetry':</span> <span class="pre">'Cmmm',</span> <span class="pre">'point_group':</span> <span class="pre">'mmm'},</span> <span class="pre">'F-43c':</span> <span class="pre">{'enc':</span> <span class="pre">'06aODDaDODbOOOcOOOdOOOlDDD0',</span> <span class="pre">'full_symbol':</span> <span class="pre">'F-43c',</span> <span class="pre">'int_number':</span> <span class="pre">219,</span> <span class="pre">'order':</span> <span class="pre">96,</span> <span class="pre">'patterson_symmetry':</span> <span class="pre">'Fm-3m',</span> <span class="pre">'point_group':</span> <span class="pre">'-43m'},</span> <span class="pre">'F-43m':</span> <span class="pre">{'enc':</span> <span class="pre">'06aODDaDODbOOOcOOOdOOOlOOO0',</span> <span class="pre">'full_symbol':</span> <span class="pre">'F-43m',</span> <span class="pre">'int_number':</span> <span class="pre">216,</span> <span class="pre">'order':</span> <span class="pre">96,</span> <span class="pre">'patterson_symmetry':</span> <span class="pre">'Fm-3m',</span> <span class="pre">'point_group':</span> <span class="pre">'-43m'},</span> <span class="pre">'F222':</span> <span class="pre">{'enc':</span> <span class="pre">'04aODDaDODbOOOcOOO0',</span> <span class="pre">'full_symbol':</span> <span class="pre">'F222',</span> <span class="pre">'int_number':</span> <span class="pre">22,</span> <span class="pre">'order':</span> <span class="pre">16,</span> <span class="pre">'patterson_symmetry':</span> <span class="pre">'Fmmm',</span> <span class="pre">'point_group':</span> <span class="pre">'222'},</span> <span class="pre">'F23':</span> <span class="pre">{'enc':</span> <span class="pre">'05aODDaDODbOOOcOOOdOOO0',</span> <span class="pre">'full_symbol':</span> <span class="pre">'F23',</span> <span class="pre">'int_number':</span> <span class="pre">196,</span> <span class="pre">'order':</span> <span class="pre">48,</span> <span class="pre">'patterson_symmetry':</span> <span class="pre">'Fm-3',</span> <span class="pre">'point_group':</span> <span class="pre">'23'},</span> <span class="pre">'F432':</span> <span class="pre">{'enc':</span> <span class="pre">'06aODDaDODbOOOcOOOdOOOeOOO0',</span> <span class="pre">'full_symbol':</span> <span class="pre">'F432',</span> <span class="pre">'int_number':</span> <span class="pre">209,</span> <span class="pre">'order':</span> <span class="pre">96,</span> <span class="pre">'patterson_symmetry':</span> <span class="pre">'Fm-3m',</span> <span class="pre">'point_group':</span> <span class="pre">'432'},</span> <span class="pre">'F4_132':</span> <span class="pre">{'enc':</span> <span class="pre">'06aODDaDODbODDcDDOdOOOeFBF0',</span> <span class="pre">'full_symbol':</span> <span class="pre">'F4_132',</span> <span class="pre">'int_number':</span> <span class="pre">210,</span> <span class="pre">'order':</span> <span class="pre">96,</span> <span class="pre">'patterson_symmetry':</span> <span class="pre">'Fm-3m',</span> <span class="pre">'point_group':</span> <span class="pre">'432'},</span> <span class="pre">'Fd-3':</span> <span class="pre">{'enc':</span> <span class="pre">'06aODDaDODbOOOcOOOdOOOhBBB1ZZZ',</span> <span class="pre">'full_symbol':</span> <span class="pre">'F2/d-3',</span> <span class="pre">'int_number':</span> <span class="pre">203,</span> <span class="pre">'order':</span> <span class="pre">96,</span> <span class="pre">'patterson_symmetry':</span> <span class="pre">'Fm-3',</span> <span class="pre">'point_group':</span> <span class="pre">'m-3'},</span> <span class="pre">'Fd-3c':</span> <span class="pre">{'enc':</span> <span class="pre">'07aODDaDODbODDcDDOdOOOeFBFhFFF1XXX',</span> <span class="pre">'full_symbol':</span> <span class="pre">'F4_1/d-32/c',</span> <span class="pre">'int_number':</span> <span class="pre">228,</span> <span class="pre">'order':</span> <span class="pre">192,</span> <span class="pre">'patterson_symmetry':</span> <span class="pre">'Fm-3m',</span> <span class="pre">'point_group':</span> <span class="pre">'m-3m'},</span> <span class="pre">'Fd-3m':</span> <span class="pre">{'enc':</span> <span class="pre">'07aODDaDODbODDcDDOdOOOeFBFhBBB1ZZZ',</span> <span class="pre">'full_symbol':</span> <span class="pre">'F4_1/d-32/m',</span> <span class="pre">'int_number':</span> <span class="pre">227,</span> <span class="pre">'order':</span> <span class="pre">192,</span> <span class="pre">'patterson_symmetry':</span> <span class="pre">'Fm-3m',</span> <span class="pre">'point_group':</span> <span class="pre">'m-3m'},</span> <span class="pre">'Fdd2':</span> <span class="pre">{'enc':</span> <span class="pre">'04aODDaDODbOOOjBBB0',</span> <span class="pre">'full_symbol':</span> <span class="pre">'Fdd2',</span> <span class="pre">'int_number':</span> <span class="pre">43,</span> <span class="pre">'order':</span> <span class="pre">16,</span> <span class="pre">'patterson_symmetry':</span> <span class="pre">'Fmmm',</span> <span class="pre">'point_group':</span> <span class="pre">'mm2'},</span> <span class="pre">'Fddd':</span> <span class="pre">{'enc':</span> <span class="pre">'05aODDaDODbOOOcOOOhBBB1ZZZ',</span> <span class="pre">'full_symbol':</span> <span class="pre">'F2/d2/d2/d',</span> <span class="pre">'int_number':</span> <span class="pre">70,</span> <span class="pre">'order':</span> <span class="pre">32,</span> <span class="pre">'patterson_symmetry':</span> <span class="pre">'Fmmm',</span> <span class="pre">'point_group':</span> <span class="pre">'mmm'},</span> <span class="pre">'Fm-3':</span> <span class="pre">{'enc':</span> <span class="pre">'15aODDaDODbOOOcOOOdOOO0',</span> <span class="pre">'full_symbol':</span> <span class="pre">'F2/m-3',</span> <span class="pre">'int_number':</span> <span class="pre">202,</span> <span class="pre">'order':</span> <span class="pre">96,</span> <span class="pre">'patterson_symmetry':</span> <span class="pre">'Fm-3',</span> <span class="pre">'point_group':</span> <span class="pre">'m-3'},</span> <span class="pre">'Fm-3c':</span> <span class="pre">{'enc':</span> <span class="pre">'16aODDaDODbOOOcOOOdOOOeDDD0',</span> <span class="pre">'full_symbol':</span> <span class="pre">'F4/m-32/c',</span> <span class="pre">'int_number':</span> <span class="pre">226,</span> <span class="pre">'order':</span> <span class="pre">192,</span> <span class="pre">'patterson_symmetry':</span> <span class="pre">'Fm-3m',</span> 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class="pre">'P6/mmm',</span> <span class="pre">'point_group':</span> <span class="pre">'6mm'},</span> <span class="pre">'Pa-3':</span> <span class="pre">{'enc':</span> <span class="pre">'13bDODcODDdOOO0',</span> <span class="pre">'full_symbol':</span> <span class="pre">'P2_1/a-3',</span> <span class="pre">'int_number':</span> <span class="pre">205,</span> <span class="pre">'order':</span> <span class="pre">24,</span> <span class="pre">'patterson_symmetry':</span> <span class="pre">'Pm-3',</span> <span class="pre">'point_group':</span> <span class="pre">'m-3'},</span> <span class="pre">'Pba2':</span> <span class="pre">{'enc':</span> <span class="pre">'02bOOOjDDO0',</span> <span class="pre">'full_symbol':</span> <span class="pre">'Pba2',</span> <span class="pre">'int_number':</span> <span class="pre">32,</span> <span class="pre">'order':</span> <span class="pre">4,</span> <span class="pre">'patterson_symmetry':</span> <span class="pre">'Pmmm',</span> <span class="pre">'point_group':</span> <span class="pre">'mm2'},</span> <span class="pre">'Pbam':</span> <span class="pre">{'enc':</span> <span class="pre">'12bOOOcDDO0',</span> <span class="pre">'full_symbol':</span> <span class="pre">'P2_1/b2_1/a2/m',</span> <span class="pre">'int_number':</span> <span class="pre">55,</span> <span class="pre">'order':</span> <span class="pre">8,</span> <span class="pre">'patterson_symmetry':</span> <span class="pre">'Pmmm',</span> <span class="pre">'point_group':</span> <span class="pre">'mmm'},</span> <span class="pre">'Pban':</span> <span class="pre">{'enc':</span> <span class="pre">'03bOOOcOOOhDDO1BBO',</span> <span class="pre">'full_symbol':</span> <span class="pre">'P2/b2/a2/n',</span> <span class="pre">'int_number':</span> <span class="pre">50,</span> <span class="pre">'order':</span> <span class="pre">8,</span> <span class="pre">'patterson_symmetry':</span> <span class="pre">'Pmmm',</span> <span class="pre">'point_group':</span> <span class="pre">'mmm'},</span> <span class="pre">'Pbca':</span> <span class="pre">{'enc':</span> <span class="pre">'12bDODcODD0',</span> <span class="pre">'full_symbol':</span> <span class="pre">'P2_1/b2_1/c2_1/a',</span> <span class="pre">'int_number':</span> <span class="pre">61,</span> <span class="pre">'order':</span> <span class="pre">8,</span> <span class="pre">'patterson_symmetry':</span> <span class="pre">'Pmmm',</span> <span class="pre">'point_group':</span> <span class="pre">'mmm'},</span> <span class="pre">'Pbcm':</span> <span class="pre">{'enc':</span> <span class="pre">'12bOODcODD0',</span> <span class="pre">'full_symbol':</span> <span class="pre">'P2/b2_1/c2_1/m',</span> <span class="pre">'int_number':</span> <span class="pre">57,</span> <span class="pre">'order':</span> <span class="pre">8,</span> <span class="pre">'patterson_symmetry':</span> <span class="pre">'Pmmm',</span> <span class="pre">'point_group':</span> <span class="pre">'mmm'},</span> <span class="pre">'Pbcn':</span> <span class="pre">{'enc':</span> <span class="pre">'12bDDDcOOD0',</span> <span class="pre">'full_symbol':</span> <span class="pre">'P2_1/b2/c2_1/n',</span> <span class="pre">'int_number':</span> <span class="pre">60,</span> <span class="pre">'order':</span> <span class="pre">8,</span> <span class="pre">'patterson_symmetry':</span> <span class="pre">'Pmmm',</span> <span class="pre">'point_group':</span> <span class="pre">'mmm'},</span> <span class="pre">'Pca2_1':</span> <span class="pre">{'enc':</span> <span class="pre">'02bOODjDOO0',</span> <span class="pre">'full_symbol':</span> <span class="pre">'Pca2_1',</span> <span class="pre">'int_number':</span> <span class="pre">29,</span> <span class="pre">'order':</span> <span class="pre">4,</span> <span class="pre">'patterson_symmetry':</span> <span class="pre">'Pmmm',</span> <span class="pre">'point_group':</span> <span class="pre">'mm2'},</span> <span class="pre">'Pcc2':</span> <span class="pre">{'enc':</span> <span class="pre">'02bOOOjOOD0',</span> <span class="pre">'full_symbol':</span> <span class="pre">'Pcc2',</span> <span class="pre">'int_number':</span> <span class="pre">27,</span> <span class="pre">'order':</span> <span class="pre">4,</span> <span class="pre">'patterson_symmetry':</span> <span class="pre">'Pmmm',</span> <span class="pre">'point_group':</span> <span class="pre">'mm2'},</span> <span class="pre">'Pcca':</span> <span class="pre">{'enc':</span> <span class="pre">'12bDOOcOOD0',</span> <span class="pre">'full_symbol':</span> <span class="pre">'P2_1/c2/c2/a',</span> <span class="pre">'int_number':</span> <span class="pre">54,</span> <span class="pre">'order':</span> <span class="pre">8,</span> <span class="pre">'patterson_symmetry':</span> <span class="pre">'Pmmm',</span> <span class="pre">'point_group':</span> <span class="pre">'mmm'},</span> <span class="pre">'Pccm':</span> <span class="pre">{'enc':</span> <span class="pre">'12bOOOcOOD0',</span> <span class="pre">'full_symbol':</span> <span class="pre">'P2/c2/c2/m',</span> <span class="pre">'int_number':</span> <span class="pre">49,</span> <span class="pre">'order':</span> <span class="pre">8,</span> <span class="pre">'patterson_symmetry':</span> <span class="pre">'Pmmm',</span> <span class="pre">'point_group':</span> <span class="pre">'mmm'},</span> <span class="pre">'Pccn':</span> <span class="pre">{'enc':</span> <span class="pre">'12bDDOcODD0',</span> <span class="pre">'full_symbol':</span> <span class="pre">'P2_1/c2_1/c2/n',</span> <span class="pre">'int_number':</span> <span class="pre">56,</span> <span class="pre">'order':</span> <span class="pre">8,</span> <span class="pre">'patterson_symmetry':</span> <span class="pre">'Pmmm',</span> <span class="pre">'point_group':</span> <span class="pre">'mmm'},</span> <span class="pre">'Pm-3':</span> <span class="pre">{'enc':</span> <span class="pre">'13bOOOcOOOdOOO0',</span> <span class="pre">'full_symbol':</span> <span class="pre">'P2/m-3',</span> <span class="pre">'int_number':</span> <span class="pre">200,</span> <span class="pre">'order':</span> <span class="pre">24,</span> <span class="pre">'patterson_symmetry':</span> <span class="pre">'Pm-3',</span> <span class="pre">'point_group':</span> <span class="pre">'m-3'},</span> <span class="pre">'Pm-3m':</span> <span class="pre">{'enc':</span> <span class="pre">'14bOOOcOOOdOOOeOOO0',</span> <span class="pre">'full_symbol':</span> <span class="pre">'P4/m-32/m',</span> <span class="pre">'int_number':</span> <span class="pre">221,</span> <span class="pre">'order':</span> <span class="pre">48,</span> <span class="pre">'patterson_symmetry':</span> <span class="pre">'Pm-3m',</span> <span class="pre">'point_group':</span> <span class="pre">'m-3m'},</span> <span class="pre">'Pm-3n':</span> <span class="pre">{'enc':</span> <span class="pre">'14bOOOcOOOdOOOeDDD0',</span> <span class="pre">'full_symbol':</span> <span class="pre">'P4_2/m-32/n',</span> <span class="pre">'int_number':</span> <span class="pre">223,</span> <span class="pre">'order':</span> <span class="pre">48,</span> <span class="pre">'patterson_symmetry':</span> <span class="pre">'Pm-3m',</span> <span class="pre">'point_group':</span> <span class="pre">'m-3m'},</span> <span class="pre">'Pma2':</span> <span class="pre">{'enc':</span> <span class="pre">'02bOOOjDOO0',</span> <span class="pre">'full_symbol':</span> <span class="pre">'Pma2',</span> <span class="pre">'int_number':</span> <span class="pre">28,</span> <span class="pre">'order':</span> <span class="pre">4,</span> <span class="pre">'patterson_symmetry':</span> <span class="pre">'Pmmm',</span> <span class="pre">'point_group':</span> <span class="pre">'mm2'},</span> <span class="pre">'Pmc2_1':</span> <span class="pre">{'enc':</span> <span class="pre">'02bOODjOOD0',</span> <span class="pre">'full_symbol':</span> <span class="pre">'Pmc2_1',</span> <span class="pre">'int_number':</span> <span class="pre">26,</span> <span class="pre">'order':</span> <span class="pre">4,</span> <span class="pre">'patterson_symmetry':</span> <span class="pre">'Pmmm',</span> <span class="pre">'point_group':</span> <span class="pre">'mm2'},</span> <span class="pre">'Pmm2':</span> <span class="pre">{'enc':</span> <span class="pre">'02bOOOjOOO0',</span> <span class="pre">'full_symbol':</span> <span class="pre">'Pmm2',</span> <span class="pre">'int_number':</span> <span class="pre">25,</span> <span class="pre">'order':</span> <span class="pre">4,</span> <span class="pre">'patterson_symmetry':</span> <span class="pre">'Pmmm',</span> <span class="pre">'point_group':</span> <span class="pre">'mm2'},</span> <span class="pre">'Pmma':</span> <span class="pre">{'enc':</span> <span class="pre">'12bDOOcOOO0',</span> <span class="pre">'full_symbol':</span> <span class="pre">'P2_1/m2/m2/a',</span> <span class="pre">'int_number':</span> <span class="pre">51,</span> <span class="pre">'order':</span> <span class="pre">8,</span> <span class="pre">'patterson_symmetry':</span> <span class="pre">'Pmmm',</span> <span class="pre">'point_group':</span> <span class="pre">'mmm'},</span> <span class="pre">'Pmmm':</span> <span class="pre">{'enc':</span> <span class="pre">'12bOOOcOOO0',</span> <span class="pre">'full_symbol':</span> <span class="pre">'P2/m2/m2/m',</span> <span class="pre">'int_number':</span> <span class="pre">47,</span> <span class="pre">'order':</span> <span class="pre">8,</span> <span class="pre">'patterson_symmetry':</span> <span class="pre">'Pmmm',</span> <span class="pre">'point_group':</span> <span class="pre">'mmm'},</span> <span class="pre">'Pmmn':</span> <span class="pre">{'enc':</span> <span class="pre">'03bOOOcDDOhDDO1BBO',</span> <span class="pre">'full_symbol':</span> <span class="pre">'P2_1/m2_1/m2/n',</span> <span class="pre">'int_number':</span> <span class="pre">59,</span> <span class="pre">'order':</span> <span class="pre">8,</span> <span class="pre">'patterson_symmetry':</span> <span class="pre">'Pmmm',</span> <span class="pre">'point_group':</span> <span class="pre">'mmm'},</span> <span class="pre">'Pmn2_1':</span> <span class="pre">{'enc':</span> <span class="pre">'02bDODjDOD0',</span> <span class="pre">'full_symbol':</span> <span class="pre">'Pmn2_1',</span> <span class="pre">'int_number':</span> <span class="pre">31,</span> <span class="pre">'order':</span> <span class="pre">4,</span> <span class="pre">'patterson_symmetry':</span> <span class="pre">'Pmmm',</span> <span class="pre">'point_group':</span> <span class="pre">'mm2'},</span> <span class="pre">'Pmna':</span> <span class="pre">{'enc':</span> <span class="pre">'12bDODcDOD0',</span> <span class="pre">'full_symbol':</span> <span class="pre">'P2/m2/n2_1/a',</span> <span class="pre">'int_number':</span> <span class="pre">53,</span> <span class="pre">'order':</span> <span class="pre">8,</span> <span class="pre">'patterson_symmetry':</span> <span class="pre">'Pmmm',</span> <span class="pre">'point_group':</span> <span class="pre">'mmm'},</span> <span class="pre">'Pn-3':</span> <span class="pre">{'enc':</span> <span class="pre">'04bOOOcOOOdOOOhDDD1YYY',</span> <span class="pre">'full_symbol':</span> <span class="pre">'P2/n-3',</span> <span class="pre">'int_number':</span> <span class="pre">201,</span> <span class="pre">'order':</span> <span class="pre">24,</span> <span class="pre">'patterson_symmetry':</span> <span class="pre">'Pm-3',</span> <span class="pre">'point_group':</span> <span class="pre">'m-3'},</span> <span class="pre">'Pn-3m':</span> <span class="pre">{'enc':</span> <span class="pre">'05bOOOcOOOdOOOeDDDhDDD1YYY',</span> <span class="pre">'full_symbol':</span> <span class="pre">'P4_2/n-32/m',</span> <span class="pre">'int_number':</span> <span class="pre">224,</span> <span class="pre">'order':</span> <span class="pre">48,</span> <span class="pre">'patterson_symmetry':</span> <span class="pre">'Pm-3m',</span> <span class="pre">'point_group':</span> <span class="pre">'m-3m'},</span> <span class="pre">'Pn-3n':</span> <span class="pre">{'enc':</span> <span class="pre">'05bOOOcOOOdOOOeOOOhDDD1YYY',</span> <span class="pre">'full_symbol':</span> <span class="pre">'P4/n-32/n',</span> <span class="pre">'int_number':</span> <span class="pre">222,</span> <span class="pre">'order':</span> <span class="pre">48,</span> <span class="pre">'patterson_symmetry':</span> <span class="pre">'Pm-3m',</span> <span class="pre">'point_group':</span> <span class="pre">'m-3m'},</span> <span class="pre">'Pna2_1':</span> <span class="pre">{'enc':</span> <span class="pre">'02bOODjDDO0',</span> <span class="pre">'full_symbol':</span> <span class="pre">'Pna2_1',</span> <span class="pre">'int_number':</span> <span class="pre">33,</span> <span class="pre">'order':</span> <span class="pre">4,</span> <span class="pre">'patterson_symmetry':</span> <span class="pre">'Pmmm',</span> <span class="pre">'point_group':</span> <span class="pre">'mm2'},</span> <span class="pre">'Pnc2':</span> <span class="pre">{'enc':</span> <span class="pre">'02bOOOjODD0',</span> <span class="pre">'full_symbol':</span> <span class="pre">'Pnc2',</span> <span class="pre">'int_number':</span> <span class="pre">30,</span> <span class="pre">'order':</span> <span class="pre">4,</span> <span class="pre">'patterson_symmetry':</span> <span class="pre">'Pmmm',</span> <span class="pre">'point_group':</span> <span class="pre">'mm2'},</span> <span class="pre">'Pnma':</span> <span class="pre">{'enc':</span> <span class="pre">'12bDODcODO0',</span> <span class="pre">'full_symbol':</span> <span class="pre">'P2_1/n2_1/m2_1/a',</span> <span class="pre">'int_number':</span> <span class="pre">62,</span> <span class="pre">'order':</span> <span class="pre">8,</span> <span class="pre">'patterson_symmetry':</span> <span class="pre">'Pmmm',</span> <span class="pre">'point_group':</span> <span class="pre">'mmm'},</span> <span class="pre">'Pnn2':</span> <span class="pre">{'enc':</span> <span class="pre">'02bOOOjDDD0',</span> <span class="pre">'full_symbol':</span> <span class="pre">'Pnn2',</span> <span class="pre">'int_number':</span> <span class="pre">34,</span> <span class="pre">'order':</span> <span class="pre">4,</span> <span class="pre">'patterson_symmetry':</span> <span class="pre">'Pmmm',</span> <span class="pre">'point_group':</span> <span class="pre">'mm2'},</span> <span class="pre">'Pnna':</span> <span class="pre">{'enc':</span> <span class="pre">'12bDOOcDDD0',</span> <span class="pre">'full_symbol':</span> <span class="pre">'P2/n2_1/n2/a',</span> <span class="pre">'int_number':</span> <span class="pre">52,</span> <span class="pre">'order':</span> <span class="pre">8,</span> <span class="pre">'patterson_symmetry':</span> <span class="pre">'Pmmm',</span> <span class="pre">'point_group':</span> <span class="pre">'mmm'},</span> <span class="pre">'Pnnm':</span> <span class="pre">{'enc':</span> <span class="pre">'12bOOOcDDD0',</span> <span class="pre">'full_symbol':</span> <span class="pre">'P2_1/n2_1/n2/m',</span> <span class="pre">'int_number':</span> <span class="pre">58,</span> <span class="pre">'order':</span> <span class="pre">8,</span> <span class="pre">'patterson_symmetry':</span> <span class="pre">'Pmmm',</span> <span class="pre">'point_group':</span> <span class="pre">'mmm'},</span> <span class="pre">'Pnnn':</span> <span class="pre">{'enc':</span> <span class="pre">'03bOOOcOOOhDDD1BBB',</span> <span class="pre">'full_symbol':</span> <span class="pre">'P2/n2/n2/n',</span> <span class="pre">'int_number':</span> <span class="pre">48,</span> <span class="pre">'order':</span> <span class="pre">8,</span> <span class="pre">'patterson_symmetry':</span> <span class="pre">'Pmmm',</span> <span class="pre">'point_group':</span> <span class="pre">'mmm'},</span> <span class="pre">'R-3':</span> <span class="pre">{'enc':</span> <span class="pre">'12aECCnOOO0',</span> <span class="pre">'full_symbol':</span> <span class="pre">'R-3',</span> <span class="pre">'int_number':</span> <span class="pre">148,</span> <span class="pre">'order':</span> <span class="pre">18,</span> <span class="pre">'patterson_symmetry':</span> <span class="pre">'R-3',</span> <span class="pre">'point_group':</span> <span class="pre">'-3'},</span> <span class="pre">'R-3c':</span> <span class="pre">{'enc':</span> <span class="pre">'13aECCnOOOeOOD0',</span> <span class="pre">'full_symbol':</span> <span class="pre">'R-32/c',</span> <span class="pre">'int_number':</span> <span class="pre">167,</span> <span class="pre">'order':</span> <span class="pre">36,</span> <span class="pre">'patterson_symmetry':</span> <span class="pre">'R-3m',</span> <span class="pre">'point_group':</span> <span class="pre">'-3m'},</span> <span class="pre">'R-3m':</span> <span class="pre">{'enc':</span> <span class="pre">'13aECCnOOOeOOO0',</span> <span class="pre">'full_symbol':</span> <span class="pre">'R-32/m',</span> <span class="pre">'int_number':</span> <span class="pre">166,</span> <span class="pre">'order':</span> <span class="pre">36,</span> <span class="pre">'patterson_symmetry':</span> <span class="pre">'R-3m',</span> <span class="pre">'point_group':</span> <span class="pre">'-3m'},</span> <span class="pre">'R3':</span> <span class="pre">{'enc':</span> <span class="pre">'02aECCnOOO0',</span> <span class="pre">'full_symbol':</span> <span class="pre">'R3',</span> <span class="pre">'int_number':</span> <span class="pre">146,</span> <span class="pre">'order':</span> <span class="pre">9,</span> <span class="pre">'patterson_symmetry':</span> <span class="pre">'R-3',</span> <span class="pre">'point_group':</span> <span class="pre">'3'},</span> <span class="pre">'R32':</span> <span class="pre">{'enc':</span> <span class="pre">'03aECCnOOOeOOO0',</span> <span class="pre">'full_symbol':</span> <span class="pre">'R32',</span> <span class="pre">'int_number':</span> <span class="pre">155,</span> <span class="pre">'order':</span> <span class="pre">18,</span> <span class="pre">'patterson_symmetry':</span> <span class="pre">'R-3m',</span> <span class="pre">'point_group':</span> <span class="pre">'32'},</span> <span class="pre">'R3c':</span> <span class="pre">{'enc':</span> <span class="pre">'03aECCnOOOkOOD0',</span> <span class="pre">'full_symbol':</span> <span class="pre">'R3c',</span> <span class="pre">'int_number':</span> <span class="pre">161,</span> <span class="pre">'order':</span> <span class="pre">18,</span> <span class="pre">'patterson_symmetry':</span> <span class="pre">'R-3m',</span> <span class="pre">'point_group':</span> <span class="pre">'3m'},</span> <span class="pre">'R3m':</span> <span class="pre">{'enc':</span> <span class="pre">'03aECCnOOOkOOO0',</span> <span class="pre">'full_symbol':</span> <span class="pre">'R3m',</span> <span class="pre">'int_number':</span> <span class="pre">160,</span> <span class="pre">'order':</span> <span class="pre">18,</span> <span class="pre">'patterson_symmetry':</span> <span class="pre">'R-3m',</span> <span class="pre">'point_group':</span> <span class="pre">'3m'}}</span></em><a class="reference external" href="https://github.com/materialsproject/pymatgen/blob/v2025.1.24/src/pymatgen/symmetry/groups.py"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pymatgen.symmetry.groups.SpaceGroup.sg_encoding" title="Link to this definition"></a></dt>
<dd></dd></dl>

<dl class="py property">
<dt class="sig sig-object py" id="pymatgen.symmetry.groups.SpaceGroup.symmetry_ops">
<em class="property"><span class="pre">property</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">symmetry_ops</span></span><em class="property"><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="pre">set</span><span class="p"><span class="pre">[</span></span><a class="reference internal" href="pymatgen.core.html#pymatgen.core.operations.SymmOp" title="pymatgen.core.operations.SymmOp"><span class="pre">SymmOp</span></a><span class="p"><span class="pre">]</span></span></em><a class="reference external" href="https://github.com/materialsproject/pymatgen/blob/v2025.1.24/src/pymatgen/symmetry/groups.py"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pymatgen.symmetry.groups.SpaceGroup.symmetry_ops" title="Link to this definition"></a></dt>
<dd><p>Full set of symmetry operations as matrices. Lazily initialized as
generation sometimes takes a bit of time.</p>
</dd></dl>

<dl class="py method">
<dt class="sig sig-object py" id="pymatgen.symmetry.groups.SpaceGroup.to_pretty_string">
<span class="sig-name descname"><span class="pre">to_pretty_string</span></span><span class="sig-paren">(</span><span class="sig-paren">)</span> <span class="sig-return"><span class="sig-return-icon">&#x2192;</span> <span class="sig-return-typehint"><span class="pre">str</span></span></span><a class="reference external" href="https://github.com/materialsproject/pymatgen/blob/v2025.1.24/src/pymatgen/core/../symmetry/groups.py#L694-L699"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pymatgen.symmetry.groups.SpaceGroup.to_pretty_string" title="Link to this definition"></a></dt>
<dd><dl class="field-list simple">
<dt class="field-odd">Returns<span class="colon">:</span></dt>
<dd class="field-odd"><p>A pretty string representation of the space group.</p>
</dd>
<dt class="field-even">Return type<span class="colon">:</span></dt>
<dd class="field-even"><p>str</p>
</dd>
</dl>
</dd></dl>

<dl class="py attribute">
<dt class="sig sig-object py" id="pymatgen.symmetry.groups.SpaceGroup.translations">
<span class="sig-name descname"><span class="pre">translations</span></span><em class="property"><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="pre">ClassVar</span><span class="p"><span class="pre">[</span></span><span class="pre">dict</span><span class="p"><span class="pre">[</span></span><span class="pre">str</span><span class="p"><span class="pre">,</span></span><span class="w"> </span><span class="pre">Fraction</span><span class="p"><span class="pre">]</span></span><span class="p"><span class="pre">]</span></span></em><em class="property"><span class="w"> </span><span class="p"><span class="pre">=</span></span><span class="w"> </span><span class="pre">{'A':</span> <span class="pre">Fraction(1,</span> <span class="pre">6),</span> <span class="pre">'B':</span> <span class="pre">Fraction(1,</span> <span class="pre">4),</span> <span class="pre">'C':</span> <span class="pre">Fraction(1,</span> <span class="pre">3),</span> <span class="pre">'D':</span> <span class="pre">Fraction(1,</span> <span class="pre">2),</span> <span class="pre">'E':</span> <span class="pre">Fraction(2,</span> <span class="pre">3),</span> <span class="pre">'F':</span> <span class="pre">Fraction(3,</span> <span class="pre">4),</span> <span class="pre">'G':</span> <span class="pre">Fraction(5,</span> <span class="pre">6),</span> <span class="pre">'O':</span> <span class="pre">Fraction(0,</span> <span class="pre">1),</span> <span class="pre">'X':</span> <span class="pre">Fraction(-3,</span> <span class="pre">8),</span> <span class="pre">'Y':</span> <span class="pre">Fraction(-1,</span> <span class="pre">4),</span> <span class="pre">'Z':</span> <span class="pre">Fraction(-1,</span> <span class="pre">8)}</span></em><a class="reference external" href="https://github.com/materialsproject/pymatgen/blob/v2025.1.24/src/pymatgen/symmetry/groups.py"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pymatgen.symmetry.groups.SpaceGroup.translations" title="Link to this definition"></a></dt>
<dd></dd></dl>

</dd></dl>

<dl class="py class">
<dt class="sig sig-object py" id="pymatgen.symmetry.groups.SymmetryGroup">
<em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">SymmetryGroup</span></span><a class="reference external" href="https://github.com/materialsproject/pymatgen/blob/v2025.1.24/src/pymatgen/core/../symmetry/groups.py#L67-L137"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pymatgen.symmetry.groups.SymmetryGroup" title="Link to this definition"></a></dt>
<dd><p>Bases: <code class="xref py py-class docutils literal notranslate"><span class="pre">Sequence</span></code>, <a class="reference internal" href="pymatgen.util.html#pymatgen.util.string.Stringify" title="pymatgen.util.string.Stringify"><code class="xref py py-class docutils literal notranslate"><span class="pre">Stringify</span></code></a>, <code class="xref py py-class docutils literal notranslate"><span class="pre">ABC</span></code></p>
<p>Abstract class representing a symmetry group.</p>
<dl class="py method">
<dt class="sig sig-object py" id="pymatgen.symmetry.groups.SymmetryGroup.is_subgroup">
<span class="sig-name descname"><span class="pre">is_subgroup</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">supergroup</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><a class="reference internal" href="#pymatgen.symmetry.groups.SymmetryGroup" title="pymatgen.symmetry.groups.SymmetryGroup"><span class="pre">SymmetryGroup</span></a></span></em><span class="sig-paren">)</span> <span class="sig-return"><span class="sig-return-icon">&#x2192;</span> <span class="sig-return-typehint"><span class="pre">bool</span></span></span><a class="reference external" href="https://github.com/materialsproject/pymatgen/blob/v2025.1.24/src/pymatgen/core/../symmetry/groups.py#L99-L113"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pymatgen.symmetry.groups.SymmetryGroup.is_subgroup" title="Link to this definition"></a></dt>
<dd><p>True if this group is a subgroup of the supplied group.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
<dd class="field-odd"><p><strong>supergroup</strong> (<a class="reference internal" href="#pymatgen.symmetry.groups.SymmetryGroup" title="pymatgen.symmetry.groups.SymmetryGroup"><em>SymmetryGroup</em></a>) – Supergroup to test.</p>
</dd>
<dt class="field-even">Returns<span class="colon">:</span></dt>
<dd class="field-even"><p>True if this group is a subgroup of the supplied group.</p>
</dd>
<dt class="field-odd">Return type<span class="colon">:</span></dt>
<dd class="field-odd"><p>bool</p>
</dd>
</dl>
</dd></dl>

<dl class="py method">
<dt class="sig sig-object py" id="pymatgen.symmetry.groups.SymmetryGroup.is_supergroup">
<span class="sig-name descname"><span class="pre">is_supergroup</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">subgroup</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><a class="reference internal" href="#pymatgen.symmetry.groups.SymmetryGroup" title="pymatgen.symmetry.groups.SymmetryGroup"><span class="pre">SymmetryGroup</span></a></span></em><span class="sig-paren">)</span> <span class="sig-return"><span class="sig-return-icon">&#x2192;</span> <span class="sig-return-typehint"><span class="pre">bool</span></span></span><a class="reference external" href="https://github.com/materialsproject/pymatgen/blob/v2025.1.24/src/pymatgen/core/../symmetry/groups.py#L115-L129"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pymatgen.symmetry.groups.SymmetryGroup.is_supergroup" title="Link to this definition"></a></dt>
<dd><p>True if this group is a supergroup of the supplied group.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
<dd class="field-odd"><p><strong>subgroup</strong> (<a class="reference internal" href="#pymatgen.symmetry.groups.SymmetryGroup" title="pymatgen.symmetry.groups.SymmetryGroup"><em>SymmetryGroup</em></a>) – Subgroup to test.</p>
</dd>
<dt class="field-even">Returns<span class="colon">:</span></dt>
<dd class="field-even"><p>True if this group is a supergroup of the supplied group.</p>
</dd>
<dt class="field-odd">Return type<span class="colon">:</span></dt>
<dd class="field-odd"><p>bool</p>
</dd>
</dl>
</dd></dl>

<dl class="py property">
<dt class="sig sig-object py" id="pymatgen.symmetry.groups.SymmetryGroup.symmetry_ops">
<em class="property"><span class="pre">abstract</span><span class="w"> </span><span class="pre">property</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">symmetry_ops</span></span><em class="property"><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="pre">set</span><span class="p"><span class="pre">[</span></span><a class="reference internal" href="pymatgen.core.html#pymatgen.core.operations.SymmOp" title="pymatgen.core.operations.SymmOp"><span class="pre">SymmOp</span></a><span class="p"><span class="pre">]</span></span></em><a class="reference external" href="https://github.com/materialsproject/pymatgen/blob/v2025.1.24/src/pymatgen/symmetry/groups.py"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pymatgen.symmetry.groups.SymmetryGroup.symmetry_ops" title="Link to this definition"></a></dt>
<dd><p>Returns:
List of symmetry operations associated with the group.</p>
</dd></dl>

<dl class="py method">
<dt class="sig sig-object py" id="pymatgen.symmetry.groups.SymmetryGroup.to_latex_string">
<span class="sig-name descname"><span class="pre">to_latex_string</span></span><span class="sig-paren">(</span><span class="sig-paren">)</span> <span class="sig-return"><span class="sig-return-icon">&#x2192;</span> <span class="sig-return-typehint"><span class="pre">str</span></span></span><a class="reference external" href="https://github.com/materialsproject/pymatgen/blob/v2025.1.24/src/pymatgen/core/../symmetry/groups.py#L131-L137"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pymatgen.symmetry.groups.SymmetryGroup.to_latex_string" title="Link to this definition"></a></dt>
<dd><dl class="field-list simple">
<dt class="field-odd">Returns<span class="colon">:</span></dt>
<dd class="field-odd"><p>A latex formatted group symbol with proper subscripts and overlines.</p>
</dd>
</dl>
</dd></dl>

</dd></dl>

<dl class="py function">
<dt class="sig sig-object py" id="pymatgen.symmetry.groups.in_array_list">
<span class="sig-name descname"><span class="pre">in_array_list</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">array_list</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">list</span><span class="p"><span class="pre">[</span></span><span class="pre">ndarray</span><span class="p"><span class="pre">]</span></span><span class="w"> </span><span class="p"><span class="pre">|</span></span><span class="w"> </span><span class="pre">ndarray</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">arr</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">ndarray</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">tol</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">float</span></span><span class="w"> </span><span class="o"><span class="pre">=</span></span><span class="w"> </span><span class="default_value"><span class="pre">1e-05</span></span></em><span class="sig-paren">)</span> <span class="sig-return"><span class="sig-return-icon">&#x2192;</span> <span class="sig-return-typehint"><span class="pre">bool</span></span></span><a class="reference external" href="https://github.com/materialsproject/pymatgen/blob/v2025.1.24/src/pymatgen/core/../symmetry/groups.py#L731-L749"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pymatgen.symmetry.groups.in_array_list" title="Link to this definition"></a></dt>
<dd><p>Extremely efficient nd-array comparison using numpy’s broadcasting. This
function checks if a particular array a, is present in a list of arrays.
It works for arrays of any size, e.g. even matrix searches.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>array_list</strong> (<em>[</em><em>array</em><em>]</em>) – A list of arrays to compare to.</p></li>
<li><p><strong>arr</strong> (<em>array</em>) – The test array for comparison.</p></li>
<li><p><strong>tol</strong> (<em>float</em>) – The tolerance. Defaults to 1e-5. If 0, an exact match is done.</p></li>
</ul>
</dd>
<dt class="field-even">Returns<span class="colon">:</span></dt>
<dd class="field-even"><p>True if arr is in array_list.</p>
</dd>
<dt class="field-odd">Return type<span class="colon">:</span></dt>
<dd class="field-odd"><p>bool</p>
</dd>
</dl>
</dd></dl>

<dl class="py function">
<dt class="sig sig-object py" id="pymatgen.symmetry.groups.sg_symbol_from_int_number">
<span class="sig-name descname"><span class="pre">sg_symbol_from_int_number</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">int_number</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">int</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">hexagonal</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">bool</span></span><span class="w"> </span><span class="o"><span class="pre">=</span></span><span class="w"> </span><span class="default_value"><span class="pre">True</span></span></em><span class="sig-paren">)</span> <span class="sig-return"><span class="sig-return-icon">&#x2192;</span> <span class="sig-return-typehint"><span class="pre">str</span></span></span><a class="reference external" href="https://github.com/materialsproject/pymatgen/blob/v2025.1.24/src/pymatgen/core/../symmetry/groups.py#L702-L728"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pymatgen.symmetry.groups.sg_symbol_from_int_number" title="Link to this definition"></a></dt>
<dd><p>Obtains a SpaceGroup name from its international number.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>int_number</strong> (<em>int</em>) – International number.</p></li>
<li><p><strong>hexagonal</strong> (<em>bool</em>) – For rhombohedral groups, whether to return the
hexagonal setting (default) or rhombohedral setting.</p></li>
</ul>
</dd>
<dt class="field-even">Returns<span class="colon">:</span></dt>
<dd class="field-even"><p><dl class="simple">
<dt>Spacegroup symbol / Space group symbol + “H” if group is</dt><dd><p>rhombohedral and hexagonal=True</p>
</dd>
</dl>
</p>
</dd>
<dt class="field-odd">Return type<span class="colon">:</span></dt>
<dd class="field-odd"><p>str</p>
</dd>
</dl>
</dd></dl>

</section>
<section id="module-pymatgen.symmetry.kpath">
<span id="pymatgen-symmetry-kpath-module"></span><h2>pymatgen.symmetry.kpath module<a class="headerlink" href="#module-pymatgen.symmetry.kpath" title="Link to this heading"></a></h2>
<p>Classes for generating high-symmetry k-paths using different conventions.</p>
<dl class="py class">
<dt class="sig sig-object py" id="pymatgen.symmetry.kpath.KPathBase">
<em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">KPathBase</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">structure</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><a class="reference internal" href="pymatgen.core.html#pymatgen.core.structure.Structure" title="pymatgen.core.structure.Structure"><span class="pre">Structure</span></a></span></em>, <em class="sig-param"><span class="n"><span class="pre">symprec</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">float</span></span><span class="w"> </span><span class="o"><span class="pre">=</span></span><span class="w"> </span><span class="default_value"><span class="pre">0.01</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">angle_tolerance</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">5</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">atol</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">1e-05</span></span></em>, <em class="sig-param"><span class="o"><span class="pre">*</span></span><span class="n"><span class="pre">args</span></span></em>, <em class="sig-param"><span class="o"><span class="pre">**</span></span><span class="n"><span class="pre">kwargs</span></span></em><span class="sig-paren">)</span><a class="reference external" href="https://github.com/materialsproject/pymatgen/blob/v2025.1.24/src/pymatgen/core/../symmetry/kpath.py#L41-L121"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pymatgen.symmetry.kpath.KPathBase" title="Link to this definition"></a></dt>
<dd><p>Bases: <code class="xref py py-class docutils literal notranslate"><span class="pre">ABC</span></code></p>
<p>This is the base class for classes used to generate high-symmetry
paths in reciprocal space (k-paths) for band structure calculations.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>structure</strong> (<a class="reference internal" href="pymatgen.core.html#pymatgen.core.structure.Structure" title="pymatgen.core.structure.Structure"><em>Structure</em></a>) – Structure object.</p></li>
<li><p><strong>symprec</strong> (<em>float</em>) – Tolerance for symmetry finding.</p></li>
<li><p><strong>angle_tolerance</strong> (<em>float</em>) – Angle tolerance for symmetry finding.</p></li>
<li><p><strong>atol</strong> (<em>float</em>) – Absolute tolerance used to compare structures
and determine symmetric equivalence of points and lines in the BZ.</p></li>
<li><p><strong>*args</strong> – Other arguments supported by subclasses.</p></li>
<li><p><strong>**kwargs</strong> – Other keyword arguments supported by subclasses.</p></li>
</ul>
</dd>
</dl>
<dl class="py method">
<dt class="sig sig-object py" id="pymatgen.symmetry.kpath.KPathBase.get_kpoints">
<span class="sig-name descname"><span class="pre">get_kpoints</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">line_density</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">20</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">coords_are_cartesian</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">True</span></span></em><span class="sig-paren">)</span><a class="reference external" href="https://github.com/materialsproject/pymatgen/blob/v2025.1.24/src/pymatgen/core/../symmetry/kpath.py#L95-L121"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pymatgen.symmetry.kpath.KPathBase.get_kpoints" title="Link to this definition"></a></dt>
<dd><p>Get kpoints along the path in Cartesian coordinates together with the critical-point labels.</p>
</dd></dl>

<dl class="py property">
<dt class="sig sig-object py" id="pymatgen.symmetry.kpath.KPathBase.kpath">
<em class="property"><span class="pre">property</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">kpath</span></span><a class="reference external" href="https://github.com/materialsproject/pymatgen/blob/v2025.1.24/src/pymatgen/symmetry/kpath.py"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pymatgen.symmetry.kpath.KPathBase.kpath" title="Link to this definition"></a></dt>
<dd><p>The symmetry line path in reciprocal space.</p>
</dd></dl>

<dl class="py property">
<dt class="sig sig-object py" id="pymatgen.symmetry.kpath.KPathBase.lattice">
<em class="property"><span class="pre">property</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">lattice</span></span><a class="reference external" href="https://github.com/materialsproject/pymatgen/blob/v2025.1.24/src/pymatgen/symmetry/kpath.py"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pymatgen.symmetry.kpath.KPathBase.lattice" title="Link to this definition"></a></dt>
<dd><p>The real space lattice.</p>
</dd></dl>

<dl class="py property">
<dt class="sig sig-object py" id="pymatgen.symmetry.kpath.KPathBase.rec_lattice">
<em class="property"><span class="pre">property</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">rec_lattice</span></span><a class="reference external" href="https://github.com/materialsproject/pymatgen/blob/v2025.1.24/src/pymatgen/symmetry/kpath.py"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pymatgen.symmetry.kpath.KPathBase.rec_lattice" title="Link to this definition"></a></dt>
<dd><p>The reciprocal space lattice.</p>
</dd></dl>

<dl class="py property">
<dt class="sig sig-object py" id="pymatgen.symmetry.kpath.KPathBase.structure">
<em class="property"><span class="pre">property</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">structure</span></span><a class="reference external" href="https://github.com/materialsproject/pymatgen/blob/v2025.1.24/src/pymatgen/symmetry/kpath.py"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pymatgen.symmetry.kpath.KPathBase.structure" title="Link to this definition"></a></dt>
<dd><p>The input structure.</p>
</dd></dl>

</dd></dl>

<dl class="py class">
<dt class="sig sig-object py" id="pymatgen.symmetry.kpath.KPathLatimerMunro">
<em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">KPathLatimerMunro</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">structure</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">has_magmoms</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">False</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">magmom_axis</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">symprec</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">0.01</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">angle_tolerance</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">5</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">atol</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">1e-05</span></span></em><span class="sig-paren">)</span><a class="reference external" href="https://github.com/materialsproject/pymatgen/blob/v2025.1.24/src/pymatgen/core/../symmetry/kpath.py#L1003-L2167"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pymatgen.symmetry.kpath.KPathLatimerMunro" title="Link to this definition"></a></dt>
<dd><p>Bases: <a class="reference internal" href="#pymatgen.symmetry.kpath.KPathBase" title="pymatgen.symmetry.kpath.KPathBase"><code class="xref py py-class docutils literal notranslate"><span class="pre">KPathBase</span></code></a></p>
<p>This class looks for a path along high-symmetry lines in the
Brillouin zone. It is based on the method outlined in:
npj Comput Mater 6, 112 (2020). 10.1038/s41524-020-00383-7
The user should ensure that the unit cell of the input structure
is as reduced as possible, i.e. that there is no linear
combination of lattice vectors which can produce a vector of
lesser magnitude than the given set (this is required to
obtain the correct Brillouin zone within the current
implementation). This is checked during initialization and a
warning is issued if the condition is not fulfilled.
In the case of magnetic structures, care must also be taken to
provide the magnetic primitive cell (i.e. that which reproduces
the entire crystal, including the correct magnetic ordering,
upon application of lattice translations). There is no algorithm to</p>
<blockquote>
<div><p>check for this, so if the input structure is</p>
</div></blockquote>
<p>incorrect, the class will output the incorrect k-path without
any warning being issued.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>structure</strong> (<a class="reference internal" href="pymatgen.core.html#pymatgen.core.structure.Structure" title="pymatgen.core.structure.Structure"><em>Structure</em></a>) – Structure object</p></li>
<li><p><strong>has_magmoms</strong> (<em>bool</em>) – Whether the input structure contains
magnetic moments as site properties with the key ‘magmom.’
Values may be in the form of 3-component vectors given in
the basis of the input lattice vectors, or as scalars, in
which case the spin axis will default to a_3, the third
real-space lattice vector (this triggers a warning).</p></li>
<li><p><strong>magmom_axis</strong> (<em>list</em><em> or </em><em>numpy array</em>) – 3-component vector specifying
direction along which magnetic moments given as scalars
should point. If all magnetic moments are provided as
vectors then this argument is not used.</p></li>
<li><p><strong>symprec</strong> (<em>float</em>) – Tolerance for symmetry finding</p></li>
<li><p><strong>angle_tolerance</strong> (<em>float</em>) – Angle tolerance for symmetry finding.</p></li>
<li><p><strong>atol</strong> (<em>float</em>) – Absolute tolerance used to determine symmetric
equivalence of points and lines in the BZ.</p></li>
</ul>
</dd>
</dl>
<dl class="py method">
<dt class="sig sig-object py" id="pymatgen.symmetry.kpath.KPathLatimerMunro.label_points">
<em class="property"><span class="pre">static</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">label_points</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">index</span></span></em><span class="sig-paren">)</span><a class="reference external" href="https://github.com/materialsproject/pymatgen/blob/v2025.1.24/src/pymatgen/core/../symmetry/kpath.py#L2129-L2161"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pymatgen.symmetry.kpath.KPathLatimerMunro.label_points" title="Link to this definition"></a></dt>
<dd><p>Axes used in generating labels for Latimer-Munro convention.</p>
</dd></dl>

<dl class="py method">
<dt class="sig sig-object py" id="pymatgen.symmetry.kpath.KPathLatimerMunro.label_symbol">
<em class="property"><span class="pre">static</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">label_symbol</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">index</span></span></em><span class="sig-paren">)</span><a class="reference external" href="https://github.com/materialsproject/pymatgen/blob/v2025.1.24/src/pymatgen/core/../symmetry/kpath.py#L2163-L2167"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pymatgen.symmetry.kpath.KPathLatimerMunro.label_symbol" title="Link to this definition"></a></dt>
<dd><p>Letters used in generating labels for the Latimer-Munro convention.</p>
</dd></dl>

<dl class="py property">
<dt class="sig sig-object py" id="pymatgen.symmetry.kpath.KPathLatimerMunro.mag_type">
<em class="property"><span class="pre">property</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">mag_type</span></span><a class="reference external" href="https://github.com/materialsproject/pymatgen/blob/v2025.1.24/src/pymatgen/symmetry/kpath.py"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pymatgen.symmetry.kpath.KPathLatimerMunro.mag_type" title="Link to this definition"></a></dt>
<dd><p>The type of magnetic space group as a string. Current implementation does not
distinguish between types 3 and 4, so return value is ‘3/4’. If has_magmoms is
False, returns ‘0’.</p>
</dd></dl>

</dd></dl>

<dl class="py class">
<dt class="sig sig-object py" id="pymatgen.symmetry.kpath.KPathSeek">
<em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">KPathSeek</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">structure</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><a class="reference internal" href="pymatgen.core.html#pymatgen.core.structure.Structure" title="pymatgen.core.structure.Structure"><span class="pre">Structure</span></a></span></em>, <em class="sig-param"><span class="n"><span class="pre">symprec</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">float</span></span><span class="w"> </span><span class="o"><span class="pre">=</span></span><span class="w"> </span><span class="default_value"><span class="pre">0.01</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">angle_tolerance</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">5</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">atol</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">1e-05</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">system_is_tri</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">True</span></span></em><span class="sig-paren">)</span><a class="reference external" href="https://github.com/materialsproject/pymatgen/blob/v2025.1.24/src/pymatgen/core/../symmetry/kpath.py#L876-L1000"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pymatgen.symmetry.kpath.KPathSeek" title="Link to this definition"></a></dt>
<dd><p>Bases: <a class="reference internal" href="#pymatgen.symmetry.kpath.KPathBase" title="pymatgen.symmetry.kpath.KPathBase"><code class="xref py py-class docutils literal notranslate"><span class="pre">KPathBase</span></code></a></p>
<p>This class looks for a path along high-symmetry lines in the Brillouin zone. It is based on
Hinuma, Y., Pizzi, G., Kumagai, Y., Oba, F., &amp; Tanaka, I. (2017). Band structure diagram paths
based on crystallography. Computational Materials Science, 128, 140-184.
<a class="reference external" href="https://doi.org/10.1016/j.commatsci.2016.10.015">https://doi.org/10.1016/j.commatsci.2016.10.015</a>. It should be used with primitive structures that
comply with the definition given in the paper. The symmetry is determined by spglib using the
SpacegroupAnalyzer class. k-points are generated using the get_kpoints() method for the
reciprocal cell basis defined in the paper.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>structure</strong> (<a class="reference internal" href="pymatgen.core.html#pymatgen.core.structure.Structure" title="pymatgen.core.structure.Structure"><em>Structure</em></a>) – Structure object</p></li>
<li><p><strong>symprec</strong> (<em>float</em>) – Tolerance for symmetry finding</p></li>
<li><p><strong>angle_tolerance</strong> (<em>float</em>) – Angle tolerance for symmetry finding.</p></li>
<li><p><strong>atol</strong> (<em>float</em>) – Absolute tolerance used to determine edge cases
for settings of structures.</p></li>
<li><p><strong>system_is_tri</strong> (<em>bool</em>) – Indicates if the system is time-reversal
invariant.</p></li>
</ul>
</dd>
</dl>
</dd></dl>

<dl class="py class">
<dt class="sig sig-object py" id="pymatgen.symmetry.kpath.KPathSetyawanCurtarolo">
<em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">KPathSetyawanCurtarolo</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">structure</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><a class="reference internal" href="pymatgen.core.html#pymatgen.core.structure.Structure" title="pymatgen.core.structure.Structure"><span class="pre">Structure</span></a></span></em>, <em class="sig-param"><span class="n"><span class="pre">symprec</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">float</span></span><span class="w"> </span><span class="o"><span class="pre">=</span></span><span class="w"> </span><span class="default_value"><span class="pre">0.01</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">angle_tolerance</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">5</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">atol</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">1e-05</span></span></em><span class="sig-paren">)</span><a class="reference external" href="https://github.com/materialsproject/pymatgen/blob/v2025.1.24/src/pymatgen/core/../symmetry/kpath.py#L124-L873"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pymatgen.symmetry.kpath.KPathSetyawanCurtarolo" title="Link to this definition"></a></dt>
<dd><p>Bases: <a class="reference internal" href="#pymatgen.symmetry.kpath.KPathBase" title="pymatgen.symmetry.kpath.KPathBase"><code class="xref py py-class docutils literal notranslate"><span class="pre">KPathBase</span></code></a></p>
<p>This class looks for a path along high-symmetry lines in
the Brillouin zone.
It is based on Setyawan, W., &amp; Curtarolo, S. (2010).
High-throughput electronic band structure calculations:
Challenges and tools. Computational Materials Science,
49(2), 299-312. doi:10.1016/j.commatsci.2010.05.010
It should be used with primitive structures that
comply with the definition given in the paper.
The symmetry is determined by spglib using the
SpacegroupAnalyzer class. The analyzer can be used to
produce the correct primitive structure with the method
get_primitive_standard_structure(international_monoclinic=False).
A warning will signal possible compatibility problems
with the given structure. k-points generated using the get_kpoints() method
are returned for the reciprocal cell basis defined in the paper.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>structure</strong> (<a class="reference internal" href="pymatgen.core.html#pymatgen.core.structure.Structure" title="pymatgen.core.structure.Structure"><em>Structure</em></a>) – Structure object.</p></li>
<li><p><strong>symprec</strong> (<em>float</em>) – Tolerance for symmetry finding.</p></li>
<li><p><strong>angle_tolerance</strong> (<em>float</em>) – Angle tolerance for symmetry finding.</p></li>
<li><p><strong>atol</strong> (<em>float</em>) – Absolute tolerance used to compare the input
structure with the one expected as primitive standard.
A warning will be issued if the cells don’t match.</p></li>
</ul>
</dd>
</dl>
<dl class="py method">
<dt class="sig sig-object py" id="pymatgen.symmetry.kpath.KPathSetyawanCurtarolo.bcc">
<span class="sig-name descname"><span class="pre">bcc</span></span><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="reference external" href="https://github.com/materialsproject/pymatgen/blob/v2025.1.24/src/pymatgen/core/../symmetry/kpath.py#L323-L333"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pymatgen.symmetry.kpath.KPathSetyawanCurtarolo.bcc" title="Link to this definition"></a></dt>
<dd><p>BCC Path.</p>
</dd></dl>

<dl class="py method">
<dt class="sig sig-object py" id="pymatgen.symmetry.kpath.KPathSetyawanCurtarolo.bctet1">
<span class="sig-name descname"><span class="pre">bctet1</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">c</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">a</span></span></em><span class="sig-paren">)</span><a class="reference external" href="https://github.com/materialsproject/pymatgen/blob/v2025.1.24/src/pymatgen/core/../symmetry/kpath.py#L353-L367"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pymatgen.symmetry.kpath.KPathSetyawanCurtarolo.bctet1" title="Link to this definition"></a></dt>
<dd><p>BCT1 Path.</p>
</dd></dl>

<dl class="py method">
<dt class="sig sig-object py" id="pymatgen.symmetry.kpath.KPathSetyawanCurtarolo.bctet2">
<span class="sig-name descname"><span class="pre">bctet2</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">c</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">a</span></span></em><span class="sig-paren">)</span><a class="reference external" href="https://github.com/materialsproject/pymatgen/blob/v2025.1.24/src/pymatgen/core/../symmetry/kpath.py#L369-L401"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pymatgen.symmetry.kpath.KPathSetyawanCurtarolo.bctet2" title="Link to this definition"></a></dt>
<dd><p>BCT2 Path.</p>
</dd></dl>

<dl class="py property">
<dt class="sig sig-object py" id="pymatgen.symmetry.kpath.KPathSetyawanCurtarolo.conventional">
<em class="property"><span class="pre">property</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">conventional</span></span><a class="reference external" href="https://github.com/materialsproject/pymatgen/blob/v2025.1.24/src/pymatgen/symmetry/kpath.py"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pymatgen.symmetry.kpath.KPathSetyawanCurtarolo.conventional" title="Link to this definition"></a></dt>
<dd><p>The conventional cell structure.</p>
</dd></dl>

<dl class="py method">
<dt class="sig sig-object py" id="pymatgen.symmetry.kpath.KPathSetyawanCurtarolo.cubic">
<span class="sig-name descname"><span class="pre">cubic</span></span><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="reference external" href="https://github.com/materialsproject/pymatgen/blob/v2025.1.24/src/pymatgen/core/../symmetry/kpath.py#L294-L304"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pymatgen.symmetry.kpath.KPathSetyawanCurtarolo.cubic" title="Link to this definition"></a></dt>
<dd><p>CUB Path.</p>
</dd></dl>

<dl class="py method">
<dt class="sig sig-object py" id="pymatgen.symmetry.kpath.KPathSetyawanCurtarolo.fcc">
<span class="sig-name descname"><span class="pre">fcc</span></span><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="reference external" href="https://github.com/materialsproject/pymatgen/blob/v2025.1.24/src/pymatgen/core/../symmetry/kpath.py#L306-L321"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pymatgen.symmetry.kpath.KPathSetyawanCurtarolo.fcc" title="Link to this definition"></a></dt>
<dd><p>FCC Path.</p>
</dd></dl>

<dl class="py method">
<dt class="sig sig-object py" id="pymatgen.symmetry.kpath.KPathSetyawanCurtarolo.hex">
<span class="sig-name descname"><span class="pre">hex</span></span><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="reference external" href="https://github.com/materialsproject/pymatgen/blob/v2025.1.24/src/pymatgen/core/../symmetry/kpath.py#L564-L580"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pymatgen.symmetry.kpath.KPathSetyawanCurtarolo.hex" title="Link to this definition"></a></dt>
<dd><p>HEX Path.</p>
</dd></dl>

<dl class="py method">
<dt class="sig sig-object py" id="pymatgen.symmetry.kpath.KPathSetyawanCurtarolo.mcl">
<span class="sig-name descname"><span class="pre">mcl</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">b</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">c</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">beta</span></span></em><span class="sig-paren">)</span><a class="reference external" href="https://github.com/materialsproject/pymatgen/blob/v2025.1.24/src/pymatgen/core/../symmetry/kpath.py#L627-L655"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pymatgen.symmetry.kpath.KPathSetyawanCurtarolo.mcl" title="Link to this definition"></a></dt>
<dd><p>MCL Path.</p>
</dd></dl>

<dl class="py method">
<dt class="sig sig-object py" id="pymatgen.symmetry.kpath.KPathSetyawanCurtarolo.mclc1">
<span class="sig-name descname"><span class="pre">mclc1</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">a</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">b</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">c</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">alpha</span></span></em><span class="sig-paren">)</span><a class="reference external" href="https://github.com/materialsproject/pymatgen/blob/v2025.1.24/src/pymatgen/core/../symmetry/kpath.py#L657-L689"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pymatgen.symmetry.kpath.KPathSetyawanCurtarolo.mclc1" title="Link to this definition"></a></dt>
<dd><p>MCLC1 Path.</p>
</dd></dl>

<dl class="py method">
<dt class="sig sig-object py" id="pymatgen.symmetry.kpath.KPathSetyawanCurtarolo.mclc2">
<span class="sig-name descname"><span class="pre">mclc2</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">a</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">b</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">c</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">alpha</span></span></em><span class="sig-paren">)</span><a class="reference external" href="https://github.com/materialsproject/pymatgen/blob/v2025.1.24/src/pymatgen/core/../symmetry/kpath.py#L691-L722"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pymatgen.symmetry.kpath.KPathSetyawanCurtarolo.mclc2" title="Link to this definition"></a></dt>
<dd><p>MCLC2 Path.</p>
</dd></dl>

<dl class="py method">
<dt class="sig sig-object py" id="pymatgen.symmetry.kpath.KPathSetyawanCurtarolo.mclc3">
<span class="sig-name descname"><span class="pre">mclc3</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">a</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">b</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">c</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">alpha</span></span></em><span class="sig-paren">)</span><a class="reference external" href="https://github.com/materialsproject/pymatgen/blob/v2025.1.24/src/pymatgen/core/../symmetry/kpath.py#L724-L757"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pymatgen.symmetry.kpath.KPathSetyawanCurtarolo.mclc3" title="Link to this definition"></a></dt>
<dd><p>MCLC3 Path.</p>
</dd></dl>

<dl class="py method">
<dt class="sig sig-object py" id="pymatgen.symmetry.kpath.KPathSetyawanCurtarolo.mclc4">
<span class="sig-name descname"><span class="pre">mclc4</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">a</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">b</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">c</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">alpha</span></span></em><span class="sig-paren">)</span><a class="reference external" href="https://github.com/materialsproject/pymatgen/blob/v2025.1.24/src/pymatgen/core/../symmetry/kpath.py#L759-L792"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pymatgen.symmetry.kpath.KPathSetyawanCurtarolo.mclc4" title="Link to this definition"></a></dt>
<dd><p>MCLC4 Path.</p>
</dd></dl>

<dl class="py method">
<dt class="sig sig-object py" id="pymatgen.symmetry.kpath.KPathSetyawanCurtarolo.mclc5">
<span class="sig-name descname"><span class="pre">mclc5</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">a</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">b</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">c</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">alpha</span></span></em><span class="sig-paren">)</span><a class="reference external" href="https://github.com/materialsproject/pymatgen/blob/v2025.1.24/src/pymatgen/core/../symmetry/kpath.py#L794-L831"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pymatgen.symmetry.kpath.KPathSetyawanCurtarolo.mclc5" title="Link to this definition"></a></dt>
<dd><p>MCLC5 Path.</p>
</dd></dl>

<dl class="py method">
<dt class="sig sig-object py" id="pymatgen.symmetry.kpath.KPathSetyawanCurtarolo.orc">
<span class="sig-name descname"><span class="pre">orc</span></span><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="reference external" href="https://github.com/materialsproject/pymatgen/blob/v2025.1.24/src/pymatgen/core/../symmetry/kpath.py#L403-L422"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pymatgen.symmetry.kpath.KPathSetyawanCurtarolo.orc" title="Link to this definition"></a></dt>
<dd><p>ORC Path.</p>
</dd></dl>

<dl class="py method">
<dt class="sig sig-object py" id="pymatgen.symmetry.kpath.KPathSetyawanCurtarolo.orcc">
<span class="sig-name descname"><span class="pre">orcc</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">a</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">b</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">c</span></span></em><span class="sig-paren">)</span><a class="reference external" href="https://github.com/materialsproject/pymatgen/blob/v2025.1.24/src/pymatgen/core/../symmetry/kpath.py#L529-L562"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pymatgen.symmetry.kpath.KPathSetyawanCurtarolo.orcc" title="Link to this definition"></a></dt>
<dd><p>ORCC Path.</p>
</dd></dl>

<dl class="py method">
<dt class="sig sig-object py" id="pymatgen.symmetry.kpath.KPathSetyawanCurtarolo.orcf1">
<span class="sig-name descname"><span class="pre">orcf1</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">a</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">b</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">c</span></span></em><span class="sig-paren">)</span><a class="reference external" href="https://github.com/materialsproject/pymatgen/blob/v2025.1.24/src/pymatgen/core/../symmetry/kpath.py#L424-L447"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pymatgen.symmetry.kpath.KPathSetyawanCurtarolo.orcf1" title="Link to this definition"></a></dt>
<dd><p>ORFC1 Path.</p>
</dd></dl>

<dl class="py method">
<dt class="sig sig-object py" id="pymatgen.symmetry.kpath.KPathSetyawanCurtarolo.orcf2">
<span class="sig-name descname"><span class="pre">orcf2</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">a</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">b</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">c</span></span></em><span class="sig-paren">)</span><a class="reference external" href="https://github.com/materialsproject/pymatgen/blob/v2025.1.24/src/pymatgen/core/../symmetry/kpath.py#L449-L475"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pymatgen.symmetry.kpath.KPathSetyawanCurtarolo.orcf2" title="Link to this definition"></a></dt>
<dd><p>ORFC2 Path.</p>
</dd></dl>

<dl class="py method">
<dt class="sig sig-object py" id="pymatgen.symmetry.kpath.KPathSetyawanCurtarolo.orcf3">
<span class="sig-name descname"><span class="pre">orcf3</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">a</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">b</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">c</span></span></em><span class="sig-paren">)</span><a class="reference external" href="https://github.com/materialsproject/pymatgen/blob/v2025.1.24/src/pymatgen/core/../symmetry/kpath.py#L477-L498"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pymatgen.symmetry.kpath.KPathSetyawanCurtarolo.orcf3" title="Link to this definition"></a></dt>
<dd><p>ORFC3 Path.</p>
</dd></dl>

<dl class="py method">
<dt class="sig sig-object py" id="pymatgen.symmetry.kpath.KPathSetyawanCurtarolo.orci">
<span class="sig-name descname"><span class="pre">orci</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">a</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">b</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">c</span></span></em><span class="sig-paren">)</span><a class="reference external" href="https://github.com/materialsproject/pymatgen/blob/v2025.1.24/src/pymatgen/core/../symmetry/kpath.py#L500-L527"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pymatgen.symmetry.kpath.KPathSetyawanCurtarolo.orci" title="Link to this definition"></a></dt>
<dd><p>ORCI Path.</p>
</dd></dl>

<dl class="py property">
<dt class="sig sig-object py" id="pymatgen.symmetry.kpath.KPathSetyawanCurtarolo.prim">
<em class="property"><span class="pre">property</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">prim</span></span><a class="reference external" href="https://github.com/materialsproject/pymatgen/blob/v2025.1.24/src/pymatgen/symmetry/kpath.py"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pymatgen.symmetry.kpath.KPathSetyawanCurtarolo.prim" title="Link to this definition"></a></dt>
<dd><p>The primitive cell structure.</p>
</dd></dl>

<dl class="py property">
<dt class="sig sig-object py" id="pymatgen.symmetry.kpath.KPathSetyawanCurtarolo.prim_rec">
<em class="property"><span class="pre">property</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">prim_rec</span></span><a class="reference external" href="https://github.com/materialsproject/pymatgen/blob/v2025.1.24/src/pymatgen/symmetry/kpath.py"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pymatgen.symmetry.kpath.KPathSetyawanCurtarolo.prim_rec" title="Link to this definition"></a></dt>
<dd><p>The primitive reciprocal cell structure.</p>
</dd></dl>

<dl class="py method">
<dt class="sig sig-object py" id="pymatgen.symmetry.kpath.KPathSetyawanCurtarolo.rhl1">
<span class="sig-name descname"><span class="pre">rhl1</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">alpha</span></span></em><span class="sig-paren">)</span><a class="reference external" href="https://github.com/materialsproject/pymatgen/blob/v2025.1.24/src/pymatgen/core/../symmetry/kpath.py#L582-L607"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pymatgen.symmetry.kpath.KPathSetyawanCurtarolo.rhl1" title="Link to this definition"></a></dt>
<dd><p>RHL1 Path.</p>
</dd></dl>

<dl class="py method">
<dt class="sig sig-object py" id="pymatgen.symmetry.kpath.KPathSetyawanCurtarolo.rhl2">
<span class="sig-name descname"><span class="pre">rhl2</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">alpha</span></span></em><span class="sig-paren">)</span><a class="reference external" href="https://github.com/materialsproject/pymatgen/blob/v2025.1.24/src/pymatgen/core/../symmetry/kpath.py#L609-L625"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pymatgen.symmetry.kpath.KPathSetyawanCurtarolo.rhl2" title="Link to this definition"></a></dt>
<dd><p>RHL2 Path.</p>
</dd></dl>

<dl class="py method">
<dt class="sig sig-object py" id="pymatgen.symmetry.kpath.KPathSetyawanCurtarolo.tet">
<span class="sig-name descname"><span class="pre">tet</span></span><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="reference external" href="https://github.com/materialsproject/pymatgen/blob/v2025.1.24/src/pymatgen/core/../symmetry/kpath.py#L335-L351"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pymatgen.symmetry.kpath.KPathSetyawanCurtarolo.tet" title="Link to this definition"></a></dt>
<dd><p>TET Path.</p>
</dd></dl>

<dl class="py method">
<dt class="sig sig-object py" id="pymatgen.symmetry.kpath.KPathSetyawanCurtarolo.tria">
<span class="sig-name descname"><span class="pre">tria</span></span><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="reference external" href="https://github.com/materialsproject/pymatgen/blob/v2025.1.24/src/pymatgen/core/../symmetry/kpath.py#L833-L852"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pymatgen.symmetry.kpath.KPathSetyawanCurtarolo.tria" title="Link to this definition"></a></dt>
<dd><p>TRI1a Path.</p>
</dd></dl>

<dl class="py method">
<dt class="sig sig-object py" id="pymatgen.symmetry.kpath.KPathSetyawanCurtarolo.trib">
<span class="sig-name descname"><span class="pre">trib</span></span><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="reference external" href="https://github.com/materialsproject/pymatgen/blob/v2025.1.24/src/pymatgen/core/../symmetry/kpath.py#L854-L873"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pymatgen.symmetry.kpath.KPathSetyawanCurtarolo.trib" title="Link to this definition"></a></dt>
<dd><p>TRI1b Path.</p>
</dd></dl>

</dd></dl>

</section>
<section id="module-pymatgen.symmetry.maggroups">
<span id="pymatgen-symmetry-maggroups-module"></span><h2>pymatgen.symmetry.maggroups module<a class="headerlink" href="#module-pymatgen.symmetry.maggroups" title="Link to this heading"></a></h2>
<p>Magnetic space groups.</p>
<dl class="py class">
<dt class="sig sig-object py" id="pymatgen.symmetry.maggroups.MagneticSpaceGroup">
<em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">MagneticSpaceGroup</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="o"><span class="pre">**</span></span><span class="n"><span class="pre">kwargs</span></span></em><span class="sig-paren">)</span><a class="reference external" href="https://github.com/materialsproject/pymatgen/blob/v2025.1.24/src/pymatgen/core/../symmetry/maggroups.py#L33-L547"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pymatgen.symmetry.maggroups.MagneticSpaceGroup" title="Link to this definition"></a></dt>
<dd><p>Bases: <a class="reference internal" href="#pymatgen.symmetry.groups.SymmetryGroup" title="pymatgen.symmetry.groups.SymmetryGroup"><code class="xref py py-class docutils literal notranslate"><span class="pre">SymmetryGroup</span></code></a></p>
<p>Representation of a magnetic space group.</p>
<p>Initialize a MagneticSpaceGroup from its Belov, Neronova and
Smirnova (BNS) number supplied as a list or its label supplied
as a string. To create a magnetic structure in pymatgen, the
Structure.from_magnetic_spacegroup() method can be used, which
relies on this class.</p>
<p>The main difference between magnetic space groups and normal
crystallographic space groups is the inclusion of a time reversal
operator that acts on an atom’s magnetic moment. This is
indicated by a prime symbol (’) next to the respective symmetry
operation in its label, e.g. the standard crystallographic
space group Pnma has magnetic subgroups Pn’ma, Pnm’a, Pnma’,
Pn’m’a, Pnm’a’, Pn’ma’, Pn’m’a’.</p>
<p>The magnetic space groups are classified as one of 4 types
where G = magnetic space group, and F = parent crystallographic
space group:</p>
<ol class="arabic simple">
<li><dl class="simple">
<dt>G=F no time reversal, i.e. the same as corresponding</dt><dd><p>crystallographic group</p>
</dd>
</dl>
</li>
<li><dl class="simple">
<dt>G=F+F1’, “grey” groups, where avg. magnetic moment is zero,</dt><dd><p>e.g. a paramagnet in zero ext. mag. field</p>
</dd>
</dl>
</li>
<li><dl class="simple">
<dt>G=D+(F-D)1’, where D is an equi-translation subgroup of F of</dt><dd><p>index 2, lattice translations do not include time reversal</p>
</dd>
</dl>
</li>
<li><p>G=D+(F-D)1’, where D is an equi-class subgroup of F of index 2</p></li>
</ol>
<p>There are two common settings for magnetic space groups, BNS
and OG. In case 4, the BNS setting != OG setting, and so a
transformation to go between the two settings is required:
specifically, the BNS setting is derived from D, and the OG
setting is derived from F.</p>
<p>This means that the OG setting refers to the unit cell if magnetic
order is neglected, and requires multiple unit cells to reproduce
the full crystal periodicity when magnetic moments are present.
This does not make the OG setting, in general, useful for
electronic structure calculations and the BNS setting is preferred.
However, this class does contain information on the OG setting and
can be initialized from OG labels or numbers if required.</p>
<p>Conventions: ITC monoclinic unique axis b, monoclinic cell choice 1,
hexagonal axis for trigonal groups, origin choice 2 for groups with
more than one origin choice (ISO-MAG).</p>
<p>Raw data comes from ISO-MAG, ISOTROPY Software Suite, iso.byu.edu
<a class="reference external" href="http://stokes.byu.edu/iso/magnetic_data.txt">http://stokes.byu.edu/iso/magnetic_data.txt</a>
with kind permission from Professor Branton Campbell, BYU</p>
<p>Data originally compiled from:
(1) Daniel B. Litvin, Magnetic Group Tables (International Union</p>
<blockquote>
<div><p>of Crystallography, 2013) www.iucr.org/publ/978-0-9553602-2-0.</p>
</div></blockquote>
<ol class="arabic simple" start="2">
<li><p>C. J. Bradley and A. P. Cracknell, The Mathematical Theory of
Symmetry in Solids (Clarendon Press, Oxford, 1972).</p></li>
</ol>
<p>See <a class="reference external" href="http://stokes.byu.edu/iso/magneticspacegroupshelp.php">http://stokes.byu.edu/iso/magneticspacegroupshelp.php</a> for more
information on magnetic symmetry.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>label</strong> – BNS number supplied as list of 2 ints or BNS label as
str or index as int (1-1651) to iterate over all space groups</p></li>
<li><p><strong>setting_transformation</strong> – Transformation to apply to convert
from BNS to OG setting, default is ‘a,b,c;0,0,0’ which
means no transformation, i.e. BNS setting is the same as
OG setting.</p></li>
</ul>
</dd>
</dl>
<dl class="py property">
<dt class="sig sig-object py" id="pymatgen.symmetry.maggroups.MagneticSpaceGroup.crystal_system">
<em class="property"><span class="pre">property</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">crystal_system</span></span><a class="reference external" href="https://github.com/materialsproject/pymatgen/blob/v2025.1.24/src/pymatgen/symmetry/maggroups.py"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pymatgen.symmetry.maggroups.MagneticSpaceGroup.crystal_system" title="Link to this definition"></a></dt>
<dd><p>Crystal system, e.g. cubic, hexagonal, etc.</p>
</dd></dl>

<dl class="py method">
<dt class="sig sig-object py" id="pymatgen.symmetry.maggroups.MagneticSpaceGroup.data_str">
<span class="sig-name descname"><span class="pre">data_str</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">include_og</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">True</span></span></em><span class="sig-paren">)</span><a class="reference external" href="https://github.com/materialsproject/pymatgen/blob/v2025.1.24/src/pymatgen/core/../symmetry/maggroups.py#L428-L537"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pymatgen.symmetry.maggroups.MagneticSpaceGroup.data_str" title="Link to this definition"></a></dt>
<dd><p>Get description of all data, including information for OG setting.</p>
<dl class="field-list simple">
<dt class="field-odd">Returns<span class="colon">:</span></dt>
<dd class="field-odd"><p>str.</p>
</dd>
</dl>
</dd></dl>

<dl class="py method">
<dt class="sig sig-object py" id="pymatgen.symmetry.maggroups.MagneticSpaceGroup.from_og">
<em class="property"><span class="pre">classmethod</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">from_og</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">label</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">Sequence</span><span class="p"><span class="pre">[</span></span><span class="pre">int</span><span class="p"><span class="pre">]</span></span><span class="w"> </span><span class="p"><span class="pre">|</span></span><span class="w"> </span><span class="pre">str</span></span></em><span class="sig-paren">)</span> <span class="sig-return"><span class="sig-return-icon">&#x2192;</span> <span class="sig-return-typehint"><span class="pre">Self</span></span></span><a class="reference external" href="https://github.com/materialsproject/pymatgen/blob/v2025.1.24/src/pymatgen/core/../symmetry/maggroups.py#L287-L306"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pymatgen.symmetry.maggroups.MagneticSpaceGroup.from_og" title="Link to this definition"></a></dt>
<dd><p>Initialize from Opechowski and Guccione (OG) label or number.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
<dd class="field-odd"><p><strong>label</strong> – OG number supplied as list of 3 ints or OG label as str</p>
</dd>
</dl>
</dd></dl>

<dl class="py method">
<dt class="sig sig-object py" id="pymatgen.symmetry.maggroups.MagneticSpaceGroup.get_orbit">
<span class="sig-name descname"><span class="pre">get_orbit</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">p</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">magmom</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">tol</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">float</span></span><span class="w"> </span><span class="o"><span class="pre">=</span></span><span class="w"> </span><span class="default_value"><span class="pre">1e-05</span></span></em><span class="sig-paren">)</span><a class="reference external" href="https://github.com/materialsproject/pymatgen/blob/v2025.1.24/src/pymatgen/core/../symmetry/maggroups.py#L365-L388"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pymatgen.symmetry.maggroups.MagneticSpaceGroup.get_orbit" title="Link to this definition"></a></dt>
<dd><p>Get the orbit for a point and its associated magnetic moment.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>p</strong> – Point as a 3x1 array.</p></li>
<li><p><strong>magmom</strong> – A magnetic moment, compatible with pymatgen.electronic_structure.core.Magmom</p></li>
<li><p><strong>tol</strong> – Tolerance for determining if sites are the same. 1e-5 should
be sufficient for most purposes. Set to 0 for exact matching
(and also needed for symbolic orbits).</p></li>
</ul>
</dd>
<dt class="field-even">Returns<span class="colon">:</span></dt>
<dd class="field-even"><p>orbit for point and magnetic moments for orbit.</p>
</dd>
<dt class="field-odd">Return type<span class="colon">:</span></dt>
<dd class="field-odd"><p>tuple[list, list]</p>
</dd>
</dl>
</dd></dl>

<dl class="py method">
<dt class="sig sig-object py" id="pymatgen.symmetry.maggroups.MagneticSpaceGroup.is_compatible">
<span class="sig-name descname"><span class="pre">is_compatible</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">lattice</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><a class="reference internal" href="pymatgen.core.html#pymatgen.core.lattice.Lattice" title="pymatgen.core.lattice.Lattice"><span class="pre">Lattice</span></a></span></em>, <em class="sig-param"><span class="n"><span class="pre">tol</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">float</span></span><span class="w"> </span><span class="o"><span class="pre">=</span></span><span class="w"> </span><span class="default_value"><span class="pre">1e-05</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">angle_tol</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">float</span></span><span class="w"> </span><span class="o"><span class="pre">=</span></span><span class="w"> </span><span class="default_value"><span class="pre">5</span></span></em><span class="sig-paren">)</span> <span class="sig-return"><span class="sig-return-icon">&#x2192;</span> <span class="sig-return-typehint"><span class="pre">bool</span></span></span><a class="reference external" href="https://github.com/materialsproject/pymatgen/blob/v2025.1.24/src/pymatgen/core/../symmetry/maggroups.py#L390-L426"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pymatgen.symmetry.maggroups.MagneticSpaceGroup.is_compatible" title="Link to this definition"></a></dt>
<dd><p>Check whether a particular lattice is compatible with the
<em>conventional</em> unit cell.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>lattice</strong> (<a class="reference internal" href="pymatgen.core.html#pymatgen.core.lattice.Lattice" title="pymatgen.core.lattice.Lattice"><em>Lattice</em></a>) – A Lattice.</p></li>
<li><p><strong>tol</strong> (<em>float</em>) – The tolerance to check for equality of lengths.</p></li>
<li><p><strong>angle_tol</strong> (<em>float</em>) – The tolerance to check for equality of angles in degrees.</p></li>
</ul>
</dd>
<dt class="field-even">Returns<span class="colon">:</span></dt>
<dd class="field-even"><p>True if the lattice is compatible with the conventional cell.</p>
</dd>
<dt class="field-odd">Return type<span class="colon">:</span></dt>
<dd class="field-odd"><p>bool</p>
</dd>
</dl>
</dd></dl>

<dl class="py property">
<dt class="sig sig-object py" id="pymatgen.symmetry.maggroups.MagneticSpaceGroup.sg_symbol">
<em class="property"><span class="pre">property</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">sg_symbol</span></span><a class="reference external" href="https://github.com/materialsproject/pymatgen/blob/v2025.1.24/src/pymatgen/symmetry/maggroups.py"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pymatgen.symmetry.maggroups.MagneticSpaceGroup.sg_symbol" title="Link to this definition"></a></dt>
<dd><p>Space group symbol.</p>
</dd></dl>

<dl class="py property">
<dt class="sig sig-object py" id="pymatgen.symmetry.maggroups.MagneticSpaceGroup.symmetry_ops">
<em class="property"><span class="pre">property</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">symmetry_ops</span></span><a class="reference external" href="https://github.com/materialsproject/pymatgen/blob/v2025.1.24/src/pymatgen/symmetry/maggroups.py"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pymatgen.symmetry.maggroups.MagneticSpaceGroup.symmetry_ops" title="Link to this definition"></a></dt>
<dd><p>Retrieve magnetic symmetry operations of the space group.</p>
<dl class="field-list simple">
<dt class="field-odd">Returns<span class="colon">:</span></dt>
<dd class="field-odd"><p>List of pymatgen.core.operations.MagSymmOp.</p>
</dd>
</dl>
</dd></dl>

</dd></dl>

</section>
<section id="module-pymatgen.symmetry.settings">
<span id="pymatgen-symmetry-settings-module"></span><h2>pymatgen.symmetry.settings module<a class="headerlink" href="#module-pymatgen.symmetry.settings" title="Link to this heading"></a></h2>
<p>This module provides classes for non-standard space-group settings.</p>
<dl class="py class">
<dt class="sig sig-object py" id="pymatgen.symmetry.settings.JonesFaithfulTransformation">
<em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">JonesFaithfulTransformation</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">P</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">p</span></span></em><span class="sig-paren">)</span><a class="reference external" href="https://github.com/materialsproject/pymatgen/blob/v2025.1.24/src/pymatgen/core/../symmetry/settings.py#L27-L208"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pymatgen.symmetry.settings.JonesFaithfulTransformation" title="Link to this definition"></a></dt>
<dd><p>Bases: <code class="xref py py-class docutils literal notranslate"><span class="pre">object</span></code></p>
<p>Transformation for space-groups defined in a non-standard setting.</p>
<p>Transform between settings using matrix P and origin shift vector p,
using same notation as reference.</p>
<p>Should initialize using from_transformation_str in Jones
faithful notation, given by a string specifying both a
transformation matrix and an origin shift, with parts delimited
by a semi-colon. Best shown by example:</p>
<ul class="simple">
<li><p><cite>a,b,c;0,0,0</cite> is the identity (no change)</p></li>
<li><p><cite>-b+c,a+c,-a+b+c;0,0,0</cite> is R3:r to R3:h (rhombohedral to
hexagonal setting)</p></li>
<li><p><cite>a,b,c;-1/4,-1/4,-1/4</cite> is Pnnn:1 to Pnnn:2 (change in origin
choice)</p></li>
<li><p><cite>b,c,a;-1/2,-1/2,-1/2</cite> is Bbab:1 to Ccca:2 (change setting
and origin)</p></li>
</ul>
<p>Can transform points (coords), lattices and symmetry operations.</p>
<p>Used for transforming magnetic space groups since these are
commonly used in multiple settings, due to needing to transform
between magnetic and non-magnetic settings.</p>
<p>See: International Tables for Crystallography (2016). Vol. A,
Chapter 1.5, pp. 75-106.</p>
<dl class="py property">
<dt class="sig sig-object py" id="pymatgen.symmetry.settings.JonesFaithfulTransformation.P">
<em class="property"><span class="pre">property</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">P</span></span><em class="property"><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="pre">list</span><span class="p"><span class="pre">[</span></span><span class="pre">list</span><span class="p"><span class="pre">[</span></span><span class="pre">float</span><span class="p"><span class="pre">]</span></span><span class="p"><span class="pre">]</span></span></em><a class="reference external" href="https://github.com/materialsproject/pymatgen/blob/v2025.1.24/src/pymatgen/symmetry/settings.py"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pymatgen.symmetry.settings.JonesFaithfulTransformation.P" title="Link to this definition"></a></dt>
<dd><p>Transformation matrix.</p>
</dd></dl>

<dl class="py method">
<dt class="sig sig-object py" id="pymatgen.symmetry.settings.JonesFaithfulTransformation.from_origin_shift">
<em class="property"><span class="pre">classmethod</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">from_origin_shift</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">origin_shift</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">str</span></span><span class="w"> </span><span class="o"><span class="pre">=</span></span><span class="w"> </span><span class="default_value"><span class="pre">'0,0,0'</span></span></em><span class="sig-paren">)</span> <span class="sig-return"><span class="sig-return-icon">&#x2192;</span> <span class="sig-return-typehint"><span class="pre">Self</span></span></span><a class="reference external" href="https://github.com/materialsproject/pymatgen/blob/v2025.1.24/src/pymatgen/core/../symmetry/settings.py#L73-L85"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pymatgen.symmetry.settings.JonesFaithfulTransformation.from_origin_shift" title="Link to this definition"></a></dt>
<dd><p>Construct SpaceGroupTransformation from its origin shift string.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
<dd class="field-odd"><p><strong>origin_shift</strong> (<em>str</em><em>, </em><em>optional</em>) – Defaults to “0,0,0”.</p>
</dd>
<dt class="field-even">Returns<span class="colon">:</span></dt>
<dd class="field-even"><p>JonesFaithfulTransformation</p>
</dd>
</dl>
</dd></dl>

<dl class="py method">
<dt class="sig sig-object py" id="pymatgen.symmetry.settings.JonesFaithfulTransformation.from_transformation_str">
<em class="property"><span class="pre">classmethod</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">from_transformation_str</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">transformation_string</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">str</span></span><span class="w"> </span><span class="o"><span class="pre">=</span></span><span class="w"> </span><span class="default_value"><span class="pre">'a,b,c;0,0,0'</span></span></em><span class="sig-paren">)</span> <span class="sig-return"><span class="sig-return-icon">&#x2192;</span> <span class="sig-return-typehint"><span class="pre">Self</span></span></span><a class="reference external" href="https://github.com/materialsproject/pymatgen/blob/v2025.1.24/src/pymatgen/core/../symmetry/settings.py#L60-L71"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pymatgen.symmetry.settings.JonesFaithfulTransformation.from_transformation_str" title="Link to this definition"></a></dt>
<dd><p>Construct SpaceGroupTransformation from its transformation string.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
<dd class="field-odd"><p><strong>transformation_string</strong> (<em>str</em><em>, </em><em>optional</em>) – Defaults to “a,b,c;0,0,0”.</p>
</dd>
<dt class="field-even">Returns<span class="colon">:</span></dt>
<dd class="field-even"><p>JonesFaithfulTransformation</p>
</dd>
</dl>
</dd></dl>

<dl class="py property">
<dt class="sig sig-object py" id="pymatgen.symmetry.settings.JonesFaithfulTransformation.inverse">
<em class="property"><span class="pre">property</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">inverse</span></span><em class="property"><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="pre">Self</span></em><a class="reference external" href="https://github.com/materialsproject/pymatgen/blob/v2025.1.24/src/pymatgen/symmetry/settings.py"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pymatgen.symmetry.settings.JonesFaithfulTransformation.inverse" title="Link to this definition"></a></dt>
<dd><p>JonesFaithfulTransformation.</p>
</dd></dl>

<dl class="py property">
<dt class="sig sig-object py" id="pymatgen.symmetry.settings.JonesFaithfulTransformation.p">
<em class="property"><span class="pre">property</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">p</span></span><em class="property"><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="pre">list</span><span class="p"><span class="pre">[</span></span><span class="pre">float</span><span class="p"><span class="pre">]</span></span></em><a class="reference external" href="https://github.com/materialsproject/pymatgen/blob/v2025.1.24/src/pymatgen/symmetry/settings.py"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pymatgen.symmetry.settings.JonesFaithfulTransformation.p" title="Link to this definition"></a></dt>
<dd><p>Translation vector.</p>
</dd></dl>

<dl class="py method">
<dt class="sig sig-object py" id="pymatgen.symmetry.settings.JonesFaithfulTransformation.parse_transformation_string">
<em class="property"><span class="pre">static</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">parse_transformation_string</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">transformation_string</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">str</span></span><span class="w"> </span><span class="o"><span class="pre">=</span></span><span class="w"> </span><span class="default_value"><span class="pre">'a,b,c;0,0,0'</span></span></em><span class="sig-paren">)</span> <span class="sig-return"><span class="sig-return-icon">&#x2192;</span> <span class="sig-return-typehint"><span class="pre">tuple</span><span class="p"><span class="pre">[</span></span><span class="pre">list</span><span class="p"><span class="pre">[</span></span><span class="pre">list</span><span class="p"><span class="pre">[</span></span><span class="pre">float</span><span class="p"><span class="pre">]</span></span><span class="p"><span class="pre">]</span></span><span class="w"> </span><span class="p"><span class="pre">|</span></span><span class="w"> </span><span class="pre">ndarray</span><span class="p"><span class="pre">,</span></span><span class="w"> </span><span class="pre">list</span><span class="p"><span class="pre">[</span></span><span class="pre">float</span><span class="p"><span class="pre">]</span></span><span class="p"><span class="pre">]</span></span></span></span><a class="reference external" href="https://github.com/materialsproject/pymatgen/blob/v2025.1.24/src/pymatgen/core/../symmetry/settings.py#L87-L137"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pymatgen.symmetry.settings.JonesFaithfulTransformation.parse_transformation_string" title="Link to this definition"></a></dt>
<dd><dl class="field-list simple">
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
<dd class="field-odd"><p><strong>transformation_string</strong> (<em>str</em><em>, </em><em>optional</em>) – Defaults to “a,b,c;0,0,0”.</p>
</dd>
<dt class="field-even">Raises<span class="colon">:</span></dt>
<dd class="field-even"><p><strong>ValueError</strong> – When transformation string fails to parse.</p>
</dd>
<dt class="field-odd">Returns<span class="colon">:</span></dt>
<dd class="field-odd"><p>transformation matrix &amp; vector</p>
</dd>
<dt class="field-even">Return type<span class="colon">:</span></dt>
<dd class="field-even"><p>tuple[list[list[float]] | np.ndarray, list[float]]</p>
</dd>
</dl>
</dd></dl>

<dl class="py method">
<dt class="sig sig-object py" id="pymatgen.symmetry.settings.JonesFaithfulTransformation.transform_coords">
<span class="sig-name descname"><span class="pre">transform_coords</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">coords</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">list</span><span class="p"><span class="pre">[</span></span><span class="pre">list</span><span class="p"><span class="pre">[</span></span><span class="pre">float</span><span class="p"><span class="pre">]</span></span><span class="p"><span class="pre">]</span></span><span class="w"> </span><span class="p"><span class="pre">|</span></span><span class="w"> </span><span class="pre">ndarray</span></span></em><span class="sig-paren">)</span> <span class="sig-return"><span class="sig-return-icon">&#x2192;</span> <span class="sig-return-typehint"><span class="pre">list</span><span class="p"><span class="pre">[</span></span><span class="pre">list</span><span class="p"><span class="pre">[</span></span><span class="pre">float</span><span class="p"><span class="pre">]</span></span><span class="p"><span class="pre">]</span></span></span></span><a class="reference external" href="https://github.com/materialsproject/pymatgen/blob/v2025.1.24/src/pymatgen/core/../symmetry/settings.py#L186-L193"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pymatgen.symmetry.settings.JonesFaithfulTransformation.transform_coords" title="Link to this definition"></a></dt>
<dd><p>Takes a list of coordinates and transforms them.</p>
</dd></dl>

<dl class="py method">
<dt class="sig sig-object py" id="pymatgen.symmetry.settings.JonesFaithfulTransformation.transform_lattice">
<span class="sig-name descname"><span class="pre">transform_lattice</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">lattice</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><a class="reference internal" href="pymatgen.core.html#pymatgen.core.lattice.Lattice" title="pymatgen.core.lattice.Lattice"><span class="pre">Lattice</span></a></span></em><span class="sig-paren">)</span> <span class="sig-return"><span class="sig-return-icon">&#x2192;</span> <span class="sig-return-typehint"><a class="reference internal" href="pymatgen.core.html#pymatgen.core.lattice.Lattice" title="pymatgen.core.lattice.Lattice"><span class="pre">Lattice</span></a></span></span><a class="reference external" href="https://github.com/materialsproject/pymatgen/blob/v2025.1.24/src/pymatgen/core/../symmetry/settings.py#L195-L197"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pymatgen.symmetry.settings.JonesFaithfulTransformation.transform_lattice" title="Link to this definition"></a></dt>
<dd><p>Transforms a lattice.</p>
</dd></dl>

<dl class="py method">
<dt class="sig sig-object py" id="pymatgen.symmetry.settings.JonesFaithfulTransformation.transform_symmop">
<span class="sig-name descname"><span class="pre">transform_symmop</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">symm_op</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><a class="reference internal" href="pymatgen.core.html#pymatgen.core.operations.SymmOp" title="pymatgen.core.operations.SymmOp"><span class="pre">SymmOp</span></a><span class="w"> </span><span class="p"><span class="pre">|</span></span><span class="w"> </span><a class="reference internal" href="pymatgen.core.html#pymatgen.core.operations.MagSymmOp" title="pymatgen.core.operations.MagSymmOp"><span class="pre">MagSymmOp</span></a></span></em><span class="sig-paren">)</span> <span class="sig-return"><span class="sig-return-icon">&#x2192;</span> <span class="sig-return-typehint"><a class="reference internal" href="pymatgen.core.html#pymatgen.core.operations.SymmOp" title="pymatgen.core.operations.SymmOp"><span class="pre">SymmOp</span></a><span class="w"> </span><span class="p"><span class="pre">|</span></span><span class="w"> </span><a class="reference internal" href="pymatgen.core.html#pymatgen.core.operations.MagSymmOp" title="pymatgen.core.operations.MagSymmOp"><span class="pre">MagSymmOp</span></a></span></span><a class="reference external" href="https://github.com/materialsproject/pymatgen/blob/v2025.1.24/src/pymatgen/core/../symmetry/settings.py#L167-L184"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pymatgen.symmetry.settings.JonesFaithfulTransformation.transform_symmop" title="Link to this definition"></a></dt>
<dd><p>Takes a symmetry operation and transforms it.</p>
</dd></dl>

<dl class="py property">
<dt class="sig sig-object py" id="pymatgen.symmetry.settings.JonesFaithfulTransformation.transformation_string">
<em class="property"><span class="pre">property</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">transformation_string</span></span><em class="property"><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="pre">str</span></em><a class="reference external" href="https://github.com/materialsproject/pymatgen/blob/v2025.1.24/src/pymatgen/symmetry/settings.py"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pymatgen.symmetry.settings.JonesFaithfulTransformation.transformation_string" title="Link to this definition"></a></dt>
<dd><p>Transformation string.</p>
</dd></dl>

</dd></dl>

</section>
<section id="module-pymatgen.symmetry.site_symmetries">
<span id="pymatgen-symmetry-site-symmetries-module"></span><h2>pymatgen.symmetry.site_symmetries module<a class="headerlink" href="#module-pymatgen.symmetry.site_symmetries" title="Link to this heading"></a></h2>
<p>Analysis of site symmetries.</p>
<dl class="py function">
<dt class="sig sig-object py" id="pymatgen.symmetry.site_symmetries.get_shared_symmetry_operations">
<span class="sig-name descname"><span class="pre">get_shared_symmetry_operations</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">struct</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><a class="reference internal" href="pymatgen.core.html#pymatgen.core.structure.Structure" title="pymatgen.core.structure.Structure"><span class="pre">Structure</span></a></span></em>, <em class="sig-param"><span class="n"><span class="pre">pointops</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">list</span><span class="p"><span class="pre">[</span></span><span class="pre">list</span><span class="p"><span class="pre">[</span></span><a class="reference internal" href="pymatgen.core.html#pymatgen.core.operations.SymmOp" title="pymatgen.core.operations.SymmOp"><span class="pre">SymmOp</span></a><span class="p"><span class="pre">]</span></span><span class="p"><span class="pre">]</span></span></span></em>, <em class="sig-param"><span class="n"><span class="pre">tol</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">float</span></span><span class="w"> </span><span class="o"><span class="pre">=</span></span><span class="w"> </span><span class="default_value"><span class="pre">0.1</span></span></em><span class="sig-paren">)</span><a class="reference external" href="https://github.com/materialsproject/pymatgen/blob/v2025.1.24/src/pymatgen/core/../symmetry/site_symmetries.py#L49-L85"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pymatgen.symmetry.site_symmetries.get_shared_symmetry_operations" title="Link to this definition"></a></dt>
<dd><p>Get all the point group operations shared by a pair of atomic sites
in the form [[point operations of site index 1],[],…,[]].</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>struct</strong> – Pymatgen structure</p></li>
<li><p><strong>pointops</strong> – list of point group operations from get_site_symmetries method</p></li>
<li><p><strong>tol</strong> (<em>float</em>) – tolerance to find symmetry operations</p></li>
</ul>
</dd>
<dt class="field-even">Returns<span class="colon">:</span></dt>
<dd class="field-even"><p>list of lists of shared point operations for each pair of atomic sites</p>
</dd>
</dl>
</dd></dl>

<dl class="py function">
<dt class="sig sig-object py" id="pymatgen.symmetry.site_symmetries.get_site_symmetries">
<span class="sig-name descname"><span class="pre">get_site_symmetries</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">struct</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><a class="reference internal" href="pymatgen.core.html#pymatgen.core.structure.Structure" title="pymatgen.core.structure.Structure"><span class="pre">Structure</span></a></span></em>, <em class="sig-param"><span class="n"><span class="pre">precision</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">float</span></span><span class="w"> </span><span class="o"><span class="pre">=</span></span><span class="w"> </span><span class="default_value"><span class="pre">0.1</span></span></em><span class="sig-paren">)</span> <span class="sig-return"><span class="sig-return-icon">&#x2192;</span> <span class="sig-return-typehint"><span class="pre">list</span><span class="p"><span class="pre">[</span></span><span class="pre">list</span><span class="p"><span class="pre">[</span></span><a class="reference internal" href="pymatgen.core.html#pymatgen.core.operations.SymmOp" title="pymatgen.core.operations.SymmOp"><span class="pre">SymmOp</span></a><span class="p"><span class="pre">]</span></span><span class="p"><span class="pre">]</span></span></span></span><a class="reference external" href="https://github.com/materialsproject/pymatgen/blob/v2025.1.24/src/pymatgen/core/../symmetry/site_symmetries.py#L16-L46"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pymatgen.symmetry.site_symmetries.get_site_symmetries" title="Link to this definition"></a></dt>
<dd><p>Get all the point group operations centered on each atomic site
in the form [[point operations of site index 1]…[[point operations of site index N]]].</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>struct</strong> – Pymatgen structure</p></li>
<li><p><strong>precision</strong> (<em>float</em>) – tolerance to find symmetry operations</p></li>
</ul>
</dd>
<dt class="field-even">Returns<span class="colon">:</span></dt>
<dd class="field-even"><p>list of lists of point operations for each atomic site</p>
</dd>
</dl>
</dd></dl>

</section>
<section id="module-pymatgen.symmetry.structure">
<span id="pymatgen-symmetry-structure-module"></span><h2>pymatgen.symmetry.structure module<a class="headerlink" href="#module-pymatgen.symmetry.structure" title="Link to this heading"></a></h2>
<p>This module implements symmetry-related structure forms.</p>
<dl class="py class">
<dt class="sig sig-object py" id="pymatgen.symmetry.structure.SymmetrizedStructure">
<em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">SymmetrizedStructure</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">structure</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><a class="reference internal" href="pymatgen.core.html#pymatgen.core.structure.Structure" title="pymatgen.core.structure.Structure"><span class="pre">Structure</span></a></span></em>, <em class="sig-param"><span class="n"><span class="pre">spacegroup</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><a class="reference internal" href="#pymatgen.symmetry.analyzer.SpacegroupOperations" title="pymatgen.symmetry.analyzer.SpacegroupOperations"><span class="pre">SpacegroupOperations</span></a></span></em>, <em class="sig-param"><span class="n"><span class="pre">equivalent_positions</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">Sequence</span><span class="p"><span class="pre">[</span></span><span class="pre">int</span><span class="p"><span class="pre">]</span></span></span></em>, <em class="sig-param"><span class="n"><span class="pre">wyckoff_letters</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">Sequence</span><span class="p"><span class="pre">[</span></span><span class="pre">str</span><span class="p"><span class="pre">]</span></span></span></em><span class="sig-paren">)</span><a class="reference external" href="https://github.com/materialsproject/pymatgen/blob/v2025.1.24/src/pymatgen/core/../symmetry/structure.py#L20-L150"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pymatgen.symmetry.structure.SymmetrizedStructure" title="Link to this definition"></a></dt>
<dd><p>Bases: <a class="reference internal" href="pymatgen.core.html#pymatgen.core.structure.Structure" title="pymatgen.core.structure.Structure"><code class="xref py py-class docutils literal notranslate"><span class="pre">Structure</span></code></a></p>
<p>This class represents a symmetrized structure, i.e. a structure
where the spacegroup and symmetry operations are defined. This class is
typically not called but instead is typically obtained by calling
pymatgen.symmetry.analyzer.SpacegroupAnalyzer.get_symmetrized_structure.</p>
<dl class="py attribute">
<dt class="sig sig-object py" id="pymatgen.symmetry.structure.SymmetrizedStructure.equivalent_indices">
<span class="sig-name descname"><span class="pre">equivalent_indices</span></span><a class="reference external" href="https://github.com/materialsproject/pymatgen/blob/v2025.1.24/src/pymatgen/symmetry/structure.py"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pymatgen.symmetry.structure.SymmetrizedStructure.equivalent_indices" title="Link to this definition"></a></dt>
<dd><p>A list of lists of indices of the sites in the structure that are
considered equivalent based on the symmetry operations of the space group.</p>
<dl class="field-list simple">
<dt class="field-odd">Type<span class="colon">:</span></dt>
<dd class="field-odd"><p>list[List[int]]</p>
</dd>
</dl>
</dd></dl>

<dl class="field-list simple">
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>structure</strong> (<a class="reference internal" href="pymatgen.core.html#pymatgen.core.structure.Structure" title="pymatgen.core.structure.Structure"><em>Structure</em></a>) – Original structure</p></li>
<li><p><strong>spacegroup</strong> (<a class="reference internal" href="#pymatgen.symmetry.analyzer.SpacegroupOperations" title="pymatgen.symmetry.analyzer.SpacegroupOperations"><em>SpacegroupOperations</em></a>) – An input SpacegroupOperations from SpacegroupAnalyzer.</p></li>
<li><p><strong>equivalent_positions</strong> (<em>list</em><em>[</em><em>int</em><em>]</em>) – Equivalent positions from SpacegroupAnalyzer.</p></li>
<li><p><strong>wyckoff_letters</strong> (<em>list</em><em>[</em><em>str</em><em>]</em>) – Wyckoff letters.</p></li>
</ul>
</dd>
</dl>
<dl class="py method">
<dt class="sig sig-object py" id="pymatgen.symmetry.structure.SymmetrizedStructure.as_dict">
<span class="sig-name descname"><span class="pre">as_dict</span></span><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="reference external" href="https://github.com/materialsproject/pymatgen/blob/v2025.1.24/src/pymatgen/core/../symmetry/structure.py#L126-L134"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pymatgen.symmetry.structure.SymmetrizedStructure.as_dict" title="Link to this definition"></a></dt>
<dd><p>MSONable dict.</p>
</dd></dl>

<dl class="py method">
<dt class="sig sig-object py" id="pymatgen.symmetry.structure.SymmetrizedStructure.copy">
<span class="sig-name descname"><span class="pre">copy</span></span><span class="sig-paren">(</span><span class="sig-paren">)</span> <span class="sig-return"><span class="sig-return-icon">&#x2192;</span> <span class="sig-return-typehint"><span class="pre">Self</span></span></span><a class="reference external" href="https://github.com/materialsproject/pymatgen/blob/v2025.1.24/src/pymatgen/core/../symmetry/structure.py#L70-L77"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pymatgen.symmetry.structure.SymmetrizedStructure.copy" title="Link to this definition"></a></dt>
<dd><p>Make a copy of the SymmetrizedStructure.</p>
</dd></dl>

<dl class="py method">
<dt class="sig sig-object py" id="pymatgen.symmetry.structure.SymmetrizedStructure.find_equivalent_sites">
<span class="sig-name descname"><span class="pre">find_equivalent_sites</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">site</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><a class="reference internal" href="pymatgen.core.html#pymatgen.core.sites.PeriodicSite" title="pymatgen.core.sites.PeriodicSite"><span class="pre">PeriodicSite</span></a></span></em><span class="sig-paren">)</span> <span class="sig-return"><span class="sig-return-icon">&#x2192;</span> <span class="sig-return-typehint"><span class="pre">list</span><span class="p"><span class="pre">[</span></span><a class="reference internal" href="pymatgen.core.html#pymatgen.core.sites.PeriodicSite" title="pymatgen.core.sites.PeriodicSite"><span class="pre">PeriodicSite</span></a><span class="p"><span class="pre">]</span></span></span></span><a class="reference external" href="https://github.com/materialsproject/pymatgen/blob/v2025.1.24/src/pymatgen/core/../symmetry/structure.py#L79-L95"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pymatgen.symmetry.structure.SymmetrizedStructure.find_equivalent_sites" title="Link to this definition"></a></dt>
<dd><p>Find all symmetrically equivalent sites for a particular site.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
<dd class="field-odd"><p><strong>site</strong> (<a class="reference internal" href="pymatgen.core.html#pymatgen.core.sites.PeriodicSite" title="pymatgen.core.sites.PeriodicSite"><em>PeriodicSite</em></a>) – A site in the structure</p>
</dd>
<dt class="field-even">Raises<span class="colon">:</span></dt>
<dd class="field-even"><p><strong>ValueError</strong> – if site is not in the structure.</p>
</dd>
<dt class="field-odd">Returns<span class="colon">:</span></dt>
<dd class="field-odd"><p>all symmetrically equivalent sites.</p>
</dd>
<dt class="field-even">Return type<span class="colon">:</span></dt>
<dd class="field-even"><p>list[<a class="reference internal" href="pymatgen.core.html#pymatgen.core.sites.PeriodicSite" title="pymatgen.core.sites.PeriodicSite">PeriodicSite</a>]</p>
</dd>
</dl>
</dd></dl>

<dl class="py method">
<dt class="sig sig-object py" id="pymatgen.symmetry.structure.SymmetrizedStructure.from_dict">
<em class="property"><span class="pre">classmethod</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">from_dict</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">dct</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">dict</span></span></em><span class="sig-paren">)</span> <span class="sig-return"><span class="sig-return-icon">&#x2192;</span> <span class="sig-return-typehint"><span class="pre">Self</span></span></span><a class="reference external" href="https://github.com/materialsproject/pymatgen/blob/v2025.1.24/src/pymatgen/core/../symmetry/structure.py#L136-L150"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pymatgen.symmetry.structure.SymmetrizedStructure.from_dict" title="Link to this definition"></a></dt>
<dd><dl class="field-list simple">
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
<dd class="field-odd"><p><strong>dct</strong> (<em>dict</em>) – Dict representation.</p>
</dd>
<dt class="field-even">Returns<span class="colon">:</span></dt>
<dd class="field-even"><p>SymmetrizedStructure</p>
</dd>
</dl>
</dd></dl>

</dd></dl>

</section>
</section>


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