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# Copyright (c) 1997-2024
# Ewgenij Gawrilow, Michael Joswig, and the polymake team
# Technische Universität Berlin, Germany
# https://polymake.org
#
# This program is free software; you can redistribute it and/or modify it
# under the terms of the GNU General Public License as published by the
# Free Software Foundation; either version 2, or (at your option) any
# later version: http://www.gnu.org/licenses/gpl.txt.
#
# This program is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
# GNU General Public License for more details.
#-------------------------------------------------------------------------------
INCLUDE
global_categories.rules
# @topic category functions/Producing a polytope from scratch
# With these clients you can create polytopes belonging to various parameterized
# families which occur frequently in polytope theory, as well as several kinds
# of random polytopes.
# Regular polytopes and their friends are listed separately.
# @topic category functions/Producing regular polytopes and their generalizations
# This includes the Platonic solids and their generalizations into two directions.
# In dimension 3 there are the Archimedean, Catalan and Johnson solids.
# In higher dimensions there are the simplices, the cubes, the cross polytopes and
# three other regular 4-polytopes.
# @topic category functions/Producing a polytope from polytopes
# An important way of constructing polytopes is to modify an
# already existing polytope.
#
# Actually, these functions don't alter the input polytope
# (it is forbidden in polymake), but create a new polytope object.
#
# Many functions can at your choice either calculate the vertex or facet coordinates,
# or constrain themselves on the purely combinatorial description of the
# resulting polytope.
# @topic category functions/Producing a vector configuration
# A way of constructing vector configurations is to modify an
# already existing vector configuration.
# @topic category functions/Transformations
# These functions take a realized polytope and produce a new one by applying a
# suitable affine or projective transformation in order to obtain some special
# coordinate description but preserve the combinatorial type.
#
# For example, before you can polarize an arbitrary polyhedron, it
# must be transformed to a combinatorially equivalent bounded polytope with the
# origin as a relatively interior point. It is achieved with the sequence
# [[orthantify]] - [[bound]] - [[center]] - [[polarize]].
# @topic category functions/Coordinate conversions
# The following functions allow for the conversion of the coordinate type of cones and polytopes.
# @topic category functions/Comparing
# Functions based on graph isomorphisms.
# @topic category functions/Producing a cone
# Various constructions of cones.
# @topic category functions/Producing a polytope from graphs
# Polytope constructions which take graphs as input.
# @topic category functions/Producing a polytope from other objects
# Polytope constructions which take other big objects as input.
# @topic category functions/Producing a point configuration
# Constructing a point configuration, either from scratch or from existing objects.
# @topic category functions/Producing other objects
# Functions producing big objects which are not contained in application polytope.
# @topic category functions/Quotient spaces
# Topologic cell complexes defined as quotients over polytopes modulo a discrete group.
# @topic category functions/Finite metric spaces
# Tight spans and their connections to polyhedral geometry
# @topic category preferences/Convex hull computation
# descriptions of various convex hull algorithms available in polymake
# Local Variables:
# mode: perl
# cperl-indent-level: 3
# indent-tabs-mode:nil
# End:
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