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<?xml version="1.0"?>
<reginadata engine="4.5">
<packet label="Container"
type="Container" typeid="1"
parent="">
<packet label="Sample Data File"
type="Text" typeid="2"
parent="Container">
<text>In this file you will find some sample packets that illustrate the objects with
which Regina can work.</text>
</packet> <!-- Sample Data File (Text) -->
<packet label="Triangulations"
type="Container" typeid="1"
parent="Container">
<packet label="Figure 8 Knot Complement"
type="Triangulation" typeid="3"
parent="Triangulations">
<tetrahedra ntet="2">
<tet desc=""> 1 108 1 75 1 30 1 198 </tet>
<tet desc=""> 0 108 0 75 0 30 0 198 </tet>
</tetrahedra>
<H1><abeliangroup rank="1"> </abeliangroup></H1>
<packet label="Tri-Quad Normal Surfaces"
type="Normal Surface List" typeid="6"
parent="Figure 8 Knot Complement">
<params embedded="T" flavourid="0"
flavour="Standard normal (tri-quad)"/>
<surface len="14" name=""> 0 1 1 1 2 1 3 1 7 1 8 1 9 1 10 1
<euler value="0"/>
<orbl value="true"/>
<twosided value="true"/>
<connected value="true"/>
<realbdry value="F"/>
<compact value="T"/> </surface>
</packet> <!-- Tri_Quad Normal Surfaces (Normal Surface List) -->
<packet label="Quad Normal Surfaces"
type="Normal Surface List" typeid="6"
parent="Figure 8 Knot Complement">
<params embedded="T" flavourid="1"
flavour="Quad normal"/>
<surface len="6" name=""> 0 2 5 1
<realbdry value="F"/>
<compact value="F"/> </surface>
<surface len="6" name=""> 1 2 5 1
<realbdry value="F"/>
<compact value="F"/> </surface>
<surface len="6" name=""> 2 1 3 2
<realbdry value="F"/>
<compact value="F"/> </surface>
<surface len="6" name=""> 2 1 4 2
<realbdry value="F"/>
<compact value="F"/> </surface>
</packet> <!-- Quad Normal Surfaces (Normal Surface List) -->
<packet label="Angle Structures"
type="Angle Structure List" typeid="9"
parent="Figure 8 Knot Complement">
<struct len="7"> 0 1 4 1 6 1 <flags value="6"/></struct>
<struct len="7"> 1 1 3 1 6 1 <flags value="6"/></struct>
<struct len="7"> 2 1 5 1 6 1 <flags value="6"/></struct>
<struct len="7"> 2 2 3 1 4 1 6 2 <flags value="4"/></struct>
<struct len="7"> 0 1 1 1 5 2 6 2 <flags value="4"/></struct>
<allowstrict value="T"/>
<allowtaut value="T"/>
</packet> <!-- Angle Structures (Angle Structure List) -->
</packet> <!-- Figure 8 Knot Complement (Triangulation) -->
<packet label="Layered Solid Torus"
type="Triangulation" typeid="3"
parent="Triangulations">
<tetrahedra ntet="4">
<tet desc=""> 1 54 1 156 -1 -1 -1 -1 </tet>
<tet desc=""> 2 54 2 156 0 135 0 120 </tet>
<tet desc=""> 3 39 3 216 1 135 1 120 </tet>
<tet desc=""> 3 57 3 147 2 216 2 39 </tet>
</tetrahedra>
<H1><abeliangroup rank="1"> </abeliangroup></H1>
<packet label="Normal Surfaces"
type="Normal Surface List" typeid="6"
parent="Layered Solid Torus">
<params embedded="T" flavourid="0"
flavour="Standard normal (tri-quad)"/>
<surface len="28" name=""> 6 1 12 1 18 1 26 1
<euler value="-1"/>
<orbl value="false"/>
<twosided value="false"/>
<connected value="true"/>
<realbdry value="T"/>
<compact value="T"/> </surface>
<surface len="28" name=""> 2 1 3 1 4 1 7 1 8 1 9 1 10 1 14 1 15 1 18 1 26 2
<euler value="-2"/>
<orbl value="true"/>
<twosided value="true"/>
<connected value="true"/>
<realbdry value="T"/>
<compact value="T"/> </surface>
<surface len="28" name=""> 5 2 9 1 10 1 11 1 14 1 15 1 18 1 26 2
<euler value="-2"/>
<orbl value="true"/>
<twosided value="true"/>
<connected value="true"/>
<realbdry value="T"/>
<compact value="T"/> </surface>
<surface len="28" name=""> 0 2 1 2 6 1 7 1 8 1 13 1 14 1 15 1 26 1
<euler value="0"/>
<orbl value="false"/>
<twosided value="false"/>
<connected value="true"/>
<realbdry value="T"/>
<compact value="T"/> </surface>
<surface len="28" name=""> 0 1 1 1 2 1 3 1 7 1 8 1 9 1 10 1 14 1 15 1 18 1 26 2
<euler value="-1"/>
<orbl value="true"/>
<twosided value="true"/>
<connected value="true"/>
<realbdry value="T"/>
<compact value="T"/> </surface>
<surface len="28" name=""> 2 1 3 1 4 1 7 1 8 1 9 1 10 1 14 1 15 1 16 1 17 1 21 1 22 1 23 1 24 1
<euler value="0"/>
<orbl value="true"/>
<twosided value="true"/>
<connected value="true"/>
<realbdry value="T"/>
<compact value="T"/> </surface>
<surface len="28" name=""> 5 2 9 1 10 1 11 1 14 1 15 1 16 1 17 1 21 1 22 1 23 1 24 1
<euler value="0"/>
<orbl value="true"/>
<twosided value="true"/>
<connected value="true"/>
<realbdry value="T"/>
<compact value="T"/> </surface>
<surface len="28" name=""> 0 1 1 1 2 1 3 1 7 1 8 1 9 1 10 1 14 1 15 1 16 1 17 1 21 1 22 1 23 1 24 1
<euler value="1"/>
<orbl value="true"/>
<twosided value="true"/>
<connected value="true"/>
<realbdry value="T"/>
<compact value="T"/> </surface>
<surface len="28" name=""> 6 2 12 2 16 1 17 1 18 1 21 1 22 1 23 1 24 1
<euler value="0"/>
<orbl value="true"/>
<twosided value="true"/>
<connected value="true"/>
<realbdry value="T"/>
<compact value="T"/> </surface>
<surface len="28" name=""> 4 2 13 2 19 2 23 1 24 1 25 1
<euler value="-2"/>
<orbl value="true"/>
<twosided value="true"/>
<connected value="true"/>
<realbdry value="T"/>
<compact value="T"/> </surface>
<surface len="28" name=""> 0 2 1 2 13 2 19 2 23 1 24 1 25 1
<euler value="0"/>
<orbl value="true"/>
<twosided value="true"/>
<connected value="true"/>
<realbdry value="T"/>
<compact value="T"/> </surface>
<surface len="28" name=""> 0 4 1 4 6 3 7 3 8 3 13 1 14 1 15 1 20 2 21 1 22 1 27 1
<euler value="1"/>
<orbl value="true"/>
<twosided value="true"/>
<connected value="true"/>
<realbdry value="T"/>
<compact value="T"/> </surface>
</packet> <!-- Normal Surfaces (Normal Surface List) -->
<packet label="Almost Normal Surfaces"
type="Normal Surface List" typeid="6"
parent="Layered Solid Torus">
<params embedded="T" flavourid="100"
flavour="Standard almost normal (tri-quad-oct)"/>
<surface len="40" name=""> 0 1 1 1 5 1 18 1 20 1 21 1 35 1
<euler value="-2"/>
<orbl value="false"/>
<twosided value="false"/>
<connected value="true"/>
<realbdry value="T"/>
<compact value="T"/> </surface>
<surface len="40" name=""> 6 1 15 1 24 1 35 1
<euler value="-1"/>
<orbl value="false"/>
<twosided value="false"/>
<connected value="true"/>
<realbdry value="T"/>
<compact value="T"/> </surface>
<surface len="40" name=""> 2 1 3 1 4 1 10 1 11 1 12 1 13 1 20 1 21 1 24 1 35 2
<euler value="-2"/>
<orbl value="true"/>
<twosided value="true"/>
<connected value="true"/>
<realbdry value="T"/>
<compact value="T"/> </surface>
<surface len="40" name=""> 0 1 1 1 7 1 10 1 11 1 12 1 13 1 20 1 21 1 24 1 35 2
<euler value="-2"/>
<orbl value="true"/>
<twosided value="true"/>
<connected value="true"/>
<realbdry value="T"/>
<compact value="T"/> </surface>
<surface len="40" name=""> 0 1 1 1 8 1 10 1 11 1 16 1 20 1 21 1 35 1
<euler value="-2"/>
<orbl value="false"/>
<twosided value="false"/>
<connected value="true"/>
<realbdry value="T"/>
<compact value="T"/> </surface>
<surface len="40" name=""> 2 1 3 1 8 1 10 1 11 1 12 1 13 1 15 1 20 1 21 1 24 2 35 3
<euler value="-4"/>
<orbl value="false"/>
<twosided value="false"/>
<connected value="true"/>
<realbdry value="T"/>
<compact value="T"/> </surface>
<surface len="40" name=""> 5 2 12 1 13 1 14 1 20 1 21 1 24 1 35 2
<euler value="-2"/>
<orbl value="true"/>
<twosided value="true"/>
<connected value="true"/>
<realbdry value="T"/>
<compact value="T"/> </surface>
<surface len="40" name=""> 0 2 1 2 6 1 10 1 11 1 16 1 20 1 21 1 35 1
<euler value="0"/>
<orbl value="false"/>
<twosided value="false"/>
<connected value="true"/>
<realbdry value="T"/>
<compact value="T"/> </surface>
<surface len="40" name=""> 0 2 1 2 6 2 10 1 11 1 17 1 20 1 21 1 24 1 35 2
<euler value="-2"/>
<orbl value="true"/>
<twosided value="true"/>
<connected value="true"/>
<realbdry value="T"/>
<compact value="T"/> </surface>
<surface len="40" name=""> 0 1 1 1 2 1 3 1 10 1 11 1 12 1 13 1 20 1 21 1 24 1 35 2
<euler value="-1"/>
<orbl value="true"/>
<twosided value="true"/>
<connected value="true"/>
<realbdry value="T"/>
<compact value="T"/> </surface>
<surface len="40" name=""> 2 1 3 1 5 1 12 1 13 1 19 1 20 1 21 1 24 2 35 3
<euler value="-4"/>
<orbl value="false"/>
<twosided value="false"/>
<connected value="true"/>
<realbdry value="T"/>
<compact value="T"/> </surface>
<surface len="40" name=""> 6 1 15 1 22 1 23 1 38 1
<euler value="-1"/>
<orbl value="false"/>
<twosided value="false"/>
<connected value="true"/>
<realbdry value="T"/>
<compact value="T"/> </surface>
<surface len="40" name=""> 2 1 3 1 4 1 10 1 11 1 12 1 13 1 20 1 21 1 22 1 23 1 30 1 31 1 32 1 33 1
<euler value="0"/>
<orbl value="true"/>
<twosided value="true"/>
<connected value="true"/>
<realbdry value="T"/>
<compact value="T"/> </surface>
<surface len="40" name=""> 0 1 1 1 7 1 10 1 11 1 12 1 13 1 20 1 21 1 22 1 23 1 30 1 31 1 32 1 33 1
<euler value="0"/>
<orbl value="true"/>
<twosided value="true"/>
<connected value="true"/>
<realbdry value="T"/>
<compact value="T"/> </surface>
<surface len="40" name=""> 5 2 12 1 13 1 14 1 20 1 21 1 22 1 23 1 30 1 31 1 32 1 33 1
<euler value="0"/>
<orbl value="true"/>
<twosided value="true"/>
<connected value="true"/>
<realbdry value="T"/>
<compact value="T"/> </surface>
<surface len="40" name=""> 0 2 1 2 6 2 10 1 11 1 17 1 20 1 21 1 22 1 23 1 30 1 31 1 32 1 33 1
<euler value="0"/>
<orbl value="true"/>
<twosided value="true"/>
<connected value="true"/>
<realbdry value="T"/>
<compact value="T"/> </surface>
<surface len="40" name=""> 0 1 1 1 2 1 3 1 10 1 11 1 12 1 13 1 20 1 21 1 22 1 23 1 30 1 31 1 32 1 33 1
<euler value="1"/>
<orbl value="true"/>
<twosided value="true"/>
<connected value="true"/>
<realbdry value="T"/>
<compact value="T"/> </surface>
<surface len="40" name=""> 6 2 15 2 22 1 23 1 24 1 30 1 31 1 32 1 33 1
<euler value="0"/>
<orbl value="true"/>
<twosided value="true"/>
<connected value="true"/>
<realbdry value="T"/>
<compact value="T"/> </surface>
<surface len="40" name=""> 0 4 1 4 6 2 10 2 11 2 16 2 20 1 21 1 27 1 30 1 31 1 32 1 33 1
<euler value="0"/>
<orbl value="true"/>
<twosided value="true"/>
<connected value="true"/>
<realbdry value="T"/>
<compact value="T"/> </surface>
<surface len="40" name=""> 0 3 1 3 2 1 3 1 6 1 10 2 11 2 18 1 20 1 21 1 26 2 30 1 31 1 36 1
<euler value="-1"/>
<orbl value="false"/>
<twosided value="false"/>
<connected value="true"/>
<realbdry value="T"/>
<compact value="T"/> </surface>
<surface len="40" name=""> 4 2 16 2 25 2 32 1 33 1 34 1
<euler value="-2"/>
<orbl value="true"/>
<twosided value="true"/>
<connected value="true"/>
<realbdry value="T"/>
<compact value="T"/> </surface>
<surface len="40" name=""> 0 2 1 2 16 2 25 2 32 1 33 1 34 1
<euler value="0"/>
<orbl value="true"/>
<twosided value="true"/>
<connected value="true"/>
<realbdry value="T"/>
<compact value="T"/> </surface>
<surface len="40" name=""> 0 4 1 4 6 1 10 1 11 1 16 3 20 1 21 1 25 2 32 1 33 1 39 1
<euler value="-1"/>
<orbl value="false"/>
<twosided value="false"/>
<connected value="true"/>
<realbdry value="T"/>
<compact value="T"/> </surface>
<surface len="40" name=""> 0 4 1 4 6 3 10 3 11 3 16 1 20 1 21 1 26 2 30 1 31 1 36 1
<euler value="1"/>
<orbl value="true"/>
<twosided value="true"/>
<connected value="true"/>
<realbdry value="T"/>
<compact value="T"/> </surface>
<surface len="40" name=""> 0 6 1 6 6 4 10 4 11 4 16 2 20 2 21 2 26 2 30 1 31 1 37 1
<euler value="0"/>
<orbl value="true"/>
<twosided value="true"/>
<connected value="true"/>
<realbdry value="T"/>
<compact value="T"/> </surface>
</packet> <!-- Almost Normal Surfaces (Normal Surface List) -->
</packet> <!-- Layered Solid Torus (Triangulation) -->
<packet label="Poincaré Homology Sphere"
type="Triangulation" typeid="3"
parent="Triangulations">
<tetrahedra ntet="5">
<tet desc=""> 1 120 2 147 3 78 4 39 </tet>
<tet desc=""> 0 156 2 54 3 147 4 78 </tet>
<tet desc=""> 0 57 1 135 3 45 4 147 </tet>
<tet desc=""> 0 78 1 57 2 99 4 201 </tet>
<tet desc=""> 0 39 1 78 2 57 3 210 </tet>
</tetrahedra>
<fundgroup>
<group generators="2">
<reln> 0^-1 1^1 0^1 1^1 0^-1 1^-1 </reln>
<reln> 0^-1 1^1 0^1 1^-2 0^1 1^1 </reln>
</group>
</fundgroup>
<H1><abeliangroup rank="0"> </abeliangroup></H1>
<H1Rel><abeliangroup rank="0"> </abeliangroup></H1Rel>
<H1Bdry><abeliangroup rank="0"> </abeliangroup></H1Bdry>
<H2><abeliangroup rank="0"> </abeliangroup></H2>
<zeroeff value="T"/>
<splitsfce value="F"/>
</packet> <!-- Poincaré Homology Sphere (Triangulation) -->
<packet label="RP2xS1"
type="Triangulation" typeid="3"
parent="Triangulations">
<tetrahedra ntet="3">
<tet desc=""> 1 228 1 228 2 141 2 120 </tet>
<tet desc=""> 0 228 0 228 2 39 2 210 </tet>
<tet desc=""> 0 114 0 156 1 39 1 201 </tet>
</tetrahedra>
<fundgroup>
<group generators="2">
<reln> 0^1 1^-1 0^1 1^1 </reln>
<reln> 0^1 1^-1 0^-1 1^1 </reln>
</group>
</fundgroup>
<H1><abeliangroup rank="1"> 2 </abeliangroup></H1>
<H1Rel><abeliangroup rank="1"> 2 </abeliangroup></H1Rel>
<H1Bdry><abeliangroup rank="0"> </abeliangroup></H1Bdry>
<H2><abeliangroup rank="0"> 2 </abeliangroup></H2>
<packet label="Note"
type="Text" typeid="2"
parent="RP2xS1">
<text>There are in fact two triangulations of this 3-manifold with three tetrahedra.</text>
</packet> <!-- Note (Text) -->
</packet> <!-- RP2xS1 (Triangulation) -->
</packet> <!-- Triangulations (Container) -->
<packet label="Tori, Annuli and Discs"
type="Surface Filter" typeid="8"
parent="Container">
<filter type="Combination filter" typeid="2">
<op type="or"/>
</filter>
<packet label="Tori and Annuli"
type="Surface Filter" typeid="8"
parent="Tori, Annuli and Discs">
<filter type="Filter by basic properties" typeid="1">
<euler> 0 </euler>
<orbl value="T-"/>
<compact value="T-"/>
</filter>
</packet> <!-- Tori and Annuli (Surface Filter) -->
<packet label="Discs"
type="Surface Filter" typeid="8"
parent="Tori, Annuli and Discs">
<filter type="Filter by basic properties" typeid="1">
<euler> 1 </euler>
<orbl value="T-"/>
<compact value="T-"/>
<realbdry value="T-"/>
</filter>
</packet> <!-- Discs (Surface Filter) -->
</packet> <!-- Tori, Annuli and Discs (Surface Filter) -->
<packet label="Homology Summary"
type="Script" typeid="7"
parent="Container">
<var name="tri" value="Triangulations"/>
<line></line>
<line># See the Regina handbook for more elaborate sample Python sessions.</line>
<line></line>
<line># Output the homology of each triangulation.</line>
<line>t = tri.getFirstTreeChild()</line>
<line>while t != None:</line>
<line> print t.getPacketLabel() + ":", t.getHomologyH1()</line>
<line> t = t.getNextTreeSibling()</line>
</packet> <!-- Homology Summary (Script) -->
</packet> <!-- Container (Container) -->
</reginadata>
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