View source for Pentellated 7-orthoplexes

{| class=wikitable align=right width=480
|-
!colspan=4|Orthogonal projections in B<sub>6</sub> Coxeter plane
|- align=center
|[[File:7-cube t6_B6.svg|120px]]<BR><small>[[7-orthoplex|7-orthoplex]]</small><BR>{{CDD|node_1|3|node|3|node|3|node|3|node|3|node|4|node}}
|[[File:7-cube t16_B6.svg|120px]]<BR><small>Pentellated 7-orthoplex</small><BR>{{CDD|node_1|3|node|3|node|3|node|3|node|3|node_1|4|node}}
|[[File:7-cube t156_B6.svg|120px]]<BR><small>Pentitruncated 7-orthoplex</small><BR>{{CDD|node_1|3|node_1|3|node|3|node|3|node|3|node_1|4|node}}
|[[File:7-cube t146_B6.svg|120px]]<BR><small>Penticantellated 7-orthoplex</small><BR>{{CDD|node_1|3|node|3|node_1|3|node|3|node|3|node_1|4|node}} 
|- align=center
|[[File:7-cube t1456_B6.svg|120px]]<BR><small>Penticantitruncated 7-orthoplex</small><BR>{{CDD|node_1|3|node_1|3|node_1|3|node|3|node|3|node_1|4|node}} 
|[[File:7-cube t136_B6.svg|120px]]<BR><small>Pentiruncinated 7-orthoplex</small><BR>{{CDD|node_1|3|node|3|node|3|node_1|3|node|3|node_1|4|node}} 
|[[File:7-cube t1356_B6.svg|120px]]<BR><small>Pentiruncitruncated 7-orthoplex</small><BR>{{CDD|node_1|3|node_1|3|node|3|node_1|3|node|3|node_1|4|node}} 
|[[File:7-cube t1346_B6.svg|120px]]<BR><small>Pentiruncicantellated 7-orthoplex</small><BR>{{CDD|node_1|3|node|3|node_1|3|node_1|3|node|3|node_1|4|node}} 
|- align=center
|[[File:7-cube t13456_B6.svg|120px]]<BR><small>Pentiruncicantitruncated 7-orthoplex</small><BR>{{CDD|node_1|3|node_1|3|node_1|3|node_1|3|node|3|node_1|4|node}} 
|[[File:7-cube t126_B6.svg|120px]]<BR><small>Pentistericated 7-orthoplex</small><BR>{{CDD|node_1|3|node|3|node|3|node|3|node_1|3|node_1|4|node}} 
|[[File:7-cube t1256_B6.svg|120px]]<BR><small>Pentisteritruncated 7-orthoplex</small><BR>{{CDD|node_1|3|node_1|3|node|3|node|3|node_1|3|node_1|4|node}}
|[[File:7-cube t1246_B6.svg|120px]]<BR><small>Pentistericantellated 7-orthoplex</small><BR>{{CDD|node_1|3|node|3|node_1|3|node|3|node_1|3|node_1|4|node}} 
|- align=center
|[[File:7-cube t12456_B6.svg|120px]]<BR><small>Pentistericantitruncated 7-orthoplex</small><BR>{{CDD|node_1|3|node_1|3|node_1|3|node|3|node_1|3|node_1|4|node}} 
|[[File:7-cube t1235_B6.svg|120px]]<BR><small>Pentisteriruncinated 7-orthoplex</small><BR>{{CDD|node_1|3|node|3|node|3|node_1|3|node_1|3|node_1|4|node}} 
|[[File:7-cube t12356_B6.svg|120px]]<BR><small>Pentisteriruncitruncated 7-orthoplex</small><BR>{{CDD|node_1|3|node_1|3|node|3|node_1|3|node_1|3|node_1|4|node}} 
|[[File:7-cube t12346_B6.svg|120px]]<BR><small>Pentisteriruncicantellated 7-orthoplex</small><BR>{{CDD|node_1|3|node|3|node_1|3|node_1|3|node_1|3|node_1|4|node}} 
|- align=center
|[[File:7-cube t123456_B6.svg|120px]]<BR><small>Pentisteriruncicantitruncated 7-orthoplex</small><BR>{{CDD|node_1|3|node_1|3|node_1|3|node_1|3|node_1|3|node_1|4|node}} 
|}
In seven-dimensional [[Geometry|geometry]], a '''pentellated 7-orthoplex''' is a convex uniform 7-polytope with 5th order [[Truncation (geometry)|truncations]] (pentellation) of the regular [[7-orthoplex|7-orthoplex]].

There are 32 unique {{not a typo|pentellations}} of the 7-orthoplex with permutations of truncations, cantellations, runcinations, and {{not a typo|sterications}}. 16 are more simply constructed relative to the [[7-cube|7-cube]].

These polytopes are a part of a set of 127 uniform 7-polytopes with B<sub>7</sub> symmetry.

==Pentellated 7-orthoplex==

{| class="wikitable" align="right" style="margin-left:10px" width="250"
! style="background:#e7dcc3;" colspan="2"|Pentellated 7-orthoplex
|-
| style="background:#e7dcc3;"|Type||uniform 7-polytope
|-
| style="background:#e7dcc3;"|[[Schläfli symbol]]|| t<sub>0,5</sub>{3<sup>5</sup>,4}
|-
| style="background:#e7dcc3;"|Coxeter diagram||{{CDD|node_1|3|node|3|node|3|node|3|node|3|node_1|4|node}}<BR>{{CDD|node_1|3|node|3|node|3|node|3|node|split1|nodes_11}}
|-
| style="background:#e7dcc3;"|6-faces||
|-
| style="background:#e7dcc3;"|5-faces||
|-
| style="background:#e7dcc3;"|4-faces||
|-
| style="background:#e7dcc3;"|Cells||
|-
| style="background:#e7dcc3;"|Faces||
|-
| style="background:#e7dcc3;"|Edges||20160
|-
| style="background:#e7dcc3;"|Vertices||2688
|-
| style="background:#e7dcc3;"|[[Vertex figure]]||
|-
| style="background:#e7dcc3;"|[[Coxeter group]]s||B<sub>7</sub>, [4,3<sup>5</sup>]
|-
| style="background:#e7dcc3;"|Properties||[[Convex polytope|convex]]
|}
=== Alternate names===
* Small hecatonicosoctaexon (acronym: Staz) (Jonathan Bowers)<ref>Klitzing, (x3o3o3o3o3x4o - )</ref>

=== Coordinates ===
Coordinates are permutations of (0,1,1,1,1,1,2){{radic|2}}

=== Images ===

==Pentitruncated 7-orthoplex==
{| class="wikitable" align="right" style="margin-left:10px" width="250"
! style="background:#e7dcc3;" colspan="2"|pentitruncated 7-orthoplex
|-
| style="background:#e7dcc3;"|Type||uniform 7-polytope
|-
| style="background:#e7dcc3;"|[[Schläfli symbol]]|| t<sub>0,1,5</sub>{3<sup>5</sup>,4}
|-
| style="background:#e7dcc3;"|Coxeter diagram||{{CDD|node_1|3|node_1|3|node|3|node|3|node|3|node_1|4|node}}<BR>{{CDD|node_1|3|node_1|3|node|3|node|3|node|split1|nodes_11}}
|-
| style="background:#e7dcc3;"|6-faces||
|-
| style="background:#e7dcc3;"|5-faces||
|-
| style="background:#e7dcc3;"|4-faces||
|-
| style="background:#e7dcc3;"|Cells||
|-
| style="background:#e7dcc3;"|Faces||
|-
| style="background:#e7dcc3;"|Edges||87360
|-
| style="background:#e7dcc3;"|Vertices||13440 
|-
| style="background:#e7dcc3;"|[[Vertex figure]]||
|-
| style="background:#e7dcc3;"|[[Coxeter group]]s||B<sub>7</sub>, [4,3<sup>5</sup>]
|-
| style="background:#e7dcc3;"|Properties||[[Convex polytope|convex]]
|}
=== Alternate names===
* Teritruncated hecatonicosoctaexon (acronym: Tetaz) (Jonathan Bowers)<ref>Klitzing, (x3x3o3o3o3x4o - )</ref>

=== Images ===

=== Coordinates===
Coordinates are permutations of (0,1,1,1,1,2,3).

==Penticantellated 7-orthoplex== 
{| class="wikitable" align="right" style="margin-left:10px" width="250"
! style="background:#e7dcc3;" colspan="2"|Penticantellated 7-orthoplex
|-
| style="background:#e7dcc3;"|Type||uniform 7-polytope
|-
| style="background:#e7dcc3;"|[[Schläfli symbol]]|| t<sub>0,2,5</sub>{3<sup>5</sup>,4}
|-
| style="background:#e7dcc3;"|Coxeter diagram||{{CDD|node_1|3|node|3|node_1|3|node|3|node|3|node_1|4|node}}<BR>{{CDD|node_1|3|node|3|node_1|3|node|3|node|split1|nodes_11}}
|-
| style="background:#e7dcc3;"|6-faces||
|-
| style="background:#e7dcc3;"|5-faces||
|-
| style="background:#e7dcc3;"|4-faces||
|-
| style="background:#e7dcc3;"|Cells||
|-
| style="background:#e7dcc3;"|Faces||
|-
| style="background:#e7dcc3;"|Edges||188160
|-
| style="background:#e7dcc3;"|Vertices||26880 
|-
| style="background:#e7dcc3;"|[[Vertex figure]]||
|-
| style="background:#e7dcc3;"|[[Coxeter group]]s||B<sub>7</sub>, [4,3<sup>5</sup>]
|-
| style="background:#e7dcc3;"|Properties||[[Convex polytope|convex]]
|}
=== Alternate names===
* Terirhombated hecatonicosoctaexon (acronym: Teroz) (Jonathan Bowers)<ref>Klitzing, (x3o3x3o3o3x4o - )</ref>

=== Coordinates ===
Coordinates are permutations of (0,1,1,1,2,2,3){{radic|2}}.

=== Images ===

==Penticantitruncated 7-orthoplex ==
{| class="wikitable" align="right" style="margin-left:10px" width="250"
! style="background:#e7dcc3;" colspan="2"|penticantitruncated 7-orthoplex
|-
| style="background:#e7dcc3;"|Type||uniform 7-polytope
|-
| style="background:#e7dcc3;"|[[Schläfli symbol]]|| t<sub>0,1,2,5</sub>{3<sup>5</sup>,4}
|-
| style="background:#e7dcc3;"|Coxeter diagram||{{CDD|node_1|3|node_1|3|node_1|3|node|3|node|3|node_1|4|node}}<BR>{{CDD|node_1|3|node_1|3|node_1|3|node|3|node|split1|nodes_11}}
|-
| style="background:#e7dcc3;"|6-faces||
|-
| style="background:#e7dcc3;"|5-faces||
|-
| style="background:#e7dcc3;"|4-faces||
|-
| style="background:#e7dcc3;"|Cells||
|-
| style="background:#e7dcc3;"|Faces||
|-
| style="background:#e7dcc3;"|Edges||295680
|-
| style="background:#e7dcc3;"|Vertices||53760
|-
| style="background:#e7dcc3;"|[[Vertex figure]]||
|-
| style="background:#e7dcc3;"|[[Coxeter group]]s||B<sub>7</sub>, [4,3<sup>5</sup>]
|-
| style="background:#e7dcc3;"|Properties||[[Convex polytope|convex]]
|}
=== Alternate names===
* Terigreatorhombated hecatonicosoctaexon (acronym: Tograz) (Jonathan Bowers)<ref>Klitzing, (x3x3x3oxo3x4o - )</ref>

===Coordinates===
Coordinates are permutations of (0,1,1,1,2,3,4){{radic|2}}.


==Pentiruncinated 7-orthoplex ==
{| class="wikitable" align="right" style="margin-left:10px" width="250"
! style="background:#e7dcc3;" colspan="2"|pentiruncinated 7-orthoplex
|-
| style="background:#e7dcc3;"|Type||uniform 7-polytope
|-
| style="background:#e7dcc3;"|[[Schläfli symbol]]|| t<sub>0,3,5</sub>{3<sup>5</sup>,4}
|-
| style="background:#e7dcc3;"|Coxeter diagram||{{CDD|node_1|3|node|3|node|3|node_1|3|node|3|node_1|4|node}}<BR>{{CDD|node_1|3|node|3|node|3|node_1|3|node|split1|nodes_11}}
|-
| style="background:#e7dcc3;"|6-faces||
|-
| style="background:#e7dcc3;"|5-faces||
|-
| style="background:#e7dcc3;"|4-faces||
|-
| style="background:#e7dcc3;"|Cells||
|-
| style="background:#e7dcc3;"|Faces||
|-
| style="background:#e7dcc3;"|Edges||174720
|-
| style="background:#e7dcc3;"|Vertices||26880
|-
| style="background:#e7dcc3;"|[[Vertex figure]]||
|-
| style="background:#e7dcc3;"|[[Coxeter group]]s||B<sub>7</sub>, [4,3<sup>5</sup>]
|-
| style="background:#e7dcc3;"|Properties||[[Convex polytope|convex]]
|}
=== Alternate names===
* Teriprismated hecatonicosoctaexon (acronym: Topaz) (Jonathan Bowers)<ref>Klitzing, (x3o3o3x3o3x4o - )</ref>

===Coordinates===
The coordinates are permutations of (0,1,1,2,2,2,3){{radic|2}}.

=== Images ===

==Pentiruncitruncated 7-orthoplex ==

{| class="wikitable" align="right" style="margin-left:10px" width="250"
! style="background:#e7dcc3;" colspan="2"|pentiruncitruncated 7-orthoplex
|-
| style="background:#e7dcc3;"|Type||uniform 7-polytope
|-
| style="background:#e7dcc3;"|[[Schläfli symbol]]|| t<sub>0,1,3,5</sub>{3<sup>5</sup>,4}
|-
| style="background:#e7dcc3;"|Coxeter diagram||{{CDD|node_1|3|node_1|3|node|3|node_1|3|node|3|node_1|4|node}}<BR>{{CDD|node_1|3|node_1|3|node|3|node_1|3|node|split1|nodes_11}}
|-
| style="background:#e7dcc3;"|6-faces||
|-
| style="background:#e7dcc3;"|5-faces||
|-
| style="background:#e7dcc3;"|4-faces||
|-
| style="background:#e7dcc3;"|Cells||
|-
| style="background:#e7dcc3;"|Faces||
|-
| style="background:#e7dcc3;"|Edges||443520
|-
| style="background:#e7dcc3;"|Vertices||80640 
|-
| style="background:#e7dcc3;"|[[Vertex figure]]||
|-
| style="background:#e7dcc3;"|[[Coxeter group]]s||B<sub>7</sub>, [4,3<sup>5</sup>]
|-
| style="background:#e7dcc3;"|Properties||[[Convex polytope|convex]]
|}
=== Alternate names===
* Teriprismatotruncated hecatonicosoctaexon (acronym: Toptaz) (Jonathan Bowers)<ref>Klitzing, (x3x3o3x3o3x4o - )</ref>

===Coordinates===
Coordinates are permutations of (0,1,1,2,2,3,4){{radic|2}}.

=== Images ===

==Pentiruncicantellated 7-orthoplex ==
{| class="wikitable" align="right" style="margin-left:10px" width="250"
! style="background:#e7dcc3;" colspan="2"|pentiruncicantellated 7-orthoplex
|-
| style="background:#e7dcc3;"|Type||uniform 7-polytope
|-
| style="background:#e7dcc3;"|[[Schläfli symbol]]|| t<sub>0,2,3,5</sub>{3<sup>5</sup>,4}
|-
| style="background:#e7dcc3;"|Coxeter diagram||{{CDD|node_1|3|node|3|node_1|3|node_1|3|node|3|node_1|4|node}}<BR>{{CDD|node_1|3|node|3|node_1|3|node_1|3|node|split1|nodes_11}}
|-
| style="background:#e7dcc3;"|6-faces||
|-
| style="background:#e7dcc3;"|5-faces||
|-
| style="background:#e7dcc3;"|4-faces||
|-
| style="background:#e7dcc3;"|Cells||
|-
| style="background:#e7dcc3;"|Faces||
|-
| style="background:#e7dcc3;"|Edges||403200
|-
| style="background:#e7dcc3;"|Vertices||80640
|-
| style="background:#e7dcc3;"|[[Vertex figure]]||
|-
| style="background:#e7dcc3;"|[[Coxeter group]]s||B<sub>7</sub>, [4,3<sup>5</sup>]
|-
| style="background:#e7dcc3;"|Properties||[[Convex polytope|convex]]
|}
=== Alternate names===
* Teriprismatorhombated hecatonicosoctaexon (acronym: Toparz) (Jonathan Bowers)<ref>Klitzing, (x3o3x3x3o3x4o - )</ref>

=== Coordinates ===
Coordinates are permutations of (0,1,1,2,3,3,4){{radic|2}}.

=== Images ===

==Pentiruncicantitruncated 7-orthoplex ==

{| class="wikitable" align="right" style="margin-left:10px" width="250"
! style="background:#e7dcc3;" colspan="2"|pentiruncicantitruncated 7-orthoplex
|-
| style="background:#e7dcc3;"|Type||uniform 7-polytope
|-
| style="background:#e7dcc3;"|[[Schläfli symbol]]|| t<sub>0,1,2,3,5</sub>{3<sup>5</sup>,4}
|-
| style="background:#e7dcc3;"|Coxeter diagram||{{CDD|node_1|3|node_1|3|node_1|3|node_1|3|node|3|node_1|4|node}}<BR>{{CDD|node_1|3|node_1|3|node_1|3|node_1|3|node|split1|nodes_11}}
|-
| style="background:#e7dcc3;"|6-faces||
|-
| style="background:#e7dcc3;"|5-faces||
|-
| style="background:#e7dcc3;"|4-faces||
|-
| style="background:#e7dcc3;"|Cells||
|-
| style="background:#e7dcc3;"|Faces||
|-
| style="background:#e7dcc3;"|Edges||725760
|-
| style="background:#e7dcc3;"|Vertices||161280
|-
| style="background:#e7dcc3;"|[[Vertex figure]]||
|-
| style="background:#e7dcc3;"|[[Coxeter group]]s||B<sub>7</sub>, [4,3<sup>5</sup>]
|-
| style="background:#e7dcc3;"|Properties||[[Convex polytope|convex]]
|}
=== Alternate names===
* Terigreatoprismated hecatonicosoctaexon (acronym: Tegopaz) (Jonathan Bowers)<ref>Klitzing, (x3x3x3x3o3x4o - )</ref>

===Coordinates===
Coordinates are permutations of (0,1,1,2,3,4,5){{radic|2}}.

=== Images ===

==Pentistericated 7-orthoplex ==
{| class="wikitable" align="right" style="margin-left:10px" width="250"
! style="background:#e7dcc3;" colspan="2"|pentistericated 7-orthoplex
|-
| style="background:#e7dcc3;"|Type||uniform 7-polytope
|-
| style="background:#e7dcc3;"|[[Schläfli symbol]]|| t<sub>0,4,5</sub>{3<sup>5</sup>,4}
|-
| style="background:#e7dcc3;"|Coxeter diagram||{{CDD|node_1|3|node|3|node|3|node|3|node_1|3|node_1|4|node}}<BR>{{CDD|node_1|3|node|3|node|3|node|3|node_1|split1|nodes_11}}
|-
| style="background:#e7dcc3;"|6-faces||
|-
| style="background:#e7dcc3;"|5-faces||
|-
| style="background:#e7dcc3;"|4-faces||
|-
| style="background:#e7dcc3;"|Cells||
|-
| style="background:#e7dcc3;"|Faces||
|-
| style="background:#e7dcc3;"|Edges||67200
|-
| style="background:#e7dcc3;"|Vertices||13440
|-
| style="background:#e7dcc3;"|[[Vertex figure]]||
|-
| style="background:#e7dcc3;"|[[Coxeter group]]s||B<sub>7</sub>, [4,3<sup>5</sup>]
|-
| style="background:#e7dcc3;"|Properties||[[Convex polytope|convex]]
|}
=== Alternate names===
* Tericellated hecatonicosoctaexon (acronym: Tocaz) (Jonathan Bowers)<ref>Klitzing, (x3o3o3o3x3x4o - )</ref>

=== Images ===

=== Coordinates===
Coordinates are permutations of (0,1,2,2,2,2,3){{radic|2}}.

==Pentisteritruncated 7-orthoplex==
{| class="wikitable" align="right" style="margin-left:10px" width="250"
! style="background:#e7dcc3;" colspan="2"|pentisteritruncated 7-orthoplex
|-
| style="background:#e7dcc3;"|Type||uniform 7-polytope
|-
| style="background:#e7dcc3;"|[[Schläfli symbol]]|| t<sub>0,1,4,5</sub>{3<sup>5</sup>,4}
|-
| style="background:#e7dcc3;"|Coxeter diagram||{{CDD|node_1|3|node_1|3|node|3|node|3|node_1|3|node_1|4|node}}<BR>{{CDD|node_1|3|node_1|3|node|3|node|3|node_1|split1|nodes_11}}
|-
| style="background:#e7dcc3;"|6-faces||
|-
| style="background:#e7dcc3;"|5-faces||
|-
| style="background:#e7dcc3;"|4-faces||
|-
| style="background:#e7dcc3;"|Cells||
|-
| style="background:#e7dcc3;"|Faces||
|-
| style="background:#e7dcc3;"|Edges||241920
|-
| style="background:#e7dcc3;"|Vertices||53760
|-
| style="background:#e7dcc3;"|[[Vertex figure]]||
|-
| style="background:#e7dcc3;"|[[Coxeter group]]s||B<sub>7</sub>, [4,3<sup>5</sup>]
|-
| style="background:#e7dcc3;"|Properties||[[Convex polytope|convex]]
|}
=== Alternate names===
* Tericellitruncated hecatonicosoctaexon (acronym: Tacotaz) (Jonathan Bowers)<ref>Klitzing, (x3x3o3o3x3x4o - )</ref>

=== Coordinates===
Coordinates are permutations of (0,1,2,2,2,3,4){{radic|2}}.

=== Images ===

==Pentistericantellated 7-orthoplex== 
{| class="wikitable" align="right" style="margin-left:10px" width="250"
! style="background:#e7dcc3;" colspan="2"|pentistericantellated 7-orthoplex
|-
| style="background:#e7dcc3;"|Type||uniform 7-polytope
|-
| style="background:#e7dcc3;"|[[Schläfli symbol]]|| t<sub>0,2,4,5</sub>{3<sup>5</sup>,4}
|-
| style="background:#e7dcc3;"|Coxeter diagram||{{CDD|node_1|3|node|3|node_1|3|node|3|node_1|3|node_1|4|node}}<BR>{{CDD|node_1|3|node|3|node_1|3|node|3|node_1|split1|nodes_11}}
|-
| style="background:#e7dcc3;"|6-faces||
|-
| style="background:#e7dcc3;"|5-faces||
|-
| style="background:#e7dcc3;"|4-faces||
|-
| style="background:#e7dcc3;"|Cells||
|-
| style="background:#e7dcc3;"|Faces||
|-
| style="background:#e7dcc3;"|Edges||403200
|-
| style="background:#e7dcc3;"|Vertices||80640
|-
| style="background:#e7dcc3;"|[[Vertex figure]]||
|-
| style="background:#e7dcc3;"|[[Coxeter group]]s||B<sub>7</sub>, [4,3<sup>5</sup>]
|-
| style="background:#e7dcc3;"|Properties||[[Convex polytope|convex]]
|}
=== Alternate names===
* Tericellirhombated hecatonicosoctaexon (acronym: Tocarz) (Jonathan Bowers)<ref>Klitzing, (x3o3x3o3x3x4o - )</ref>

=== Coordinates===
Coordinates are permutations of (0,1,2,2,3,3,4){{radic|2}}.

=== Images ===

==Pentistericantitruncated 7-orthoplex ==
{| class="wikitable" align="right" style="margin-left:10px" width="250"
! style="background:#e7dcc3;" colspan="2"|pentistericantitruncated 7-orthoplex
|-
| style="background:#e7dcc3;"|Type||uniform 7-polytope
|-
| style="background:#e7dcc3;"|[[Schläfli symbol]]|| t<sub>0,1,2,4,5</sub>{3<sup>5</sup>,4}
|-
| style="background:#e7dcc3;"|Coxeter diagram||{{CDD|node_1|3|node_1|3|node_1|3|node|3|node_1|3|node_1|4|node}}<BR>{{CDD|node_1|3|node_1|3|node_1|3|node|3|node_1|split1|nodes_11}}
|-
| style="background:#e7dcc3;"|6-faces||
|-
| style="background:#e7dcc3;"|5-faces||
|-
| style="background:#e7dcc3;"|4-faces||
|-
| style="background:#e7dcc3;"|Cells||
|-
| style="background:#e7dcc3;"|Faces||
|-
| style="background:#e7dcc3;"|Edges||645120
|-
| style="background:#e7dcc3;"|Vertices||161280
|-
| style="background:#e7dcc3;"|[[Vertex figure]]||
|-
| style="background:#e7dcc3;"|[[Coxeter group]]s||B<sub>7</sub>, [4,3<sup>5</sup>]
|-
| style="background:#e7dcc3;"|Properties||[[Convex polytope|convex]]
|}
=== Alternate names===
* Tericelligreatorhombated hecatonicosoctaexon (acronym: Tecagraz) (Jonathan Bowers)<ref>Klitzing, (x3x3x3o3x3x4o - )</ref>

=== Coordinates===
Coordinates are permutations of (0,1,2,2,3,4,5){{radic|2}}.

=== Images ===

==Pentisteriruncinated 7-orthoplex ==
{| class="wikitable" align="right" style="margin-left:10px" width="250"
! style="background:#e7dcc3;" colspan="2"|Pentisteriruncinated 7-orthoplex
|-
| style="background:#e7dcc3;"|Type||uniform 7-polytope
|-
| style="background:#e7dcc3;"|[[Schläfli symbol]]|| t<sub>0,3,4,5</sub>{3<sup>5</sup>,4}
|-
| style="background:#e7dcc3;"|Coxeter diagram||{{CDD|node_1|3|node|3|node|3|node_1|3|node_1|3|node_1|4|node}}<BR>{{CDD|node_1|3|node|3|node|3|node_1|3|node_1|split1|nodes_11}}
|-
| style="background:#e7dcc3;"|6-faces||
|-
| style="background:#e7dcc3;"|5-faces||
|-
| style="background:#e7dcc3;"|4-faces||
|-
| style="background:#e7dcc3;"|Cells||
|-
| style="background:#e7dcc3;"|Faces||
|-
| style="background:#e7dcc3;"|Edges||241920
|-
| style="background:#e7dcc3;"|Vertices||53760
|-
| style="background:#e7dcc3;"|[[Vertex figure]]||
|-
| style="background:#e7dcc3;"|[[Coxeter group]]s||B<sub>7</sub>, [4,3<sup>5</sup>]
|-
| style="background:#e7dcc3;"|Properties||[[Convex polytope|convex]]
|}
=== Alternate names===
* Bipenticantitruncated 7-orthoplex as t<sub>1,2,3,6</sub>{3<sup>5</sup>,4}
* Tericelliprismated hecatonicosoctaexon (acronym: Tecpaz) (Jonathan Bowers)<ref>Klitzing, (x3o3o3x3x3x4o - )</ref>

=== Coordinates===
Coordinates are permutations of (0,1,2,3,3,3,4){{radic|2}}.

=== Images ===

==Pentisteriruncitruncated 7-orthoplex ==
{| class="wikitable" align="right" style="margin-left:10px" width="250"
! style="background:#e7dcc3;" colspan="2"|pentisteriruncitruncated 7-orthoplex
|-
| style="background:#e7dcc3;"|Type||uniform 7-polytope
|-
| style="background:#e7dcc3;"|[[Schläfli symbol]]|| t<sub>0,1,3,4,5</sub>{3<sup>5</sup>,4}
|-
| style="background:#e7dcc3;"|Coxeter diagram||{{CDD|node_1|3|node_1|3|node|3|node_1|3|node_1|3|node_1|4|node}}<BR>{{CDD|node_1|3|node_1|3|node|3|node_1|3|node_1|split1|nodes_11}}
|-
| style="background:#e7dcc3;"|6-faces||
|-
| style="background:#e7dcc3;"|5-faces||
|-
| style="background:#e7dcc3;"|4-faces||
|-
| style="background:#e7dcc3;"|Cells||
|-
| style="background:#e7dcc3;"|Faces||
|-
| style="background:#e7dcc3;"|Edges||645120
|-
| style="background:#e7dcc3;"|Vertices||161280
|-
| style="background:#e7dcc3;"|[[Vertex figure]]||
|-
| style="background:#e7dcc3;"|[[Coxeter group]]s||B<sub>7</sub>, [4,3<sup>5</sup>]
|-
| style="background:#e7dcc3;"|Properties||[[Convex polytope|convex]]
|}
=== Alternate names===
* Tericelliprismatotruncated hecatonicosoctaexon (acronym: Tecpotaz) (Jonathan Bowers)<ref>Klitzing, (x3x3o3x3x3x4o - )</ref>

=== Coordinates===
Coordinates are permutations of (0,1,2,3,3,4,5){{radic|2}}.

=== Images ===

==Pentisteriruncicantellated 7-orthoplex ==
{| class="wikitable" align="right" style="margin-left:10px" width="250"
! style="background:#e7dcc3;" colspan="2"|pentisteriruncicantellated 7-orthoplex
|-
| style="background:#e7dcc3;"|Type||uniform 7-polytope
|-
| style="background:#e7dcc3;"|[[Schläfli symbol]]|| t<sub>0,2,3,4,5</sub>{3<sup>5</sup>,4}
|-
| style="background:#e7dcc3;"|Coxeter diagram||{{CDD|node_1|3|node|3|node_1|3|node_1|3|node_1|3|node_1|4|node}}<BR>{{CDD|node_1|3|node|3|node_1|3|node_1|3|node_1|split1|nodes_11}}
|-
| style="background:#e7dcc3;"|6-faces||
|-
| style="background:#e7dcc3;"|5-faces||
|-
| style="background:#e7dcc3;"|4-faces||
|-
| style="background:#e7dcc3;"|Cells||
|-
| style="background:#e7dcc3;"|Faces||
|-
| style="background:#e7dcc3;"|Edges||645120 
|-
| style="background:#e7dcc3;"|Vertices||161280
|-
| style="background:#e7dcc3;"|[[Vertex figure]]||
|-
| style="background:#e7dcc3;"|[[Coxeter group]]s||B<sub>7</sub>, [4,3<sup>5</sup>]
|-
| style="background:#e7dcc3;"|Properties||[[Convex polytope|convex]]
|}
=== Alternate names===
* Bipentiruncicantitruncated 7-orthoplex as t<sub>1,2,3,4,6</sub>{3<sup>5</sup>,4}
* Tericelliprismatorhombated hecatonicosoctaexon (acronym: Tacparez) (Jonathan Bowers)<ref>Klitzing, (x3o3x3x3x3x4o - )</ref>

=== Coordinates===
Coordinates are permutations of (0,1,2,3,4,4,5){{radic|2}}.

=== Images ===

==Pentisteriruncicantitruncated 7-orthoplex== 
{| class="wikitable" align="right" style="margin-left:10px" width="250"
! style="background:#e7dcc3;" colspan="2"|pentisteriruncicantitruncated 7-orthoplex
|-
| style="background:#e7dcc3;"|Type||uniform 7-polytope
|-
| style="background:#e7dcc3;"|[[Schläfli symbol]]|| t<sub>0,1,2,3,4,5</sub>{3<sup>5</sup>,4}
|-
| style="background:#e7dcc3;"|Coxeter diagram||{{CDD|node_1|3|node_1|3|node_1|3|node_1|3|node_1|3|node_1|4|node}}<BR>{{CDD|node_1|3|node_1|3|node_1|3|node_1|3|node_1|split1|nodes_11}}
|-
| style="background:#e7dcc3;"|6-faces||
|-
| style="background:#e7dcc3;"|5-faces||
|-
| style="background:#e7dcc3;"|4-faces||
|-
| style="background:#e7dcc3;"|Cells||
|-
| style="background:#e7dcc3;"|Faces||
|-
| style="background:#e7dcc3;"|Edges||1128960
|-
| style="background:#e7dcc3;"|Vertices||322560
|-
| style="background:#e7dcc3;"|[[Vertex figure]]||
|-
| style="background:#e7dcc3;"|[[Coxeter group]]s||B<sub>7</sub>, [4,3<sup>5</sup>]
|-
| style="background:#e7dcc3;"|Properties||[[Convex polytope|convex]]
|}
=== Alternate names===
* Great hecatonicosoctaexon (acronym: Gotaz) (Jonathan Bowers)<ref>Klitzing, (x3x3x3x3x3x4o - )</ref>

=== Coordinates===
Coordinates are permutations of (0,1,2,3,4,5,6){{radic|2}}.

=== Images ===

== Notes ==
{{reflist}}

== References==
* [[Biography:Harold Scott MacDonald Coxeter|H.S.M. Coxeter]]: 
** H.S.M. Coxeter, ''Regular Polytopes'', 3rd Edition, Dover New York, 1973 
** '''Kaleidoscopes: Selected Writings of H.S.M. Coxeter''', edited by F. Arthur Sherk, Peter McMullen, Anthony C. Thompson, Asia Ivic Weiss, Wiley-Interscience Publication, 1995, {{isbn|978-0-471-01003-6}} [http://www.wiley.com/WileyCDA/WileyTitle/productCd-0471010030.html]
*** (Paper 22) H.S.M. Coxeter, ''Regular and Semi Regular Polytopes I'', [Math. Zeit. 46 (1940) 380-407, MR 2,10]
*** (Paper 23) H.S.M. Coxeter, ''Regular and Semi-Regular Polytopes II'', [Math. Zeit. 188 (1985) 559-591]
*** (Paper 24) H.S.M. Coxeter, ''Regular and Semi-Regular Polytopes III'', [Math. Zeit. 200 (1988) 3-45]
* [[Biography:Norman Johnson (mathematician)|Norman Johnson]] ''Uniform Polytopes'', Manuscript (1991)
** N.W. Johnson: ''The Theory of Uniform Polytopes and Honeycombs'', Ph.D. 
* {{KlitzingPolytopes|polyexa.htm|7D|uniform polytopes (polyexa)}} 

== External links ==
* [http://www.polytope.net/hedrondude/topes.htm Polytopes of Various Dimensions]
* [http://tetraspace.alkaline.org/glossary.htm Multi-dimensional Glossary]

{{Polytopes}}

[[Category:7-polytopes]]

{{Sourceattribution|Pentellated 7-orthoplexes}}