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| {| align=right class=wikitable width=300
| | I would like to introduce myself to you, I am Andrew and my wife doesn't like it at all. I am currently a journey agent. Her family members life in Alaska but her husband wants them to move. It's not a typical [http://isaworld.pe.kr/?document_srl=392088 phone psychic readings] factor but what she likes performing is to play domino but she doesn't have psychic readings ([http://findyourflirt.net/index.php?m=member_profile&p=profile&id=117823 findyourflirt.net]) the time lately.<br><br>Here is my blog post; telephone psychic ([http://hknews.classicmall.com.hk/groups/some-simple-tips-for-personal-development-progress/ hknews.classicmall.com.hk]) |
| |+ Graphs of three [[List of regular polytopes#Convex 4|regular]] and related [[uniform polytope]]s
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| | || || || || || || || || || ||
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| |- style="vertical-align:top; text-align:center;"
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| |colspan=4|[[File:7-simplex t0.svg|100px]]<br/>[[7-simplex]]
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| |colspan=4|[[File:7-simplex t1.svg|100px]]<br/>[[Rectified 7-simplex]]
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| |colspan=4|[[File:7-simplex t01.svg|100px]]<br/>[[Truncated 7-simplex]]
| |
| |- style="vertical-align:top; text-align:center;"
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| |colspan=4|[[File:7-simplex t02.svg|100px]]<br/>[[Cantellated 7-simplex]]
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| |colspan=4|[[File:7-simplex t03.svg|100px]]<br/>[[Runcinated 7-simplex]]
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| |colspan=4|[[File:7-simplex t04.svg|100px]]<br/>[[Stericated 7-simplex]]
| |
| |- style="vertical-align:top; text-align:center;"
| |
| |colspan=6|[[File:7-simplex t05.svg|150px]]<br/>[[Pentellated 7-simplex]]
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| |colspan=6|[[File:7-simplex t06.svg|150px]]<br/>[[Hexicated 7-simplex]]
| |
| |- style="vertical-align:top; text-align:center;"
| |
| |colspan=4|[[File:7-cube t6.svg|100px]]<br/>[[7-orthoplex]]
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| |colspan=4|[[File:7-cube t56.svg|100px]]<br/>[[Truncated 7-orthoplex]]
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| |colspan=4|[[File:7-cube t5.svg|100px]]<br/>[[Rectified 7-orthoplex]]
| |
| |- style="vertical-align:top; text-align:center;"
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| |colspan=4|[[File:7-cube t46.svg|100px]]<br/>[[Cantellated 7-orthoplex]]
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| |colspan=4|[[File:7-cube t36.svg|100px]]<br/>[[Runcinated 7-orthoplex]]
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| |colspan=4|[[File:7-cube t26.svg|100px]]<br/>[[Stericated 7-orthoplex]]
| |
| |- style="vertical-align:top; text-align:center;"
| |
| |colspan=4|[[File:7-cube t16.svg|100px]]<br/>[[Pentellated 7-orthoplex]]
| |
| |colspan=4|[[File:7-cube t06.svg|100px]]<br/>[[Hexicated 7-cube]]
| |
| |colspan=4|[[File:7-cube t05.svg|100px]]<br/>[[Pentellated 7-cube]]
| |
| |- style="vertical-align:top; text-align:center;"
| |
| |colspan=4|[[File:7-cube t04.svg|100px]]<br/>[[Stericated 7-cube]]
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| |colspan=4|[[File:7-cube t02.svg|100px]]<br/>[[Cantellated 7-cube]]
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| |colspan=4|[[File:7-cube t03.svg|100px]]<br/>[[Runcinated 7-cube]]
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| |- style="vertical-align:top; text-align:center;"
| |
| |colspan=4|[[File:7-cube t0.svg|100px]]<br/>[[7-cube]]
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| |colspan=4|[[File:7-cube t01.svg|100px]]<br/>[[Truncated 7-cube]]
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| |colspan=4|[[File:7-cube t1.svg|100px]]<br/>[[Rectified 7-cube]]
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| |- style="vertical-align:top; text-align:center;"
| |
| |colspan=4|[[File:7-demicube t0 D7.svg|100px]]<br/>[[7-demicube]]
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| |colspan=4|[[File:7-demicube t01 D7.svg|100px]]<br/>[[Truncated 7-demicube]]
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| |colspan=4|[[File:7-demicube t02 D7.svg|100px]]<br/>[[Cantellated 7-demicube]]
| |
| |- style="vertical-align:top; text-align:center;"
| |
| |colspan=4|[[File:7-demicube t03 D7.svg|100px]]<br/>[[Runcinated 7-demicube]]
| |
| |colspan=4|[[File:7-demicube t04 D7.svg|100px]]<br/>[[Stericated 7-demicube]]
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| |colspan=4|[[File:7-demicube t05 D7.svg|100px]]<br/>[[Pentellated 7-demicube]]
| |
| |- style="vertical-align:top; text-align:center;"
| |
| |colspan=4|[[File:E7 graph.svg|100px]]<br/>[[3 21 polytope|3<sub>21</sub>]]
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| |colspan=4|[[File:Gosset 2 31 polytope.svg|100px]]<br/>[[2 31 polytope|2<sub>31</sub>]]
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| |colspan=4|[[File:Gosset 1 32 petrie.svg|100px]]<br/>[[1 32 polytope|1<sub>32</sub>]]
| |
| |}
| |
| In [[seven-dimensional space|seven-dimensional]] [[geometry]], a '''7-polytope''' is a [[polytope]] contained by 6-polytope facets. Each [[5-polytope]] [[Ridge (geometry)|ridge]] being shared by exactly two [[6-polytope]] [[Facet (mathematics)|facets]].
| |
| | |
| A '''uniform 7-polytope''' is one which is [[vertex-transitive]], and constructed from uniform [[6-polytope]] facets.
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| | |
| A proposed name for 7-polytopes is '''polyexon''' or '''polyecton'''.
| |
| | |
| == Regular 7-polytopes ==
| |
| | |
| Regular 7-polytopes are represented by the [[Schläfli symbol]] {p,q,r,s,t,u} with '''u''' {p,q,r,s,t} 6-polytopes [[Facet (mathematics)|facets]] around each 4-face.
| |
| | |
| There are exactly three such [[List of regular polytopes#Convex 4|convex regular 7-polytopes]]:
| |
| # {3,3,3,3,3,3} - [[7-simplex]]
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| # {4,3,3,3,3,3} - [[7-cube]]
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| # {3,3,3,3,3,4} - [[7-orthoplex]]
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| | |
| There are no nonconvex regular 7-polytopes.
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| | |
| == Euler characteristic ==
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| | |
| The [[Euler characteristic]] for 7-polytopes that are topological [[6-sphere]]s (including all convex 7-polytopes) is two. χ=V-E+F-C+f<sub>4</sub>-f<sub>5</sub>+f<sub>6</sub>=2.
| |
| | |
| == Uniform 7-polytopes by fundamental Coxeter groups ==
| |
| | |
| Uniform 7-polytopes with reflective symmetry can be generated by these four Coxeter groups, represented by permutations of rings of the [[Coxeter-Dynkin diagram]]s:
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| | |
| {| class="wikitable"
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| |-
| |
| !#
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| !colspan=2|[[Coxeter group]]
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| ![[Coxeter-Dynkin diagram|Coxeter-Dynkin<BR>diagram]]
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| !Regular and semiregular forms
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| !Uniform count
| |
| |-
| |
| |1||A<sub>7</sub>|| [3<sup>6</sup>]||{{CDD|node|3|node|3|node|3|node|3|node|3|node|3|node}}
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| |
| |
| * [[7-simplex]] - {3<sup>6</sup>}, {{CDD|node_1|3|node|3|node|3|node|3|node|3|node|3|node}}
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| |71
| |
| |-
| |
| |2||B<sub>7</sub>||[4,3<sup>5</sup>]||{{CDD|node|4|node|3|node|3|node|3|node|3|node|3|node}}
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| |
| |
| * [[7-cube]] - {4,3<sup>5</sup>}, {{CDD|node_1|4|node|3|node|3|node|3|node|3|node|3|node}}
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| * [[7-orthoplex]] - {3<sup>5</sup>,4}, {{CDD|node|4|node|3|node|3|node|3|node|3|node|3|node_1}}
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| |127
| |
| |-
| |
| |3||D<sub>7</sub>||[3<sup>4,1,1</sup>]||{{CDD|nodes|split2|node|3|node|3|node|3|node|3|node}}
| |
| |
| |
| * [[7-demicube]], {3<sup>1,4,1</sup>}, {{CDD|nodes_10ru|split2|node|3|node|3|node|3|node|3|node}}
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| * [[7-orthoplex]], {3<sup>4,1,1</sup>}, {{CDD|nodes|split2|node|3|node|3|node|3|node|3|node_1}}
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| |95 (32 unique)
| |
| |-
| |
| |4||[[E7 (mathematics)|E<sub>7</sub>]]||[3<sup>3,2,1</sup>]||{{CDD|nodea|3a|nodea|3a|branch|3a|nodea|3a|nodea|3a|nodea}}
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| |
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| * '''[[Gosset 3 21 polytope|3<sub>21</sub>]]''' - {{CDD|nodea|3a|nodea|3a|branch|3a|nodea|3a|nodea|3a|nodea_1}}
| |
| * '''[[Gosset 1 32 polytope|1<sub>32</sub>]]''' - {{CDD|nodea|3a|nodea|3a|branch_01lr|3a|nodea|3a|nodea|3a|nodea}}
| |
| * '''[[Gosset 2 31 polytope|2<sub>31</sub>]]''' - {{CDD|nodea_1|3a|nodea|3a|branch|3a|nodea|3a|nodea|3a|nodea}}
| |
| |127
| |
| |}
| |
| | |
| {| class="wikitable"
| |
| |+ Prismatic finite Coxeter groups
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| |-
| |
| !#
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| !colspan=2|[[Coxeter group]]
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| ![[Coxeter-Dynkin diagram]]
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| |-
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| !colspan=4|6+1
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| |-
| |
| |1 ||A<sub>6</sub>×A<sub>1</sub>|| [3<sup>5</sup>]×[ ]|| {{CDD|node|3|node|3|node|3|node|3|node|3|node|2|node}}
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| |-
| |
| |2 ||BC<sub>6</sub>×A<sub>1</sub>|| [4,3<sup>4</sup>]×[ ]|| {{CDD|node|4|node|3|node|3|node|3|node|3|node|2|node}}
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| |-
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| |3 ||D<sub>6</sub>×A<sub>1</sub>|| [3<sup>3,1,1</sup>]×[ ]|| {{CDD|nodes|split2|node|3|node|3|node|3|node|2|node}}
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| |-
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| |4 ||E<sub>6</sub>×A<sub>1</sub>|| [3<sup>2,2,1</sup>]×[ ]|| {{CDD|nodea|3a|nodea|3a|branch|3a|nodea|3a|nodea|2|nodea}}
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| |-
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| !colspan=4|5+2
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| |-
| |
| |1 ||A<sub>5</sub>×I<sub>2</sub>(p)|| [3,3,3]×[p]|| {{CDD|node|3|node|3|node|3|node|3|node|2|node|p|node}}
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| |-
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| |2 ||BC<sub>5</sub>×I<sub>2</sub>(p)|| [4,3,3]×[p]|| {{CDD|node|4|node|3|node|3|node|3|node|2|node|p|node}}
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| |-
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| |3 ||D<sub>5</sub>×I<sub>2</sub>(p)|| [3<sup>2,1,1</sup>]×[p]|| {{CDD|nodes|split2|node|3|node|3|node|2|node|p|node}}
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| |-
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| !colspan=4|5+1+1
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| |-
| |
| |1 ||A<sub>5</sub>×A<sub>1</sub><sup>2</sup>|| [3,3,3]×[ ]<sup>2</sup>|| {{CDD|node|3|node|3|node|3|node|3|node|2|node|2|node}}
| |
| |-
| |
| |2 ||BC<sub>5</sub>×A<sub>1</sub><sup>2</sup>|| [4,3,3]×[ ]<sup>2</sup>|| {{CDD|node|4|node|3|node|3|node|3|node|2|node|2|node}}
| |
| |-
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| |3 ||D<sub>5</sub>×A<sub>1</sub><sup>2</sup>|| [3<sup>2,1,1</sup>]×[ ]<sup>2</sup>|| {{CDD|nodes|split2|node|3|node|3|node|2|node|2|node}}
| |
| |-
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| !colspan=4|4+3
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| |-
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| |4 ||A<sub>4</sub>×A<sub>3</sub>|| [3,3,3]×[3,3]|| {{CDD|node|3|node|3|node|3|node|2|node|3|node|3|node}}
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| |-
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| |5 ||A<sub>4</sub>×BC<sub>3</sub>|| [3,3,3]×[4,3]|| {{CDD|node|3|node|3|node|3|node|2|node|4|node|3|node}}
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| |-
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| |6 ||A<sub>4</sub>×H<sub>3</sub>|| [3,3,3]×[5,3]|| {{CDD|node|3|node|3|node|3|node|2|node|5|node|3|node}}
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| |-
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| |7 ||BC<sub>4</sub>×A<sub>3</sub>|| [4,3,3]×[3,3]|| {{CDD|node|4|node|3|node|3|node|2|node|3|node|3|node}}
| |
| |-
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| |8 ||BC<sub>4</sub>×BC<sub>3</sub>|| [4,3,3]×[4,3]|| {{CDD|node|4|node|3|node|3|node|2|node|4|node|3|node}}
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| |-
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| |9 ||BC<sub>4</sub>×H<sub>3</sub>|| [4,3,3]×[5,3]|| {{CDD|node|4|node|3|node|3|node|2|node|5|node|3|node}}
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| |-
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| |10 ||H<sub>4</sub>×A<sub>3</sub>|| [5,3,3]×[3,3]|| {{CDD|node|5|node|3|node|3|node|2|node|3|node|3|node}}
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| |-
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| |11 ||H<sub>4</sub>×BC<sub>3</sub>|| [5,3,3]×[4,3]|| {{CDD|node|5|node|3|node|3|node|2|node|4|node|3|node}}
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| |-
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| |12 ||H<sub>4</sub>×H<sub>3</sub>|| [5,3,3]×[5,3]|| {{CDD|node|5|node|3|node|3|node|2|node|5|node|3|node}}
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| |-
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| |13 ||F<sub>4</sub>×A<sub>3</sub>|| [3,4,3]×[3,3]|| {{CDD|node|3|node|4|node|3|node|2|node|3|node|3|node}}
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| |-
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| |14 ||F<sub>4</sub>×BC<sub>3</sub>|| [3,4,3]×[4,3]|| {{CDD|node|3|node|4|node|3|node|2|node|4|node|3|node}}
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| |-
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| |15 ||F<sub>4</sub>×H<sub>3</sub>|| [3,4,3]×[5,3]|| {{CDD|node|3|node|4|node|3|node|2|node|5|node|3|node}}
| |
| |-
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| |16 ||D<sub>4</sub>×A<sub>3</sub>|| [3<sup>1,1,1</sup>]×[3,3]|| {{CDD|nodes|split2|node|3|node|2|node|3|node|3|node}}
| |
| |-
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| |17 ||D<sub>4</sub>×BC<sub>3</sub>|| [3<sup>1,1,1</sup>]×[4,3]|| {{CDD|nodes|split2|node|3|node|2|node|4|node|3|node}}
| |
| |-
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| |18 ||D<sub>4</sub>×H<sub>3</sub>|| [3<sup>1,1,1</sup>]×[5,3]|| {{CDD|nodes|split2|node|3|node|2|node|5|node|3|node}}
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| |-
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| !colspan=4|4+2+1
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| |-
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| |5 ||A<sub>4</sub>×I<sub>2</sub>(p)×A<sub>1</sub>|| [3,3,3]×[p]×[ ]|| {{CDD|node|3|node|3|node|3|node|2|node|p|node|2|node}}
| |
| |-
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| |6 ||BC<sub>4</sub>×I<sub>2</sub>(p)×A<sub>1</sub>|| [4,3,3]×[p]×[ ]|| {{CDD|node|4|node|3|node|3|node|2|node|p|node|2|node}}
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| |-
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| |7 ||F<sub>4</sub>×I<sub>2</sub>(p)×A<sub>1</sub>|| [3,4,3]×[p]×[ ]|| {{CDD|node|3|node|4|node|3|node|2|node|p|node|2|node}}
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| |-
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| |8 ||H<sub>4</sub>×I<sub>2</sub>(p)×A<sub>1</sub>|| [5,3,3]×[p]×[ ]|| {{CDD|node|5|node|3|node|3|node|2|node|p|node|2|node}}
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| |-
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| |9 ||D<sub>4</sub>×I<sub>2</sub>(p)×A<sub>1</sub>|| [3<sup>1,1,1</sup>]×[p]×[ ]|| {{CDD|nodes|split2|node|3|node|2|node|p|node|2|node}}
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| |-
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| !colspan=4|4+1+1+1
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| |-
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| |5 ||A<sub>4</sub>×A<sub>1</sub><sup>3</sup>|| [3,3,3]×[ ]<sup>3</sup>|| {{CDD|node|3|node|3|node|3|node|2|node|2|node|2|node}}
| |
| |-
| |
| |6 ||BC<sub>4</sub>×A<sub>1</sub><sup>3</sup>|| [4,3,3]×[ ]<sup>3</sup>|| {{CDD|node|4|node|3|node|3|node|2|node|2|node|2|node}}
| |
| |-
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| |7 ||F<sub>4</sub>×A<sub>1</sub><sup>3</sup>|| [3,4,3]×[ ]<sup>3</sup>|| {{CDD|node|3|node|4|node|3|node|2|node|2|node|2|node}}
| |
| |-
| |
| |8 ||H<sub>4</sub>×A<sub>1</sub><sup>3</sup>|| [5,3,3]×[ ]<sup>3</sup>|| {{CDD|node|5|node|3|node|3|node|2|node|2|node|2|node}}
| |
| |-
| |
| |9 ||D<sub>4</sub>×A<sub>1</sub><sup>3</sup>|| [3<sup>1,1,1</sup>]×[ ]<sup>3</sup>|| {{CDD|nodes|split2|node|3|node|2|node|2|node|2|node}}
| |
| |-
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| !colspan=4|3+3+1
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| |-
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| |10 ||A<sub>3</sub>×A<sub>3</sub>×A<sub>1</sub>|| [3,3]×[3,3]×[ ]|| {{CDD|node|3|node|3|node|2|node|3|node|3|node|2|node}}
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| |-
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| |11 ||A<sub>3</sub>×BC<sub>3</sub>×A<sub>1</sub>|| [3,3]×[4,3]×[ ]|| {{CDD|node|3|node|3|node|2|node|4|node|3|node|2|node}}
| |
| |-
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| |12 ||A<sub>3</sub>×H<sub>3</sub>×A<sub>1</sub>|| [3,3]×[5,3]×[ ]|| {{CDD|node|3|node|3|node|2|node|5|node|3|node|2|node}}
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| |-
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| |13 ||BC<sub>3</sub>×BC<sub>3</sub>×A<sub>1</sub>|| [4,3]×[4,3]×[ ]|| {{CDD|node|4|node|3|node|2|node|4|node|3|node|2|node}}
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| |-
| |
| |14 ||BC<sub>3</sub>×H<sub>3</sub>×A<sub>1</sub>|| [4,3]×[5,3]×[ ]|| {{CDD|node|4|node|3|node|2|node|5|node|3|node|2|node}}
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| |-
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| |15 ||H<sub>3</sub>×A<sub>3</sub>×A<sub>1</sub>|| [5,3]×[5,3]×[ ]|| {{CDD|node|5|node|3|node|2|node|5|node|3|node|2|node}}
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| |-
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| !colspan=4|3+2+2
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| |-
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| |1 ||A<sub>3</sub>×I<sub>2</sub>(p)×I<sub>2</sub>(q)|| [3,3]×[p]×[q]|| {{CDD|node|3|node|3|node|2|node|p|node|2|node|q|node}}
| |
| |-
| |
| |2 ||BC<sub>3</sub>×I<sub>2</sub>(p)×I<sub>2</sub>(q)|| [4,3]×[p]×[q]|| {{CDD|node|4|node|3|node|2|node|p|node|2|node|q|node}}
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| |-
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| |3 ||H<sub>3</sub>×I<sub>2</sub>(p)×I<sub>2</sub>(q)|| [5,3]×[p]×[q]|| {{CDD|node|5|node|3|node|2|node|p|node|2|node|q|node}}
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| |-
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| !colspan=4|3+2+1+1
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| |-
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| |1 ||A<sub>3</sub>×I<sub>2</sub>(p)×A<sub>1</sub><sup>2</sup>|| [3,3]×[p]×[ ]<sup>2</sup>|| {{CDD|node|3|node|3|node|2|node|p|node|2|node|2|node}}
| |
| |-
| |
| |2 ||BC<sub>3</sub>×I<sub>2</sub>(p)×A<sub>1</sub><sup>2</sup>|| [4,3]×[p]×[ ]<sup>2</sup>|| {{CDD|node|4|node|3|node|2|node|p|node|2|node|2|node}}
| |
| |-
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| |3 ||H<sub>3</sub>×I<sub>2</sub>(p)×A<sub>1</sub><sup>2</sup>|| [5,3]×[p]×[ ]<sup>2</sup>|| {{CDD|node|5|node|3|node|2|node|p|node|2|node|2|node}}
| |
| |-
| |
| !colspan=4|3+1+1+1+1
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| |-
| |
| |1 ||A<sub>3</sub>×A<sub>1</sub><sup>4</sup>|| [3,3]×[ ]<sup>4</sup>|| {{CDD|node|3|node|3|node|2|node|2|node|2|node|2|node}}
| |
| |-
| |
| |2 ||BC<sub>3</sub>×A<sub>1</sub><sup>4</sup>|| [4,3]×[ ]<sup>4</sup>|| {{CDD|node|4|node|3|node|2|node|2|node|2|node|2|node}}
| |
| |-
| |
| |3 ||H<sub>3</sub>×A<sub>1</sub><sup>4</sup>|| [5,3]×[ ]<sup>4</sup>|| {{CDD|node|5|node|3|node|2|node|2|node|2|node|2|node}}
| |
| |-
| |
| !colspan=4|2+2+2+1
| |
| |-
| |
| |1 ||I<sub>2</sub>(p)×I<sub>2</sub>(q)×I<sub>2</sub>(r)×A<sub>1</sub>|| [p]×[q]×[r]×[ ]|| {{CDD|node|p|node|2|node|q|node|2|node|r|node|2|node}}
| |
| |-
| |
| !colspan=4|2+2+1+1+1
| |
| |-
| |
| |1 ||I<sub>2</sub>(p)×I<sub>2</sub>(q)×A<sub>1</sub><sup>3</sup>|| [p]×[q]×[ ]<sup>3</sup>|| {{CDD|node|p|node|2|node|q|node|2|node|2|node|2|node}}
| |
| |-
| |
| !colspan=4|2+1+1+1+1+1
| |
| |-
| |
| |1 ||I<sub>2</sub>(p)×A<sub>1</sub><sup>5</sup>|| [p]×[ ]<sup>5</sup>|| {{CDD|node|p|node|2|node|2|node|2|node|2|node|2|node}}
| |
| |-
| |
| !colspan=4|1+1+1+1+1+1+1
| |
| |-
| |
| |1 ||A<sub>1</sub><sup>7</sup>|| [ ]<sup>7</sup>|| {{CDD|node|2|node|2|node|2|node|2|node|2|node|2|node}}
| |
| |}
| |
| | |
| == The A<sub>7</sub> family ==
| |
| | |
| The A<sub>7</sub> family has symmetry of order 40320 (8 [[factorial]]).
| |
| | |
| There are 71 (64+8-1) forms based on all permutations of the [[Coxeter-Dynkin diagram]]s with one or more rings. All 71 are enumerated below. [[Norman Johnson (mathematician)|Norman Johnson]]'s truncation names are given. Bowers names and acronym are also given for cross-referencing.
| |
| | |
| See also a [[list of A7 polytopes]] for symmetric [[Coxeter plane]] graphs of these polytopes.
| |
| | |
| {| class="wikitable"
| |
| |-
| |
| !rowspan=2|#
| |
| !rowspan=2|[[Coxeter-Dynkin diagram]]
| |
| !rowspan=2|Truncation<br />indices
| |
| !rowspan=2|[[Norman Johnson (mathematician)|Johnson name]]<br />Bowers name (and acronym)
| |
| !rowspan=2|Basepoint
| |
| !colspan=7|Element counts
| |
| |-
| |
| ! 6|| 5|| 4|| 3|| 2|| 1|| 0
| |
| |- style="text-align:center;"
| |
| |1||{{CDD|node|3|node|3|node|3|node|3|node|3|node|3|node_1}}||t<sub>0</sub>||[[7-simplex]] (oca)||(0,0,0,0,0,0,0,1)||8||28||56||70||56||28||8
| |
| |- style="text-align:center;"
| |
| |2||{{CDD|node|3|node|3|node|3|node|3|node|3|node_1|3|node}}||t<sub>1</sub>||[[Rectified 7-simplex]] (roc)||(0,0,0,0,0,0,1,1)||16||84||224||350||336||168||28
| |
| |- style="text-align:center;"
| |
| |3||{{CDD|node|3|node|3|node|3|node|3|node_1|3|node|3|node}}||t<sub>2</sub>||[[Birectified 7-simplex]] (broc)||(0,0,0,0,0,1,1,1)||16||112||392||770||840||420||56
| |
| |- style="text-align:center; background:#e0f0e0;"
| |
| |4||{{CDD|node|3|node|3|node|3|node_1|3|node|3|node|3|node}}||t<sub>3</sub>||[[Trirectified 7-simplex]] (he)||(0,0,0,0,1,1,1,1)||16||112||448||980||1120||560||70
| |
| |- style="text-align:center;"
| |
| |5||{{CDD|node|3|node|3|node|3|node|3|node|3|node_1|3|node_1}}||t<sub>0,1</sub>||[[Truncated 7-simplex]] (toc)||(0,0,0,0,0,0,1,2)||16||84||224||350||336||196||56
| |
| |- style="text-align:center;"
| |
| |6||{{CDD|node|3|node|3|node|3|node|3|node_1|3|node|3|node_1}}||t<sub>0,2</sub>||[[Cantellated 7-simplex]] (saro)||(0,0,0,0,0,1,1,2)||44||308||980||1750||1876||1008||168
| |
| |- style="text-align:center;"
| |
| |7||{{CDD|node|3|node|3|node|3|node|3|node_1|3|node_1|3|node}}||t<sub>1,2</sub>||[[Bitruncated 7-simplex]] (bittoc)||(0,0,0,0,0,1,2,2)||||||||||||588||168
| |
| |- style="text-align:center;"
| |
| |8||{{CDD|node|3|node|3|node|3|node_1|3|node|3|node|3|node_1}}||t<sub>0,3</sub>||[[Runcinated 7-simplex]] (spo)||(0,0,0,0,1,1,1,2)||100||756||2548||4830||4760||2100||280
| |
| |- style="text-align:center;"
| |
| |9||{{CDD|node|3|node|3|node|3|node_1|3|node|3|node_1|3|node}}||t<sub>1,3</sub>||[[Bicantellated 7-simplex]] (sabro)||(0,0,0,0,1,1,2,2)||||||||||||2520||420
| |
| |- style="text-align:center;"
| |
| |10||{{CDD|node|3|node|3|node|3|node_1|3|node_1|3|node|3|node}}||t<sub>2,3</sub>||[[Tritruncated 7-simplex]] (tattoc)||(0,0,0,0,1,2,2,2)||||||||||||980||280
| |
| |- style="text-align:center;"
| |
| |11||{{CDD|node|3|node|3|node_1|3|node|3|node|3|node|3|node_1}}||t<sub>0,4</sub>||[[Stericated 7-simplex]] (sco)||(0,0,0,1,1,1,1,2)||||||||||||2240||280
| |
| |- style="text-align:center;"
| |
| |12||{{CDD|node|3|node|3|node_1|3|node|3|node|3|node_1|3|node}}||t<sub>1,4</sub>||[[Biruncinated 7-simplex]] (sibpo)||(0,0,0,1,1,1,2,2)||||||||||||4200||560
| |
| |- style="text-align:center; background:#e0f0e0;"
| |
| |13||{{CDD|node|3|node|3|node_1|3|node|3|node_1|3|node|3|node}}||t<sub>2,4</sub>||[[Tricantellated 7-simplex]] (stiroh)||(0,0,0,1,1,2,2,2)||||||||||||3360||560
| |
| |- style="text-align:center;"
| |
| |14||{{CDD|node|3|node_1|3|node|3|node|3|node|3|node|3|node_1}}||t<sub>0,5</sub>||[[Pentellated 7-simplex]] (seto)||(0,0,1,1,1,1,1,2)||||||||||||1260||168
| |
| |- style="text-align:center; background:#e0f0e0;"
| |
| |15||{{CDD|node|3|node_1|3|node|3|node|3|node|3|node_1|3|node}}||t<sub>1,5</sub>||[[Bistericated 7-simplex]] (sabach)||(0,0,1,1,1,1,2,2)||||||||||||3360||420
| |
| |- style="text-align:center; background:#e0f0e0;"
| |
| |16||{{CDD|node_1|3|node|3|node|3|node|3|node|3|node|3|node_1}}||t<sub>0,6</sub>||[[Hexicated 7-simplex]] (suph)||(0,1,1,1,1,1,1,2)||||||||||||336||56
| |
| |- style="text-align:center;"
| |
| |17||{{CDD|node|3|node|3|node|3|node|3|node_1|3|node_1|3|node_1}}||t<sub>0,1,2</sub>||[[Cantitruncated 7-simplex]] (garo)||(0,0,0,0,0,1,2,3)||||||||||||1176||336
| |
| |- style="text-align:center;"
| |
| |18||{{CDD|node|3|node|3|node|3|node_1|3|node|3|node_1|3|node_1}}||t<sub>0,1,3</sub>||[[Runcitruncated 7-simplex]] (patto)||(0,0,0,0,1,1,2,3)||||||||||||4620||840
| |
| |- style="text-align:center;"
| |
| |19||{{CDD|node|3|node|3|node|3|node_1|3|node_1|3|node|3|node_1}}||t<sub>0,2,3</sub>||[[Runcicantellated 7-simplex]] (paro)||(0,0,0,0,1,2,2,3)||||||||||||3360||840
| |
| |- style="text-align:center;"
| |
| |20||{{CDD|node|3|node|3|node|3|node_1|3|node_1|3|node_1|3|node}}||t<sub>1,2,3</sub>||[[Bicantitruncated 7-simplex]] (gabro)||(0,0,0,0,1,2,3,3)||||||||||||2940||840
| |
| |- style="text-align:center;"
| |
| |21||{{CDD|node|3|node|3|node_1|3|node|3|node|3|node_1|3|node_1}}||t<sub>0,1,4</sub>||[[Steritruncated 7-simplex]] (cato)||(0,0,0,1,1,1,2,3)||||||||||||7280||1120
| |
| |- style="text-align:center;"
| |
| |22||{{CDD|node|3|node|3|node_1|3|node|3|node_1|3|node|3|node_1}}||t<sub>0,2,4</sub>||[[Stericantellated 7-simplex]] (caro)||(0,0,0,1,1,2,2,3)||||||||||||10080||1680
| |
| |- style="text-align:center;"
| |
| |23||{{CDD|node|3|node|3|node_1|3|node|3|node_1|3|node_1|3|node}}||t<sub>1,2,4</sub>||[[Biruncitruncated 7-simplex]] (bipto)||(0,0,0,1,1,2,3,3)||||||||||||8400||1680
| |
| |- style="text-align:center;"
| |
| |24||{{CDD|node|3|node|3|node_1|3|node_1|3|node|3|node|3|node_1}}||t<sub>0,3,4</sub>||[[Steriruncinated 7-simplex]] (cepo)||(0,0,0,1,2,2,2,3)||||||||||||5040||1120
| |
| |- style="text-align:center;"
| |
| |25||{{CDD|node|3|node|3|node_1|3|node_1|3|node|3|node_1|3|node}}||t<sub>1,3,4</sub>||[[Biruncicantellated 7-simplex]] (bipro)||(0,0,0,1,2,2,3,3)||||||||||||7560||1680
| |
| |- style="text-align:center; background:#e0f0e0;"
| |
| |26||{{CDD|node|3|node|3|node_1|3|node_1|3|node_1|3|node|3|node}}||t<sub>2,3,4</sub>||[[Tricantitruncated 7-simplex]] (gatroh)||(0,0,0,1,2,3,3,3)||||||||||||3920||1120
| |
| |- style="text-align:center;"
| |
| |27||{{CDD|node|3|node_1|3|node|3|node|3|node|3|node_1|3|node_1}}||t<sub>0,1,5</sub>||[[Pentitruncated 7-simplex]] (teto)||(0,0,1,1,1,1,2,3)||||||||||||5460||840
| |
| |- style="text-align:center;"
| |
| |28||{{CDD|node|3|node_1|3|node|3|node|3|node_1|3|node|3|node_1}}||t<sub>0,2,5</sub>||[[Penticantellated 7-simplex]] (tero)||(0,0,1,1,1,2,2,3)||||||||||||11760||1680
| |
| |- style="text-align:center;"
| |
| |29||{{CDD|node|3|node_1|3|node|3|node|3|node_1|3|node_1|3|node}}||t<sub>1,2,5</sub>||[[Bisteritruncated 7-simplex]] (bacto)||(0,0,1,1,1,2,3,3)||||||||||||9240||1680
| |
| |- style="text-align:center;"
| |
| |30||{{CDD|node|3|node_1|3|node|3|node_1|3|node|3|node|3|node_1}}||t<sub>0,3,5</sub>||[[Pentiruncinated 7-simplex]] (tepo)||(0,0,1,1,2,2,2,3)||||||||||||10920||1680
| |
| |- style="text-align:center; background:#e0f0e0;"
| |
| |31||{{CDD|node|3|node_1|3|node|3|node_1|3|node|3|node_1|3|node}}||t<sub>1,3,5</sub>||[[Bistericantellated 7-simplex]] (bacroh)||(0,0,1,1,2,2,3,3)||||||||||||15120||2520
| |
| |- style="text-align:center;"
| |
| |32||{{CDD|node|3|node_1|3|node_1|3|node|3|node|3|node|3|node_1}}||t<sub>0,4,5</sub>||[[Pentistericated 7-simplex]] (teco)||(0,0,1,2,2,2,2,3)||||||||||||4200||840
| |
| |- style="text-align:center;"
| |
| |33||{{CDD|node_1|3|node|3|node|3|node|3|node|3|node_1|3|node_1}}||t<sub>0,1,6</sub>||[[Hexitruncated 7-simplex]] (puto)||(0,1,1,1,1,1,2,3)||||||||||||1848||336
| |
| |- style="text-align:center;"
| |
| |34||{{CDD|node_1|3|node|3|node|3|node|3|node_1|3|node|3|node_1}}||t<sub>0,2,6</sub>||[[Hexicantellated 7-simplex]] (puro)||(0,1,1,1,1,2,2,3)||||||||||||5880||840
| |
| |- style="text-align:center; background:#e0f0e0;"
| |
| |35||{{CDD|node_1|3|node|3|node|3|node_1|3|node|3|node|3|node_1}}||t<sub>0,3,6</sub>||[[Hexiruncinated 7-simplex]] (puph)||(0,1,1,1,2,2,2,3)||||||||||||8400||1120
| |
| |- style="text-align:center;"
| |
| |36||{{CDD|node|3|node|3|node|3|node_1|3|node_1|3|node_1|3|node_1}}||t<sub>0,1,2,3</sub>||[[Runcicantitruncated 7-simplex]] (gapo)||(0,0,0,0,1,2,3,4)||||||||||||5880||1680
| |
| |- style="text-align:center;"
| |
| |37||{{CDD|node|3|node|3|node_1|3|node|3|node_1|3|node_1|3|node_1}}||t<sub>0,1,2,4</sub>||[[Stericantitruncated 7-simplex]] (cagro)||(0,0,0,1,1,2,3,4)||||||||||||16800||3360
| |
| |- style="text-align:center;"
| |
| |38||{{CDD|node|3|node|3|node_1|3|node_1|3|node|3|node_1|3|node_1}}||t<sub>0,1,3,4</sub>||[[Steriruncitruncated 7-simplex]] (capto)||(0,0,0,1,2,2,3,4)||||||||||||13440||3360
| |
| |- style="text-align:center;"
| |
| |39||{{CDD|node|3|node|3|node_1|3|node_1|3|node_1|3|node|3|node_1}}||t<sub>0,2,3,4</sub>||[[Steriruncicantellated 7-simplex]] (capro)||(0,0,0,1,2,3,3,4)||||||||||||13440||3360
| |
| |- style="text-align:center;"
| |
| |40||{{CDD|node|3|node|3|node_1|3|node_1|3|node_1|3|node_1|3|node}}||t<sub>1,2,3,4</sub>||[[Biruncicantitruncated 7-simplex]] (gibpo)||(0,0,0,1,2,3,4,4)||||||||||||11760||3360
| |
| |- style="text-align:center;"
| |
| |41||{{CDD|node|3|node_1|3|node|3|node|3|node_1|3|node_1|3|node_1}}||t<sub>0,1,2,5</sub>||[[Penticantitruncated 7-simplex]] (tegro)||(0,0,1,1,1,2,3,4)||||||||||||18480||3360
| |
| |- style="text-align:center;"
| |
| |42||{{CDD|node|3|node_1|3|node|3|node_1|3|node|3|node_1|3|node_1}}||t<sub>0,1,3,5</sub>||[[Pentiruncitruncated 7-simplex]] (tapto)||(0,0,1,1,2,2,3,4)||||||||||||27720||5040
| |
| |- style="text-align:center;"
| |
| |43||{{CDD|node|3|node_1|3|node|3|node_1|3|node_1|3|node|3|node_1}}||t<sub>0,2,3,5</sub>||[[Pentiruncicantellated 7-simplex]] (tapro)||(0,0,1,1,2,3,3,4)||||||||||||25200||5040
| |
| |- style="text-align:center;"
| |
| |44||{{CDD|node|3|node_1|3|node|3|node_1|3|node_1|3|node_1|3|node}}||t<sub>1,2,3,5</sub>||[[Bistericantitruncated 7-simplex]] (bacogro)||(0,0,1,1,2,3,4,4)||||||||||||22680||5040
| |
| |- style="text-align:center;"
| |
| |45||{{CDD|node|3|node_1|3|node_1|3|node|3|node|3|node_1|3|node_1}}||t<sub>0,1,4,5</sub>||[[Pentisteritruncated 7-simplex]] (tecto)||(0,0,1,2,2,2,3,4)||||||||||||15120||3360
| |
| |- style="text-align:center;"
| |
| |46||{{CDD|node|3|node_1|3|node_1|3|node|3|node_1|3|node|3|node_1}}||t<sub>0,2,4,5</sub>||[[Pentistericantellated 7-simplex]] (tecro)||(0,0,1,2,2,3,3,4)||||||||||||25200||5040
| |
| |- style="text-align:center; background:#e0f0e0;"
| |
| |47||{{CDD|node|3|node_1|3|node_1|3|node|3|node_1|3|node_1|3|node}}||t<sub>1,2,4,5</sub>||[[Bisteriruncitruncated 7-simplex]] (bicpath)||(0,0,1,2,2,3,4,4)||||||||||||20160||5040
| |
| |- style="text-align:center;"
| |
| |48||{{CDD|node|3|node_1|3|node_1|3|node_1|3|node|3|node|3|node_1}}||t<sub>0,3,4,5</sub>||[[Pentisteriruncinated 7-simplex]] (tacpo)||(0,0,1,2,3,3,3,4)||||||||||||15120||3360
| |
| |- style="text-align:center;"
| |
| |49||{{CDD|node_1|3|node|3|node|3|node|3|node_1|3|node_1|3|node_1}}||t<sub>0,1,2,6</sub>||[[Hexicantitruncated 7-simplex]] (pugro)||(0,1,1,1,1,2,3,4)||||||||||||8400||1680
| |
| |- style="text-align:center;"
| |
| |50||{{CDD|node_1|3|node|3|node|3|node_1|3|node|3|node_1|3|node_1}}||t<sub>0,1,3,6</sub>||[[Hexiruncitruncated 7-simplex]] (pugato)||(0,1,1,1,2,2,3,4)||||||||||||20160||3360
| |
| |- style="text-align:center;"
| |
| |51||{{CDD|node_1|3|node|3|node|3|node_1|3|node_1|3|node|3|node_1}}||t<sub>0,2,3,6</sub>||[[Hexiruncicantellated 7-simplex]] (pugro)||(0,1,1,1,2,3,3,4)||||||||||||16800||3360
| |
| |- style="text-align:center;"
| |
| |52||{{CDD|node_1|3|node|3|node_1|3|node|3|node|3|node_1|3|node_1}}||t<sub>0,1,4,6</sub>||[[Hexisteritruncated 7-simplex]] (pucto)||(0,1,1,2,2,2,3,4)||||||||||||20160||3360
| |
| |- style="text-align:center; background:#e0f0e0;"
| |
| |53||{{CDD|node_1|3|node|3|node_1|3|node|3|node_1|3|node|3|node_1}}||t<sub>0,2,4,6</sub>||[[Hexistericantellated 7-simplex]] (pucroh)||(0,1,1,2,2,3,3,4)||||||||||||30240||5040
| |
| |- style="text-align:center; background:#e0f0e0;"
| |
| |54||{{CDD|node_1|3|node_1|3|node|3|node|3|node|3|node_1|3|node_1}}||t<sub>0,1,5,6</sub>||[[Hexipentitruncated 7-simplex]] (putath)||(0,1,2,2,2,2,3,4)||||||||||||8400||1680
| |
| |- style="text-align:center;"
| |
| |55||{{CDD|node|3|node|3|node_1|3|node_1|3|node_1|3|node_1|3|node_1}}||t<sub>0,1,2,3,4</sub>||[[Steriruncicantitruncated 7-simplex]] (gecco)||(0,0,0,1,2,3,4,5)||||||||||||23520||6720
| |
| |- style="text-align:center;"
| |
| |56||{{CDD|node|3|node_1|3|node|3|node_1|3|node_1|3|node_1|3|node_1}}||t<sub>0,1,2,3,5</sub>||[[Pentiruncicantitruncated 7-simplex]] (tegapo)||(0,0,1,1,2,3,4,5)||||||||||||45360||10080
| |
| |- style="text-align:center;"
| |
| |57||{{CDD|node|3|node_1|3|node_1|3|node|3|node_1|3|node_1|3|node_1}}||t<sub>0,1,2,4,5</sub>||[[Pentistericantitruncated 7-simplex]] (tecagro)||(0,0,1,2,2,3,4,5)||||||||||||40320||10080
| |
| |- style="text-align:center;"
| |
| |58||{{CDD|node|3|node_1|3|node_1|3|node_1|3|node|3|node_1|3|node_1}}||t<sub>0,1,3,4,5</sub>||[[Pentisteriruncitruncated 7-simplex]] (tacpeto)||(0,0,1,2,3,3,4,5)||||||||||||40320||10080
| |
| |- style="text-align:center;"
| |
| |59||{{CDD|node|3|node_1|3|node_1|3|node_1|3|node_1|3|node|3|node_1}}||t<sub>0,2,3,4,5</sub>||[[Pentisteriruncicantellated 7-simplex]] (tacpro)||(0,0,1,2,3,4,4,5)||||||||||||40320||10080
| |
| |- style="text-align:center; background:#e0f0e0;"
| |
| |60||{{CDD|node|3|node_1|3|node_1|3|node_1|3|node_1|3|node_1|3|node}}||t<sub>1,2,3,4,5</sub>||[[Bisteriruncicantitruncated 7-simplex]] (gabach)||(0,0,1,2,3,4,5,5)||||||||||||35280||10080
| |
| |- style="text-align:center;"
| |
| |61||{{CDD|node_1|3|node|3|node|3|node_1|3|node_1|3|node_1|3|node_1}}||t<sub>0,1,2,3,6</sub>||[[Hexiruncicantitruncated 7-simplex]] (pugopo)||(0,1,1,1,2,3,4,5)||||||||||||30240||6720
| |
| |- style="text-align:center;"
| |
| |62||{{CDD|node_1|3|node|3|node_1|3|node|3|node_1|3|node_1|3|node_1}}||t<sub>0,1,2,4,6</sub>||[[Hexistericantitruncated 7-simplex]] (pucagro)||(0,1,1,2,2,3,4,5)||||||||||||50400||10080
| |
| |- style="text-align:center;"
| |
| |63||{{CDD|node_1|3|node|3|node_1|3|node_1|3|node|3|node_1|3|node_1}}||t<sub>0,1,3,4,6</sub>||[[Hexisteriruncitruncated 7-simplex]] (pucpato)||(0,1,1,2,3,3,4,5)||||||||||||45360||10080
| |
| |- style="text-align:center; background:#e0f0e0;"
| |
| |64||{{CDD|node_1|3|node|3|node_1|3|node_1|3|node_1|3|node|3|node_1}}||t<sub>0,2,3,4,6</sub>||[[Hexisteriruncicantellated 7-simplex]] (pucproh)||(0,1,1,2,3,4,4,5)||||||||||||45360||10080
| |
| |- style="text-align:center;"
| |
| |65||{{CDD|node_1|3|node_1|3|node|3|node|3|node_1|3|node_1|3|node_1}}||t<sub>0,1,2,5,6</sub>||[[Hexipenticantitruncated 7-simplex]] (putagro)||(0,1,2,2,2,3,4,5)||||||||||||30240||6720
| |
| |- style="text-align:center; background:#e0f0e0;"
| |
| |66||{{CDD|node_1|3|node_1|3|node|3|node_1|3|node|3|node_1|3|node_1}}||t<sub>0,1,3,5,6</sub>||[[Hexipentiruncitruncated 7-simplex]] (putpath)||(0,1,2,2,3,3,4,5)||||||||||||50400||10080
| |
| |- style="text-align:center;"
| |
| |67||{{CDD|node|3|node_1|3|node_1|3|node_1|3|node_1|3|node_1|3|node_1}}||t<sub>0,1,2,3,4,5</sub>||[[Pentisteriruncicantitruncated 7-simplex]] (geto)||(0,0,1,2,3,4,5,6)||||||||||||70560||20160
| |
| |- style="text-align:center;"
| |
| |68||{{CDD|node_1|3|node|3|node_1|3|node_1|3|node_1|3|node_1|3|node_1}}||t<sub>0,1,2,3,4,6</sub>||[[Hexisteriruncicantitruncated 7-simplex]] (pugaco)||(0,1,1,2,3,4,5,6)||||||||||||80640||20160
| |
| |- style="text-align:center;"
| |
| |69||{{CDD|node_1|3|node_1|3|node|3|node_1|3|node_1|3|node_1|3|node_1}}||t<sub>0,1,2,3,5,6</sub>||[[Hexipentiruncicantitruncated 7-simplex]] (putgapo)||(0,1,2,2,3,4,5,6)||||||||||||80640||20160
| |
| |- style="text-align:center; background:#e0f0e0;"
| |
| |70||{{CDD|node_1|3|node_1|3|node_1|3|node|3|node_1|3|node_1|3|node_1}}||t<sub>0,1,2,4,5,6</sub>||[[Hexipentistericantitruncated 7-simplex]] (putcagroh)||(0,1,2,3,3,4,5,6)||||||||||||80640||20160
| |
| |- style="text-align:center; background:#e0f0e0;"
| |
| |71||{{CDD|node_1|3|node_1|3|node_1|3|node_1|3|node_1|3|node_1|3|node_1}}||t<sub>0,1,2,3,4,5,6</sub>||[[Omnitruncated 7-simplex]] (guph)||(0,1,2,3,4,5,6,7)||||||||||||141120||40320
| |
| |}
| |
| | |
| == The B<sub>7</sub> family ==
| |
| | |
| The B<sub>7</sub> family has symmetry of order 645120 (7 [[factorial]] x 2<sup>7</sup>).
| |
| | |
| There are 127 forms based on all permutations of the [[Coxeter-Dynkin diagram]]s with one or more rings. Johnson and Bowers names.
| |
| | |
| See also a [[list of B7 polytopes]] for symmetric [[Coxeter plane]] graphs of these polytopes.
| |
| | |
| {| class=wikitable
| |
| !rowspan=2|#
| |
| !rowspan=2|[[Coxeter-Dynkin diagram]]<BR>t-notation
| |
| !rowspan=2|Name (BSA)
| |
| !rowspan=2|Base point
| |
| !colspan=7|Element counts
| |
| |-
| |
| !6||5||4||3||2||1||0
| |
| |- style="text-align:center; background:#f0e0e0;"
| |
| !1
| |
| |<!-- [x3o3o3o3o3o4o] -->{{CDD|node|4|node|3|node|3|node|3|node|3|node|3|node_1}}<BR>t<sub>0</sub>{3,3,3,3,3,4}||[[7-orthoplex]] (zee)|||(0,0,0,0,0,0,1)√2||128||448||672||560||280||84||14
| |
| |- style="text-align:center; background:#f0e0e0;"
| |
| !2
| |
| |<!-- [o3x3o3o3o3o4o] -->{{CDD|node|4|node|3|node|3|node|3|node|3|node_1|3|node}}<BR>t<sub>1</sub>{3,3,3,3,3,4}||[[Rectified 7-orthoplex]] (rez)|||(0,0,0,0,0,1,1)√2||142||1344||3360||3920||2520||840||84
| |
| |- style="text-align:center; background:#f0e0e0;"
| |
| !3
| |
| |<!-- [o3o3x3o3o3o4o] -->{{CDD|node|4|node|3|node|3|node|3|node_1|3|node|3|node}}<BR>t<sub>2</sub>{3,3,3,3,3,4}||[[Birectified 7-orthoplex]] (barz)|||(0,0,0,0,1,1,1)√2||142||1428||6048||10640||8960||3360||280
| |
| |- style="text-align:center; background:#e0f0e0;"
| |
| !4
| |
| |<!-- [o3o3o3x3o3o4o] -->{{CDD|node|4|node|3|node|3|node_1|3|node|3|node|3|node}}<BR>t<sub>3</sub>{4,3,3,3,3,3}||[[Trirectified 7-cube]] (sez)|||(0,0,0,1,1,1,1)√2||142||1428||6328||14560||15680||6720||560
| |
| |- style="text-align:center; background:#e0e0f0;"
| |
| !5
| |
| |<!-- [o3o3o3o3x3o4o] -->{{CDD|node|4|node|3|node_1|3|node|3|node|3|node|3|node}}<BR>t<sub>2</sub>{4,3,3,3,3,3}||[[Birectified 7-cube]] (bersa)|||(0,0,1,1,1,1,1)√2||142||1428||5656||11760||13440||6720||672
| |
| |- style="text-align:center; background:#e0e0f0;"
| |
| !6
| |
| |<!-- [o3o3o3o3o3x4o] -->{{CDD|node|4|node_1|3|node|3|node|3|node|3|node|3|node}}<BR>t<sub>1</sub>{4,3,3,3,3,3}||[[Rectified 7-cube]] (rasa)|||(0,1,1,1,1,1,1)√2||142||980||2968||5040||5152||2688||448
| |
| |- style="text-align:center; background:#e0e0f0;"
| |
| !7
| |
| |<!-- [o3o3o3o3o3o4x] -->{{CDD|node_1|4|node|3|node|3|node|3|node|3|node|3|node}}<BR>t<sub>0</sub>{4,3,3,3,3,3}||[[7-cube]] (hept)|||(0,0,0,0,0,0,0)√2 + (1,1,1,1,1,1,1)||14||84||280||560||672||448||128
| |
| |- style="text-align:center; background:#f0e0e0;"
| |
| !8
| |
| |<!-- [x3x3o3o3o3o4o] -->{{CDD|node|4|node|3|node|3|node|3|node|3|node_1|3|node_1}}<BR>t<sub>0,1</sub>{3,3,3,3,3,4}||[[Truncated 7-orthoplex]] (Taz)|||(0,0,0,0,0,1,2)√2||142||1344||3360||4760||2520||924||168
| |
| |- style="text-align:center; background:#f0e0e0;"
| |
| !9
| |
| |<!-- [x3o3x3o3o3o4o] -->{{CDD|node|4|node|3|node|3|node|3|node_1|3|node|3|node_1}}<BR>t<sub>0,2</sub>{3,3,3,3,3,4}||[[Cantellated 7-orthoplex]] (Sarz)|||(0,0,0,0,1,1,2)√2||226||4200||15456||24080||19320||7560||840
| |
| |- style="text-align:center; background:#f0e0e0;"
| |
| !10
| |
| |<!-- [o3x3x3o3o3o4o] -->{{CDD|node|4|node|3|node|3|node|3|node_1|3|node_1|3|node}}<BR>t<sub>1,2</sub>{3,3,3,3,3,4}||[[Bitruncated 7-orthoplex]] (Botaz)|||(0,0,0,0,1,2,2)√2|||||| || || ||4200||840
| |
| |- style="text-align:center; background:#f0e0e0;"
| |
| !11
| |
| |<!-- [x3o3o3x3o3o4o] -->{{CDD|node|4|node|3|node|3|node_1|3|node|3|node|3|node_1}}<BR>t<sub>0,3</sub>{3,3,3,3,3,4}||[[Runcinated 7-orthoplex]] (Spaz)|||(0,0,0,1,1,1,2)√2|||||| || || ||23520||2240
| |
| |- style="text-align:center; background:#f0e0e0;"
| |
| !12
| |
| |<!-- [o3x3o3x3o3o4o] -->{{CDD|node|4|node|3|node|3|node_1|3|node|3|node_1|3|node}}<BR>t<sub>1,3</sub>{3,3,3,3,3,4}||[[Bicantellated 7-orthoplex]] (Sebraz)|||(0,0,0,1,1,2,2)√2|||||| || || ||26880||3360
| |
| |- style="text-align:center; background:#f0e0e0;"
| |
| !13
| |
| |<!-- [o3o3x3x3o3o4o] -->{{CDD|node|4|node|3|node|3|node_1|3|node_1|3|node|3|node}}<BR>t<sub>2,3</sub>{3,3,3,3,3,4}||[[Tritruncated 7-orthoplex]] (Totaz)|||(0,0,0,1,2,2,2)√2|||||| || || ||10080||2240
| |
| |- style="text-align:center; background:#f0e0e0;"
| |
| !14
| |
| |<!-- [x3o3o3o3x3o4o] -->{{CDD|node|4|node|3|node_1|3|node|3|node|3|node|3|node_1}}<BR>t<sub>0,4</sub>{3,3,3,3,3,4}||[[Stericated 7-orthoplex]] (Scaz)|||(0,0,1,1,1,1,2)√2|||||| || || ||33600||3360
| |
| |- style="text-align:center; background:#f0e0e0;"
| |
| !15
| |
| |<!-- [o3x3o3o3x3o4o] -->{{CDD|node|4|node|3|node_1|3|node|3|node|3|node_1|3|node}}<BR>t<sub>1,4</sub>{3,3,3,3,3,4}||[[Biruncinated 7-orthoplex]] (Sibpaz)|||(0,0,1,1,1,2,2)√2|||||| || || ||60480||6720
| |
| |- style="text-align:center; background:#e0f0e0;"
| |
| !16
| |
| |<!-- [o3o3x3o3x3o4o] -->{{CDD|node|4|node|3|node_1|3|node|3|node_1|3|node|3|node}}<BR>t<sub>2,4</sub>{4,3,3,3,3,3}||[[Tricantellated 7-cube]] (Strasaz)|||(0,0,1,1,2,2,2)√2|||||| || || ||47040||6720
| |
| |- style="text-align:center; background:#e0e0f0;"
| |
| !17
| |
| |<!-- [o3o3o3x3x3o4o] -->{{CDD|node|4|node|3|node_1|3|node_1|3|node|3|node|3|node}}<BR>t<sub>2,3</sub>{4,3,3,3,3,3}||[[Tritruncated 7-cube]] (Tatsa)|||(0,0,1,2,2,2,2)√2|||||| || || ||13440||3360
| |
| |- style="text-align:center; background:#f0e0e0;"
| |
| !18
| |
| |<!-- [x3o3o3o3o3x4o] -->{{CDD|node|4|node_1|3|node|3|node|3|node|3|node|3|node_1}}<BR>t<sub>0,5</sub>{3,3,3,3,3,4}||[[Pentellated 7-orthoplex]] (Staz)|||(0,1,1,1,1,1,2)√2|||||| || || ||20160||2688
| |
| |- style="text-align:center; background:#e0f0e0;"
| |
| !19
| |
| |<!-- [o3x3o3o3o3x4o] -->{{CDD|node|4|node_1|3|node|3|node|3|node|3|node_1|3|node}}<BR>t<sub>1,5</sub>{4,3,3,3,3,3}||[[Bistericated 7-cube]] (Sabcosaz)|||(0,1,1,1,1,2,2)√2|||||| || || ||53760||6720
| |
| |- style="text-align:center; background:#e0e0f0;"
| |
| !20
| |
| |<!-- [o3o3x3o3o3x4o] -->{{CDD|node|4|node_1|3|node|3|node|3|node_1|3|node|3|node}}<BR>t<sub>1,4</sub>{4,3,3,3,3,3}||[[Biruncinated 7-cube]] (Sibposa)|||(0,1,1,1,2,2,2)√2|||||| || || ||67200||8960
| |
| |- style="text-align:center; background:#e0e0f0;"
| |
| !21
| |
| |<!-- [o3o3o3x3o3x4o] -->{{CDD|node|4|node_1|3|node|3|node_1|3|node|3|node|3|node}}<BR>t<sub>1,3</sub>{4,3,3,3,3,3}||[[Bicantellated 7-cube]] (Sibrosa)|||(0,1,1,2,2,2,2)√2|||||| || || ||40320||6720
| |
| |- style="text-align:center; background:#e0e0f0;"
| |
| !22
| |
| |<!-- [o3o3o3o3x3x4o] -->{{CDD|node|4|node_1|3|node_1|3|node|3|node|3|node|3|node}}<BR>t<sub>1,2</sub>{4,3,3,3,3,3}||[[Bitruncated 7-cube]] (Betsa)|||(0,1,2,2,2,2,2)√2|||||| || || ||9408||2688
| |
| |- style="text-align:center; background:#e0f0e0;"
| |
| !23
| |
| |<!-- [x3o3o3o3o3o4x] -->{{CDD|node_1|4|node|3|node|3|node|3|node|3|node|3|node_1}}<BR>t<sub>0,6</sub>{4,3,3,3,3,3}||[[Hexicated 7-cube]] (Suposaz)|||(0,0,0,0,0,0,1)√2 + (1,1,1,1,1,1,1)|||||| || || ||5376||896
| |
| |- style="text-align:center; background:#e0e0f0;"
| |
| !24
| |
| |<!-- [o3x3o3o3o3o4x] -->{{CDD|node_1|4|node|3|node|3|node|3|node|3|node_1|3|node}}<BR>t<sub>0,5</sub>{4,3,3,3,3,3}||[[Pentellated 7-cube]] (Stesa)|||(0,0,0,0,0,1,1)√2 + (1,1,1,1,1,1,1)|||||| || || ||20160||2688
| |
| |- style="text-align:center; background:#e0e0f0;"
| |
| !25
| |
| |<!-- [o3o3x3o3o3o4x] -->{{CDD|node_1|4|node|3|node|3|node|3|node_1|3|node|3|node}}<BR>t<sub>0,4</sub>{4,3,3,3,3,3}||[[Stericated 7-cube]] (Scosa)|||(0,0,0,0,1,1,1)√2 + (1,1,1,1,1,1,1)|||||| || || ||35840||4480
| |
| |- style="text-align:center; background:#e0e0f0;"
| |
| !26
| |
| |<!-- [o3o3o3x3o3o4x] -->{{CDD|node_1|4|node|3|node|3|node_1|3|node|3|node|3|node}}<BR>t<sub>0,3</sub>{4,3,3,3,3,3}||[[Runcinated 7-cube]] (Spesa)|||(0,0,0,1,1,1,1)√2 + (1,1,1,1,1,1,1)|||||| || || ||33600||4480
| |
| |- style="text-align:center; background:#e0e0f0;"
| |
| !27
| |
| |<!-- [o3o3o3o3x3o4x] -->{{CDD|node_1|4|node|3|node_1|3|node|3|node|3|node|3|node}}<BR>t<sub>0,2</sub>{4,3,3,3,3,3}||[[Cantellated 7-cube]] (Sersa)|||(0,0,1,1,1,1,1)√2 + (1,1,1,1,1,1,1)|||||| || || ||16128||2688
| |
| |- style="text-align:center; background:#e0e0f0;"
| |
| !28
| |
| |<!-- [o3o3o3o3o3x4x] -->{{CDD|node_1|4|node_1|3|node|3|node|3|node|3|node|3|node}}<BR>t<sub>0,1</sub>{4,3,3,3,3,3}||[[Truncated 7-cube]] (Tasa)|||(0,1,1,1,1,1,1)√2 + (1,1,1,1,1,1,1)||142||980||2968||5040||5152||3136||896
| |
| |- style="text-align:center; background:#f0e0e0;"
| |
| !29
| |
| |<!-- [x3x3x3o3o3o4o] -->{{CDD|node|4|node|3|node|3|node|3|node_1|3|node_1|3|node_1}}<BR>t<sub>0,1,2</sub>{3,3,3,3,3,4}||[[Cantitruncated 7-orthoplex]] (Garz)|||(0,1,2,3,3,3,3)√2|||||| || || ||8400||1680
| |
| |- style="text-align:center; background:#f0e0e0;"
| |
| !30
| |
| |<!-- [x3x3o3x3o3o4o] -->{{CDD|node|4|node|3|node|3|node_1|3|node|3|node_1|3|node_1}}<BR>t<sub>0,1,3</sub>{3,3,3,3,3,4}||[[Runcitruncated 7-orthoplex]] (Potaz)|||(0,1,2,2,3,3,3)√2|||||| || || ||50400||6720
| |
| |- style="text-align:center; background:#f0e0e0;"
| |
| !31
| |
| |<!-- [x3o3x3x3o3o4o] -->{{CDD|node|4|node|3|node|3|node_1|3|node_1|3|node|3|node_1}}<BR>t<sub>0,2,3</sub>{3,3,3,3,3,4}||[[Runcicantellated 7-orthoplex]] (Parz)|||(0,1,1,2,3,3,3)√2|||||| || || ||33600||6720
| |
| |- style="text-align:center; background:#f0e0e0;"
| |
| !32
| |
| |<!-- [o3x3x3x3o3o4o] -->{{CDD|node|4|node|3|node|3|node_1|3|node_1|3|node_1|3|node}}<BR>t<sub>1,2,3</sub>{3,3,3,3,3,4}||[[Bicantitruncated 7-orthoplex]] (Gebraz)|||(0,0,1,2,3,3,3)√2|||||| || || ||30240||6720
| |
| |- style="text-align:center; background:#f0e0e0;"
| |
| !33
| |
| |<!-- [x3x3o3o3x3o4o] -->{{CDD|node|4|node|3|node_1|3|node|3|node|3|node_1|3|node_1}}<BR>t<sub>0,1,4</sub>{3,3,3,3,3,4}||[[Steritruncated 7-orthoplex]] (Catz)|||(0,0,1,1,1,2,3)√2|||||| || || ||107520||13440
| |
| |- style="text-align:center; background:#f0e0e0;"
| |
| !34
| |
| |<!-- [x3o3x3o3x3o4o] -->{{CDD|node|4|node|3|node_1|3|node|3|node_1|3|node|3|node_1}}<BR>t<sub>0,2,4</sub>{3,3,3,3,3,4}||[[Stericantellated 7-orthoplex]] (Craze)|||(0,0,1,1,2,2,3)√2|||||| || || ||141120||20160
| |
| |- style="text-align:center; background:#f0e0e0;"
| |
| !35
| |
| |<!-- [o3x3x3o3x3o4o] -->{{CDD|node|4|node|3|node_1|3|node|3|node_1|3|node_1|3|node}}<BR>t<sub>1,2,4</sub>{3,3,3,3,3,4}||[[Biruncitruncated 7-orthoplex]] (Baptize)|||(0,0,1,1,2,3,3)√2|||||| || || ||120960||20160
| |
| |- style="text-align:center; background:#f0e0e0;"
| |
| !36
| |
| |<!-- [x3o3o3x3x3o4o] -->{{CDD|node|4|node|3|node_1|3|node_1|3|node|3|node|3|node_1}}<BR>t<sub>0,3,4</sub>{3,3,3,3,3,4}||[[Steriruncinated 7-orthoplex]] (Copaz)|||(0,1,1,1,2,3,3)√2|||||| || || ||67200||13440
| |
| |- style="text-align:center; background:#f0e0e0;"
| |
| !37
| |
| |<!-- [o3x3o3x3x3o4o] -->{{CDD|node|4|node|3|node_1|3|node_1|3|node|3|node_1|3|node}}<BR>t<sub>1,3,4</sub>{3,3,3,3,3,4}||[[Biruncicantellated 7-orthoplex]] (Boparz)|||(0,0,1,2,2,3,3)√2|||||| || || ||100800||20160
| |
| |- style="text-align:center; background:#e0f0e0;"
| |
| !38
| |
| |<!-- [o3o3x3x3x3o4o] -->{{CDD|node|4|node|3|node_1|3|node_1|3|node_1|3|node|3|node}}<BR>t<sub>2,3,4</sub>{4,3,3,3,3,3}||[[Tricantitruncated 7-cube]] (Gotrasaz)|||(0,0,0,1,2,3,3)√2|||||| || || ||53760||13440
| |
| |- style="text-align:center; background:#f0e0e0;"
| |
| !39
| |
| |<!-- [x3x3o3o3o3x4o] -->{{CDD|node|4|node_1|3|node|3|node|3|node|3|node_1|3|node_1}}<BR>t<sub>0,1,5</sub>{3,3,3,3,3,4}||[[Pentitruncated 7-orthoplex]] (Tetaz)|||(0,1,1,1,1,2,3)√2|||||| || || ||87360||13440
| |
| |- style="text-align:center; background:#f0e0e0;"
| |
| !40
| |
| |<!-- [x3o3x3o3o3x4o] -->{{CDD|node|4|node_1|3|node|3|node|3|node_1|3|node|3|node_1}}<BR>t<sub>0,2,5</sub>{3,3,3,3,3,4}||[[Penticantellated 7-orthoplex]] (Teroz)|||(0,1,1,1,2,2,3)√2|||||| || || ||188160||26880
| |
| |- style="text-align:center; background:#f0e0e0;"
| |
| !41
| |
| |<!-- [o3x3x3o3o3x4o] -->{{CDD|node|4|node_1|3|node|3|node|3|node_1|3|node_1|3|node}}<BR>t<sub>1,2,5</sub>{3,3,3,3,3,4}||[[Bisteritruncated 7-orthoplex]] (Boctaz)|||(0,1,1,1,2,3,3)√2|||||| || || ||147840||26880
| |
| |- style="text-align:center; background:#f0e0e0;"
| |
| !42
| |
| |<!-- [x3o3o3x3o3x4o] -->{{CDD|node|4|node_1|3|node|3|node_1|3|node|3|node|3|node_1}}<BR>t<sub>0,3,5</sub>{3,3,3,3,3,4}||[[Pentiruncinated 7-orthoplex]] (Topaz)|||(0,1,1,2,2,2,3)√2|||||| || || ||174720||26880
| |
| |- style="text-align:center; background:#e0f0e0;"
| |
| !43
| |
| |<!-- [o3x3o3x3o3x4o] -->{{CDD|node|4|node_1|3|node|3|node_1|3|node|3|node_1|3|node}}<BR>t<sub>1,3,5</sub>{4,3,3,3,3,3}||[[Bistericantellated 7-cube]] (Bacresaz)|||(0,1,1,2,2,3,3)√2|||||| || || ||241920||40320
| |
| |- style="text-align:center; background:#e0e0f0;"
| |
| !44
| |
| |<!-- [o3o3x3x3o3x4o] -->{{CDD|node|4|node_1|3|node|3|node_1|3|node_1|3|node|3|node}}<BR>t<sub>1,3,4</sub>{4,3,3,3,3,3}||[[Biruncicantellated 7-cube]] (Bopresa)|||(0,1,1,2,3,3,3)√2|||||| || || ||120960||26880
| |
| |- style="text-align:center; background:#f0e0e0;"
| |
| !45
| |
| |<!-- [x3o3o3o3x3x4o] -->{{CDD|node|4|node_1|3|node_1|3|node|3|node|3|node|3|node_1}}<BR>t<sub>0,4,5</sub>{3,3,3,3,3,4}||[[Pentistericated 7-orthoplex]] (Tocaz)|||(0,1,2,2,2,2,3)√2|||||| || || ||67200||13440
| |
| |- style="text-align:center; background:#e0e0f0;"
| |
| !46
| |
| |<!-- [o3x3o3o3x3x4o] -->{{CDD|node|4|node_1|3|node_1|3|node|3|node|3|node_1|3|node}}<BR>t<sub>1,2,5</sub>{4,3,3,3,3,3}||[[Bisteritruncated 7-cube]] (Bactasa)|||(0,1,2,2,2,3,3)√2|||||| || || ||147840||26880
| |
| |- style="text-align:center; background:#e0e0f0;"
| |
| !47
| |
| |<!-- [o3o3x3o3x3x4o] -->{{CDD|node|4|node_1|3|node_1|3|node|3|node_1|3|node|3|node}}<BR>t<sub>1,2,4</sub>{4,3,3,3,3,3}||[[Biruncitruncated 7-cube]] (Biptesa)|||(0,1,2,2,3,3,3)√2|||||| || || ||134400||26880
| |
| |- style="text-align:center; background:#e0e0f0;"
| |
| !48
| |
| |<!-- [o3o3o3x3x3x4o] -->{{CDD|node|4|node_1|3|node_1|3|node_1|3|node|3|node|3|node}}<BR>t<sub>1,2,3</sub>{4,3,3,3,3,3}||[[Bicantitruncated 7-cube]] (Gibrosa)|||(0,1,2,3,3,3,3)√2|||||| || || ||47040||13440
| |
| |- style="text-align:center; background:#f0e0e0;"
| |
| !49
| |
| |<!-- [x3x3o3o3o3o4x] -->{{CDD|node_1|4|node|3|node|3|node|3|node|3|node_1|3|node_1}}<BR>t<sub>0,1,6</sub>{3,3,3,3,3,4}||[[Hexitruncated 7-orthoplex]] (Putaz)|||(0,0,0,0,0,1,2)√2 + (1,1,1,1,1,1,1)|||||| || || ||29568||5376
| |
| |- style="text-align:center; background:#f0e0e0;"
| |
| !50
| |
| |<!-- [x3o3x3o3o3o4x] -->{{CDD|node_1|4|node|3|node|3|node|3|node_1|3|node|3|node_1}}<BR>t<sub>0,2,6</sub>{3,3,3,3,3,4}||[[Hexicantellated 7-orthoplex]] (Puraz)|||(0,0,0,0,1,1,2)√2 + (1,1,1,1,1,1,1)|||||| || || ||94080||13440
| |
| |- style="text-align:center; background:#e0e0f0;"
| |
| !51
| |
| |<!-- [o3x3x3o3o3o4x] -->{{CDD|node_1|4|node|3|node|3|node|3|node_1|3|node_1|3|node}}<BR>t<sub>0,4,5</sub>{4,3,3,3,3,3}||[[Pentistericated 7-cube]] (Tacosa)|||(0,0,0,0,1,2,2)√2 + (1,1,1,1,1,1,1)|||||| || || ||67200||13440
| |
| |- style="text-align:center; background:#e0f0e0;"
| |
| !52
| |
| |<!-- [x3o3o3x3o3o4x] -->{{CDD|node_1|4|node|3|node|3|node_1|3|node|3|node|3|node_1}}<BR>t<sub>0,3,6</sub>{4,3,3,3,3,3}||[[Hexiruncinated 7-cube]] (Pupsez)|||(0,0,0,1,1,1,2)√2 + (1,1,1,1,1,1,1)|||||| || || ||134400||17920
| |
| |- style="text-align:center; background:#e0e0f0;"
| |
| !53
| |
| |<!-- [o3x3o3x3o3o4x] -->{{CDD|node_1|4|node|3|node|3|node_1|3|node|3|node_1|3|node}}<BR>t<sub>0,3,5</sub>{4,3,3,3,3,3}||[[Pentiruncinated 7-cube]] (Tapsa)|||(0,0,0,1,1,2,2)√2 + (1,1,1,1,1,1,1)|||||| || || ||174720||26880
| |
| |- style="text-align:center; background:#e0e0f0;"
| |
| !54
| |
| |<!-- [o3o3x3x3o3o4x] -->{{CDD|node_1|4|node|3|node|3|node_1|3|node_1|3|node|3|node}}<BR>t<sub>0,3,4</sub>{4,3,3,3,3,3}||[[Steriruncinated 7-cube]] (Capsa)|||(0,0,0,1,2,2,2)√2 + (1,1,1,1,1,1,1)|||||| || || ||80640||17920
| |
| |- style="text-align:center; background:#e0e0f0;"
| |
| !55
| |
| |<!-- [x3o3o3o3x3o4x] -->{{CDD|node_1|4|node|3|node_1|3|node|3|node|3|node|3|node_1}}<BR>t<sub>0,2,6</sub>{4,3,3,3,3,3}||[[Hexicantellated 7-cube]] (Purosa)|||(0,0,1,1,1,1,2)√2 + (1,1,1,1,1,1,1)|||||| || || ||94080||13440
| |
| |- style="text-align:center; background:#e0e0f0;"
| |
| !56
| |
| |<!-- [o3x3o3o3x3o4x] -->{{CDD|node_1|4|node|3|node_1|3|node|3|node|3|node_1|3|node}}<BR>t<sub>0,2,5</sub>{4,3,3,3,3,3}||[[Penticantellated 7-cube]] (Tersa)|||(0,0,1,1,1,2,2)√2 + (1,1,1,1,1,1,1)|||||| || || ||188160||26880
| |
| |- style="text-align:center; background:#e0e0f0;"
| |
| !57
| |
| |<!-- [o3o3x3o3x3o4x] -->{{CDD|node_1|4|node|3|node_1|3|node|3|node_1|3|node|3|node}}<BR>t<sub>0,2,4</sub>{4,3,3,3,3,3}||[[Stericantellated 7-cube]] (Carsa)|||(0,0,1,1,2,2,2)√2 + (1,1,1,1,1,1,1)|||||| || || ||161280||26880
| |
| |- style="text-align:center; background:#e0e0f0;"
| |
| !58
| |
| |<!-- [o3o3o3x3x3o4x] -->{{CDD|node_1|4|node|3|node_1|3|node_1|3|node|3|node|3|node}}<BR>t<sub>0,2,3</sub>{4,3,3,3,3,3}||[[Runcicantellated 7-cube]] (Parsa)|||(0,0,1,2,2,2,2)√2 + (1,1,1,1,1,1,1)|||||| || || ||53760||13440
| |
| |- style="text-align:center; background:#e0e0f0;"
| |
| !59
| |
| |<!-- [x3o3o3o3o3x4x] -->{{CDD|node_1|4|node_1|3|node|3|node|3|node|3|node|3|node_1}}<BR>t<sub>0,1,6</sub>{4,3,3,3,3,3}||[[Hexitruncated 7-cube]] (Putsa)|||(0,1,1,1,1,1,2)√2 + (1,1,1,1,1,1,1)|||||| || || ||29568||5376
| |
| |- style="text-align:center; background:#e0e0f0;"
| |
| !60
| |
| |<!-- [o3x3o3o3o3x4x] -->{{CDD|node_1|4|node_1|3|node|3|node|3|node|3|node_1|3|node}}<BR>t<sub>0,1,5</sub>{4,3,3,3,3,3}||[[Pentitruncated 7-cube]] (Tetsa)|||(0,1,1,1,1,2,2)√2 + (1,1,1,1,1,1,1)|||||| || || ||87360||13440
| |
| |- style="text-align:center; background:#e0e0f0;"
| |
| !61
| |
| |<!-- [o3o3x3o3o3x4x] -->{{CDD|node_1|4|node_1|3|node|3|node|3|node_1|3|node|3|node}}<BR>t<sub>0,1,4</sub>{4,3,3,3,3,3}||[[Steritruncated 7-cube]] (Catsa)|||(0,1,1,1,2,2,2)√2 + (1,1,1,1,1,1,1)|||||| || || ||116480||17920
| |
| |- style="text-align:center; background:#e0e0f0;"
| |
| !62
| |
| |<!-- [o3o3o3x3o3x4x] -->{{CDD|node_1|4|node_1|3|node|3|node_1|3|node|3|node|3|node}}<BR>t<sub>0,1,3</sub>{4,3,3,3,3,3}||[[Runcitruncated 7-cube]] (Petsa)|||(0,1,1,2,2,2,2)√2 + (1,1,1,1,1,1,1)|||||| || || ||73920||13440
| |
| |- style="text-align:center; background:#e0e0f0;"
| |
| !63
| |
| |<!-- [o3o3o3o3x3x4x] -->{{CDD|node_1|4|node_1|3|node_1|3|node|3|node|3|node|3|node}}<BR>t<sub>0,1,2</sub>{4,3,3,3,3,3}||[[Cantitruncated 7-cube]] (Gersa)|||(0,1,2,2,2,2,2)√2 + (1,1,1,1,1,1,1)|||||| || || ||18816||5376
| |
| |- style="text-align:center; background:#f0e0e0;"
| |
| !64
| |
| |<!-- [x3x3x3x3o3o4o] -->{{CDD|node|4|node|3|node|3|node_1|3|node_1|3|node_1|3|node_1}}<BR>t<sub>0,1,2,3</sub>{3,3,3,3,3,4}||[[Runcicantitruncated 7-orthoplex]] (Gopaz)|||(0,1,2,3,4,4,4)√2|||||| || || ||60480||13440
| |
| |- style="text-align:center; background:#f0e0e0;"
| |
| !65
| |
| |<!-- [x3x3x3o3x3o4o] -->{{CDD|node|4|node|3|node_1|3|node|3|node_1|3|node_1|3|node_1}}<BR>t<sub>0,1,2,4</sub>{3,3,3,3,3,4}||[[Stericantitruncated 7-orthoplex]] (Cogarz)|||(0,0,1,1,2,3,4)√2|||||| || || ||241920||40320
| |
| |- style="text-align:center; background:#f0e0e0;"
| |
| !66
| |
| |<!-- [x3x3o3x3x3o4o] -->{{CDD|node|4|node|3|node_1|3|node_1|3|node|3|node_1|3|node_1}}<BR>t<sub>0,1,3,4</sub>{3,3,3,3,3,4}||[[Steriruncitruncated 7-orthoplex]] (Captaz)|||(0,0,1,2,2,3,4)√2|||||| || || ||181440||40320
| |
| |- style="text-align:center; background:#f0e0e0;"
| |
| !67
| |
| |<!-- [x3o3x3x3x3o4o] -->{{CDD|node|4|node|3|node_1|3|node_1|3|node_1|3|node|3|node_1}}<BR>t<sub>0,2,3,4</sub>{3,3,3,3,3,4}||[[Steriruncicantellated 7-orthoplex]] (Caparz)|||(0,0,1,2,3,3,4)√2|||||| || || ||181440||40320
| |
| |- style="text-align:center; background:#f0e0e0;"
| |
| !68
| |
| |<!-- [o3x3x3x3x3o4o] -->{{CDD|node|4|node|3|node_1|3|node_1|3|node_1|3|node_1|3|node}}<BR>t<sub>1,2,3,4</sub>{3,3,3,3,3,4}||[[Biruncicantitruncated 7-orthoplex]] (Gibpaz)|||(0,0,1,2,3,4,4)√2|||||| || || ||161280||40320
| |
| |- style="text-align:center; background:#f0e0e0;"
| |
| !69
| |
| |<!-- [x3x3x3o3o3x4o] -->{{CDD|node|4|node_1|3|node|3|node|3|node_1|3|node_1|3|node_1}}<BR>t<sub>0,1,2,5</sub>{3,3,3,3,3,4}||[[Penticantitruncated 7-orthoplex]] (Tograz)|||(0,1,1,1,2,3,4)√2|||||| || || ||295680||53760
| |
| |- style="text-align:center; background:#f0e0e0;"
| |
| !70
| |
| |<!-- [x3x3o3x3o3x4o] -->{{CDD|node|4|node_1|3|node|3|node_1|3|node|3|node_1|3|node_1}}<BR>t<sub>0,1,3,5</sub>{3,3,3,3,3,4}||[[Pentiruncitruncated 7-orthoplex]] (Toptaz)|||(0,1,1,2,2,3,4)√2|||||| || || ||443520||80640
| |
| |- style="text-align:center; background:#f0e0e0;"
| |
| !71
| |
| |<!-- [x3o3x3x3o3x4o] -->{{CDD|node|4|node_1|3|node|3|node_1|3|node_1|3|node|3|node_1}}<BR>t<sub>0,2,3,5</sub>{3,3,3,3,3,4}||[[Pentiruncicantellated 7-orthoplex]] (Toparz)|||(0,1,1,2,3,3,4)√2|||||| || || ||403200||80640
| |
| |- style="text-align:center; background:#f0e0e0;"
| |
| !72
| |
| |<!-- [o3x3x3x3o3x4o] -->{{CDD|node|4|node_1|3|node|3|node_1|3|node_1|3|node_1|3|node}}<BR>t<sub>1,2,3,5</sub>{3,3,3,3,3,4}||[[Bistericantitruncated 7-orthoplex]] (Becogarz)|||(0,1,1,2,3,4,4)√2|||||| || || ||362880||80640
| |
| |- style="text-align:center; background:#f0e0e0;"
| |
| !73
| |
| |<!-- [x3x3o3o3x3x4o] -->{{CDD|node|4|node_1|3|node_1|3|node|3|node|3|node_1|3|node_1}}<BR>t<sub>0,1,4,5</sub>{3,3,3,3,3,4}||[[Pentisteritruncated 7-orthoplex]] (Tacotaz)|||(0,1,2,2,2,3,4)√2|||||| || || ||241920||53760
| |
| |- style="text-align:center; background:#f0e0e0;"
| |
| !74
| |
| |<!-- [x3o3x3o3x3x4o] -->{{CDD|node|4|node_1|3|node_1|3|node|3|node_1|3|node|3|node_1}}<BR>t<sub>0,2,4,5</sub>{3,3,3,3,3,4}||[[Pentistericantellated 7-orthoplex]] (Tocarz)|||(0,1,2,2,3,3,4)√2|||||| || || ||403200||80640
| |
| |- style="text-align:center; background:#e0f0e0;"
| |
| !75
| |
| |<!-- [o3x3x3o3x3x4o] -->{{CDD|node|4|node_1|3|node_1|3|node|3|node_1|3|node_1|3|node}}<BR>t<sub>1,2,4,5</sub>{4,3,3,3,3,3}||[[Bisteriruncitruncated 7-cube]] (Bocaptosaz)|||(0,1,2,2,3,4,4)√2|||||| |||| ||322560||80640
| |
| |- style="text-align:center; background:#f0e0e0;"
| |
| !76
| |
| |<!-- [x3o3o3x3x3x4o] -->{{CDD|node|4|node_1|3|node_1|3|node_1|3|node|3|node|3|node_1}}<BR>t<sub>0,3,4,5</sub>{3,3,3,3,3,4}||[[Pentisteriruncinated 7-orthoplex]] (Tecpaz)|||(0,1,2,3,3,3,4)√2|||||| || || ||241920||53760
| |
| |- style="text-align:center; background:#e0e0f0;"
| |
| !77
| |
| |<!-- [o3x3o3x3x3x4o] -->{{CDD|node|4|node_1|3|node_1|3|node_1|3|node|3|node_1|3|node}}<BR>t<sub>1,2,3,5</sub>{4,3,3,3,3,3}||[[Bistericantitruncated 7-cube]] (Becgresa)|||(0,1,2,3,3,4,4)√2|||||| || || ||362880||80640
| |
| |- style="text-align:center; background:#e0e0f0;"
| |
| !78
| |
| |<!-- [o3o3x3x3x3x4o] -->{{CDD|node|4|node_1|3|node_1|3|node_1|3|node_1|3|node|3|node}}<BR>t<sub>1,2,3,4</sub>{4,3,3,3,3,3}||[[Biruncicantitruncated 7-cube]] (Gibposa)|||(0,1,2,3,4,4,4)√2|||||| || || ||188160||53760
| |
| |- style="text-align:center; background:#f0e0e0;"
| |
| !79
| |
| |<!-- [x3x3x3o3o3o4x] -->{{CDD|node_1|4|node|3|node|3|node|3|node_1|3|node_1|3|node_1}}<BR>t<sub>0,1,2,6</sub>{3,3,3,3,3,4}||[[Hexicantitruncated 7-orthoplex]] (Pugarez)|||(0,0,0,0,1,2,3)√2 + (1,1,1,1,1,1,1)|||||| || || ||134400||26880
| |
| |- style="text-align:center; background:#f0e0e0;"
| |
| !80
| |
| |<!-- [x3x3o3x3o3o4x] -->{{CDD|node_1|4|node|3|node|3|node_1|3|node|3|node_1|3|node_1}}<BR>t<sub>0,1,3,6</sub>{3,3,3,3,3,4}||[[Hexiruncitruncated 7-orthoplex]] (Papataz)|||(0,0,0,1,1,2,3)√2 + (1,1,1,1,1,1,1)|||||| || || ||322560||53760
| |
| |- style="text-align:center; background:#f0e0e0;"
| |
| !81
| |
| |<!-- [x3o3x3x3o3o4x] -->{{CDD|node_1|4|node|3|node|3|node_1|3|node_1|3|node|3|node_1}}<BR>t<sub>0,2,3,6</sub>{3,3,3,3,3,4}||[[Hexiruncicantellated 7-orthoplex]] (Puparez)|||(0,0,0,1,2,2,3)√2 + (1,1,1,1,1,1,1)|||||| || || ||268800||53760
| |
| |- style="text-align:center; background:#e0e0f0;"
| |
| !82
| |
| |<!-- [o3x3x3x3o3o4x] -->{{CDD|node_1|4|node|3|node|3|node_1|3|node_1|3|node_1|3|node}}<BR>t<sub>0,3,4,5</sub>{4,3,3,3,3,3}||[[Pentisteriruncinated 7-cube]] (Tecpasa)|||(0,0,0,1,2,3,3)√2 + (1,1,1,1,1,1,1)|||||| || || ||241920||53760
| |
| |- style="text-align:center; background:#f0e0e0;"
| |
| !83
| |
| |<!-- [x3x3o3o3x3o4x] -->{{CDD|node_1|4|node|3|node_1|3|node|3|node|3|node_1|3|node_1}}<BR>t<sub>0,1,4,6</sub>{3,3,3,3,3,4}||[[Hexisteritruncated 7-orthoplex]] (Pucotaz)|||(0,0,1,1,1,2,3)√2 + (1,1,1,1,1,1,1)|||||| || || ||322560||53760
| |
| |- style="text-align:center; background:#e0f0e0;"
| |
| !84
| |
| |<!-- [x3o3x3o3x3o4x] -->{{CDD|node_1|4|node|3|node_1|3|node|3|node_1|3|node|3|node_1}}<BR>t<sub>0,2,4,6</sub>{4,3,3,3,3,3}||[[Hexistericantellated 7-cube]] (Pucrosaz)|||(0,0,1,1,2,2,3)√2 + (1,1,1,1,1,1,1)|||||| || || ||483840||80640
| |
| |- style="text-align:center; background:#e0e0f0;"
| |
| !85
| |
| |<!-- [o3x3x3o3x3o4x] -->{{CDD|node_1|4|node|3|node_1|3|node|3|node_1|3|node_1|3|node}}<BR>t<sub>0,2,4,5</sub>{4,3,3,3,3,3}||[[Pentistericantellated 7-cube]] (Tecresa)|||(0,0,1,1,2,3,3)√2 + (1,1,1,1,1,1,1)|||||| || || ||403200||80640
| |
| |- style="text-align:center; background:#e0e0f0;"
| |
| !86
| |
| |<!-- [x3o3o3x3x3o4x] -->{{CDD|node_1|4|node|3|node_1|3|node_1|3|node|3|node|3|node_1}}<BR>t<sub>0,2,3,6</sub>{4,3,3,3,3,3}||[[Hexiruncicantellated 7-cube]] (Pupresa)|||(0,0,1,2,2,2,3)√2 + (1,1,1,1,1,1,1)|||||| || || ||268800||53760
| |
| |- style="text-align:center; background:#e0e0f0;"
| |
| !87
| |
| |<!-- [o3x3o3x3x3o4x] -->{{CDD|node_1|4|node|3|node_1|3|node_1|3|node|3|node_1|3|node}}<BR>t<sub>0,2,3,5</sub>{4,3,3,3,3,3}||[[Pentiruncicantellated 7-cube]] (Topresa)|||(0,0,1,2,2,3,3)√2 + (1,1,1,1,1,1,1)|||||| || || ||403200||80640
| |
| |- style="text-align:center; background:#e0e0f0;"
| |
| !88
| |
| |<!-- [o3o3x3x3x3o4x] -->{{CDD|node_1|4|node|3|node_1|3|node_1|3|node_1|3|node|3|node}}<BR>t<sub>0,2,3,4</sub>{4,3,3,3,3,3}||[[Steriruncicantellated 7-cube]] (Copresa)|||(0,0,1,2,3,3,3)√2 + (1,1,1,1,1,1,1)|||||| || || ||215040||53760
| |
| |- style="text-align:center; background:#e0f0e0;"
| |
| !89
| |
| |<!-- [x3x3o3o3o3x4x] -->{{CDD|node_1|4|node_1|3|node|3|node|3|node|3|node_1|3|node_1}}<BR>t<sub>0,1,5,6</sub>{4,3,3,3,3,3}||[[Hexipentitruncated 7-cube]] (Putatosez)|||(0,1,1,1,1,2,3)√2 + (1,1,1,1,1,1,1)|||||| || || ||134400||26880
| |
| |- style="text-align:center; background:#e0e0f0;"
| |
| !90
| |
| |<!-- [x3o3x3o3o3x4x] -->{{CDD|node_1|4|node_1|3|node|3|node|3|node_1|3|node|3|node_1}}<BR>t<sub>0,1,4,6</sub>{4,3,3,3,3,3}||[[Hexisteritruncated 7-cube]] (Pacutsa)|||(0,1,1,1,2,2,3)√2 + (1,1,1,1,1,1,1)|||||| || || ||322560||53760
| |
| |- style="text-align:center; background:#e0e0f0;"
| |
| !91
| |
| |<!-- [o3x3x3o3o3x4x] -->{{CDD|node_1|4|node_1|3|node|3|node|3|node_1|3|node_1|3|node}}<BR>t<sub>0,1,4,5</sub>{4,3,3,3,3,3}||[[Pentisteritruncated 7-cube]] (Tecatsa)|||(0,1,1,1,2,3,3)√2 + (1,1,1,1,1,1,1)|||||| || || ||241920||53760
| |
| |- style="text-align:center; background:#e0e0f0;"
| |
| !92
| |
| |<!-- [x3o3o3x3o3x4x] -->{{CDD|node_1|4|node_1|3|node|3|node_1|3|node|3|node|3|node_1}}<BR>t<sub>0,1,3,6</sub>{4,3,3,3,3,3}||[[Hexiruncitruncated 7-cube]] (Pupetsa)|||(0,1,1,2,2,2,3)√2 + (1,1,1,1,1,1,1)|||||| || || ||322560||53760
| |
| |- style="text-align:center; background:#e0e0f0;"
| |
| !93
| |
| |<!-- [o3x3o3x3o3x4x] -->{{CDD|node_1|4|node_1|3|node|3|node_1|3|node|3|node_1|3|node}}<BR>t<sub>0,1,3,5</sub>{4,3,3,3,3,3}||[[Pentiruncitruncated 7-cube]] (Toptosa)|||(0,1,1,2,2,3,3)√2 + (1,1,1,1,1,1,1)|||||| || || ||443520||80640
| |
| |- style="text-align:center; background:#e0e0f0;"
| |
| !94
| |
| |<!-- [o3o3x3x3o3x4x] -->{{CDD|node_1|4|node_1|3|node|3|node_1|3|node_1|3|node|3|node}}<BR>t<sub>0,1,3,4</sub>{4,3,3,3,3,3}||[[Steriruncitruncated 7-cube]] (Captesa)|||(0,1,1,2,3,3,3)√2 + (1,1,1,1,1,1,1)|||||| || || ||215040||53760
| |
| |- style="text-align:center; background:#e0e0f0;"
| |
| !95
| |
| |<!-- [x3o3o3o3x3x4x] -->{{CDD|node_1|4|node_1|3|node_1|3|node|3|node|3|node|3|node_1}}<BR>t<sub>0,1,2,6</sub>{4,3,3,3,3,3}||[[Hexicantitruncated 7-cube]] (Pugrosa)|||(0,1,2,2,2,2,3)√2 + (1,1,1,1,1,1,1)|||||| || || ||134400||26880
| |
| |- style="text-align:center; background:#e0e0f0;"
| |
| !96
| |
| |<!-- [o3x3o3o3x3x4x] -->{{CDD|node_1|4|node_1|3|node_1|3|node|3|node|3|node_1|3|node}}<BR>t<sub>0,1,2,5</sub>{4,3,3,3,3,3}||[[Penticantitruncated 7-cube]] (Togresa)|||(0,1,2,2,2,3,3)√2 + (1,1,1,1,1,1,1)|||||| || || ||295680||53760
| |
| |- style="text-align:center; background:#e0e0f0;"
| |
| !97
| |
| |<!-- [o3o3x3o3x3x4x] -->{{CDD|node_1|4|node_1|3|node_1|3|node|3|node_1|3|node|3|node}}<BR>t<sub>0,1,2,4</sub>{4,3,3,3,3,3}||[[Stericantitruncated 7-cube]] (Cogarsa)|||(0,1,2,2,3,3,3)√2 + (1,1,1,1,1,1,1)|||||| || || ||268800||53760
| |
| |- style="text-align:center; background:#e0e0f0;"
| |
| !98
| |
| |<!-- [o3o3o3x3x3x4x] -->{{CDD|node_1|4|node_1|3|node_1|3|node_1|3|node|3|node|3|node}}<BR>t<sub>0,1,2,3</sub>{4,3,3,3,3,3}||[[Runcicantitruncated 7-cube]] (Gapsa)|||(0,1,2,3,3,3,3)√2 + (1,1,1,1,1,1,1)|||||| || || ||94080||26880
| |
| |- style="text-align:center; background:#f0e0e0;"
| |
| !99
| |
| |<!-- [x3x3x3x3x3o4o] -->{{CDD|node|4|node|3|node_1|3|node_1|3|node_1|3|node_1|3|node_1}}<BR>t<sub>0,1,2,3,4</sub>{3,3,3,3,3,4}||[[Steriruncicantitruncated 7-orthoplex]] (Gocaz)|||(0,0,1,2,3,4,5)√2|||||| || || ||322560||80640
| |
| |- style="text-align:center; background:#f0e0e0;"
| |
| !100
| |
| |<!-- [x3x3x3x3o3x4o] -->{{CDD|node|4|node_1|3|node|3|node_1|3|node_1|3|node_1|3|node_1}}<BR>t<sub>0,1,2,3,5</sub>{3,3,3,3,3,4}||[[Pentiruncicantitruncated 7-orthoplex]] (Tegopaz)|||(0,1,1,2,3,4,5)√2|||||| || || ||725760||161280
| |
| |- style="text-align:center; background:#f0e0e0;"
| |
| !101
| |
| |<!-- [x3x3x3o3x3x4o] -->{{CDD|node|4|node_1|3|node_1|3|node|3|node_1|3|node_1|3|node_1}}<BR>t<sub>0,1,2,4,5</sub>{3,3,3,3,3,4}||[[Pentistericantitruncated 7-orthoplex]] (Tecagraz)|||(0,1,2,2,3,4,5)√2|||||| || || ||645120||161280
| |
| |- style="text-align:center; background:#f0e0e0;"
| |
| !102
| |
| |<!-- [x3x3o3x3x3x4o] -->{{CDD|node|4|node_1|3|node_1|3|node_1|3|node|3|node_1|3|node_1}}<BR>t<sub>0,1,3,4,5</sub>{3,3,3,3,3,4}||[[Pentisteriruncitruncated 7-orthoplex]] (Tecpotaz)|||(0,1,2,3,3,4,5)√2|||||| || || ||645120||161280
| |
| |- style="text-align:center; background:#f0e0e0;"
| |
| !103
| |
| |<!-- [x3o3x3x3x3x4o] -->{{CDD|node|4|node_1|3|node_1|3|node_1|3|node_1|3|node|3|node_1}}<BR>t<sub>0,2,3,4,5</sub>{3,3,3,3,3,4}||[[Pentisteriruncicantellated 7-orthoplex]] (Tacparez)|||(0,1,2,3,4,4,5)√2|||||| || || ||645120||161280
| |
| |- style="text-align:center; background:#e0f0e0;"
| |
| !104
| |
| |<!-- [o3x3x3x3x3x4o] -->{{CDD|node|4|node_1|3|node_1|3|node_1|3|node_1|3|node_1|3|node}}<BR>t<sub>1,2,3,4,5</sub>{4,3,3,3,3,3}||[[Bisteriruncicantitruncated 7-cube]] (Gabcosaz)|||(0,1,2,3,4,5,5)√2|||||| || || ||564480||161280
| |
| |- style="text-align:center; background:#f0e0e0;"
| |
| !105
| |
| |<!-- [x3x3x3x3o3o4x] -->{{CDD|node_1|4|node|3|node|3|node_1|3|node_1|3|node_1|3|node_1}}<BR>t<sub>0,1,2,3,6</sub>{3,3,3,3,3,4}||[[Hexiruncicantitruncated 7-orthoplex]] (Pugopaz)|||(0,0,0,1,2,3,4)√2 + (1,1,1,1,1,1,1)|||||| || || ||483840||107520
| |
| |- style="text-align:center; background:#f0e0e0;"
| |
| !106
| |
| |<!-- [x3x3x3o3x3o4x] -->{{CDD|node_1|4|node|3|node_1|3|node|3|node_1|3|node_1|3|node_1}}<BR>t<sub>0,1,2,4,6</sub>{3,3,3,3,3,4}||[[Hexistericantitruncated 7-orthoplex]] (Pucagraz)|||(0,0,1,1,2,3,4)√2 + (1,1,1,1,1,1,1)|||||| || || ||806400||161280
| |
| |- style="text-align:center; background:#f0e0e0;"
| |
| !107
| |
| |<!-- [x3x3o3x3x3o4x] -->{{CDD|node_1|4|node|3|node_1|3|node_1|3|node|3|node_1|3|node_1}}<BR>t<sub>0,1,3,4,6</sub>{3,3,3,3,3,4}||[[Hexisteriruncitruncated 7-orthoplex]] (Pucpotaz)|||(0,0,1,2,2,3,4)√2 + (1,1,1,1,1,1,1)|||||| || || ||725760||161280
| |
| |- style="text-align:center; background:#e0f0e0;"
| |
| !108
| |
| |<!-- [x3o3x3x3x3o4x] -->{{CDD|node_1|4|node|3|node_1|3|node_1|3|node_1|3|node|3|node_1}}<BR>t<sub>0,2,3,4,6</sub>{4,3,3,3,3,3}||[[Hexisteriruncicantellated 7-cube]] (Pucprosaz)|||(0,0,1,2,3,3,4)√2 + (1,1,1,1,1,1,1)|||||| || || ||725760||161280
| |
| |- style="text-align:center; background:#e0e0f0;"
| |
| !109
| |
| |<!-- [o3x3x3x3x3o4x] -->{{CDD|node_1|4|node|3|node_1|3|node_1|3|node_1|3|node_1|3|node}}<BR>t<sub>0,2,3,4,5</sub>{4,3,3,3,3,3}||[[Pentisteriruncicantellated 7-cube]] (Tocpresa)|||(0,0,1,2,3,4,4)√2 + (1,1,1,1,1,1,1)|||||| || || ||645120||161280
| |
| |- style="text-align:center; background:#f0e0e0;"
| |
| !110
| |
| |<!-- [x3x3x3o3o3x4x] -->{{CDD|node_1|4|node_1|3|node|3|node|3|node_1|3|node_1|3|node_1}}<BR>t<sub>0,1,2,5,6</sub>{3,3,3,3,3,4}||[[Hexipenticantitruncated 7-orthoplex]] (Putegraz)|||(0,1,1,1,2,3,4)√2 + (1,1,1,1,1,1,1)|||||| || || ||483840||107520
| |
| |- style="text-align:center; background:#e0f0e0;"
| |
| !111
| |
| |<!-- [x3x3o3x3o3x4x] -->{{CDD|node_1|4|node_1|3|node|3|node_1|3|node|3|node_1|3|node_1}}<BR>t<sub>0,1,3,5,6</sub>{4,3,3,3,3,3}||[[Hexipentiruncitruncated 7-cube]] (Putpetsaz)|||(0,1,1,2,2,3,4)√2 + (1,1,1,1,1,1,1)|||||| || || ||806400||161280
| |
| |- style="text-align:center; background:#e0e0f0;"
| |
| !112
| |
| |<!-- [x3o3x3x3o3x4x] -->{{CDD|node_1|4|node_1|3|node|3|node_1|3|node_1|3|node|3|node_1}}<BR>t<sub>0,1,3,4,6</sub>{4,3,3,3,3,3}||[[Hexisteriruncitruncated 7-cube]] (Pucpetsa)|||(0,1,1,2,3,3,4)√2 + (1,1,1,1,1,1,1)|||||| || || ||725760||161280
| |
| |- style="text-align:center; background:#e0e0f0;"
| |
| !113
| |
| |<!-- [o3x3x3x3o3x4x] -->{{CDD|node_1|4|node_1|3|node|3|node_1|3|node_1|3|node_1|3|node}}<BR>t<sub>0,1,3,4,5</sub>{4,3,3,3,3,3}||[[Pentisteriruncitruncated 7-cube]] (Tecpetsa)|||(0,1,1,2,3,4,4)√2 + (1,1,1,1,1,1,1)|||||| || || ||645120||161280
| |
| |- style="text-align:center; background:#e0e0f0;"
| |
| !114
| |
| |<!-- [x3x3o3o3x3x4x] -->{{CDD|node_1|4|node_1|3|node_1|3|node|3|node|3|node_1|3|node_1}}<BR>t<sub>0,1,2,5,6</sub>{4,3,3,3,3,3}||[[Hexipenticantitruncated 7-cube]] (Putgresa)|||(0,1,2,2,2,3,4)√2 + (1,1,1,1,1,1,1)|||||| || || ||483840||107520
| |
| |- style="text-align:center; background:#e0e0f0;"
| |
| !115
| |
| |<!-- [x3o3x3o3x3x4x] -->{{CDD|node_1|4|node_1|3|node_1|3|node|3|node_1|3|node|3|node_1}}<BR>t<sub>0,1,2,4,6</sub>{4,3,3,3,3,3}||[[Hexistericantitruncated 7-cube]] (Pucagrosa)|||(0,1,2,2,3,3,4)√2 + (1,1,1,1,1,1,1)|||||| || || ||806400||161280
| |
| |- style="text-align:center; background:#e0e0f0;"
| |
| !116
| |
| |<!-- [o3x3x3o3x3x4x] -->{{CDD|node_1|4|node_1|3|node_1|3|node|3|node_1|3|node_1|3|node}}<BR>t<sub>0,1,2,4,5</sub>{4,3,3,3,3,3}||[[Pentistericantitruncated 7-cube]] (Tecgresa)|||(0,1,2,2,3,4,4)√2 + (1,1,1,1,1,1,1)|||||| || || ||645120||161280
| |
| |- style="text-align:center; background:#e0e0f0;"
| |
| !117
| |
| |<!-- [x3o3o3x3x3x4x] -->{{CDD|node_1|4|node_1|3|node_1|3|node_1|3|node|3|node|3|node_1}}<BR>t<sub>0,1,2,3,6</sub>{4,3,3,3,3,3}||[[Hexiruncicantitruncated 7-cube]] (Pugopsa)|||(0,1,2,3,3,3,4)√2 + (1,1,1,1,1,1,1)|||||| || || ||483840||107520
| |
| |- style="text-align:center; background:#e0e0f0;"
| |
| !118
| |
| |<!-- [o3x3o3x3x3x4x] -->{{CDD|node_1|4|node_1|3|node_1|3|node_1|3|node|3|node_1|3|node}}<BR>t<sub>0,1,2,3,5</sub>{4,3,3,3,3,3}||[[Pentiruncicantitruncated 7-cube]] (Togapsa)|||(0,1,2,3,3,4,4)√2 + (1,1,1,1,1,1,1)|||||| || || ||725760||161280
| |
| |- style="text-align:center; background:#e0e0f0;"
| |
| !119
| |
| |<!-- [o3o3x3x3x3x4x] -->{{CDD|node_1|4|node_1|3|node_1|3|node_1|3|node_1|3|node|3|node}}<BR>t<sub>0,1,2,3,4</sub>{4,3,3,3,3,3}||[[Steriruncicantitruncated 7-cube]] (Gacosa)|||(0,1,2,3,4,4,4)√2 + (1,1,1,1,1,1,1)|||||| || || ||376320||107520
| |
| |- style="text-align:center; background:#f0e0e0;"
| |
| !120
| |
| |<!-- [x3x3x3x3x3x4o] -->{{CDD|node|4|node_1|3|node_1|3|node_1|3|node_1|3|node_1|3|node_1}}<BR>t<sub>0,1,2,3,4,5</sub>{3,3,3,3,3,4}||[[Pentisteriruncicantitruncated 7-orthoplex]] (Gotaz)|||(0,1,2,3,4,5,6)√2|||||| || || ||1128960||322560
| |
| |- style="text-align:center; background:#f0e0e0;"
| |
| !121
| |
| |<!-- [x3x3x3x3x3o4x] -->{{CDD|node_1|4|node|3|node_1|3|node_1|3|node_1|3|node_1|3|node_1}}<BR>t<sub>0,1,2,3,4,6</sub>{3,3,3,3,3,4}||[[Hexisteriruncicantitruncated 7-orthoplex]] (Pugacaz)|||(0,0,1,2,3,4,5)√2 + (1,1,1,1,1,1,1)|||||| || || ||1290240||322560
| |
| |- style="text-align:center; background:#f0e0e0;"
| |
| !122
| |
| |<!-- [x3x3x3x3o3x4x] -->{{CDD|node_1|4|node_1|3|node|3|node_1|3|node_1|3|node_1|3|node_1}}<BR>t<sub>0,1,2,3,5,6</sub>{3,3,3,3,3,4}||[[Hexipentiruncicantitruncated 7-orthoplex]] (Putgapaz)|||(0,1,1,2,3,4,5)√2 + (1,1,1,1,1,1,1)|||||| || || ||1290240||322560
| |
| |- style="text-align:center; background:#e0f0e0;"
| |
| !123
| |
| |<!-- [x3x3x3o3x3x4x] -->{{CDD|node_1|4|node_1|3|node_1|3|node|3|node_1|3|node_1|3|node_1}}<BR>t<sub>0,1,2,4,5,6</sub>{4,3,3,3,3,3}||[[Hexipentistericantitruncated 7-cube]] (Putcagrasaz)|||(0,1,2,2,3,4,5)√2 + (1,1,1,1,1,1,1)|||||| || || ||1290240||322560
| |
| |- style="text-align:center; background:#e0e0f0;"
| |
| !124
| |
| |<!-- [x3x3o3x3x3x4x] -->{{CDD|node_1|4|node_1|3|node_1|3|node_1|3|node|3|node_1|3|node_1}}<BR>t<sub>0,1,2,3,5,6</sub>{4,3,3,3,3,3}||[[Hexipentiruncicantitruncated 7-cube]] (Putgapsa)|||(0,1,2,3,3,4,5)√2 + (1,1,1,1,1,1,1)|||||| || || ||1290240||322560
| |
| |- style="text-align:center; background:#e0e0f0;"
| |
| !125
| |
| |<!-- [x3o3x3x3x3x4x] -->{{CDD|node_1|4|node_1|3|node_1|3|node_1|3|node_1|3|node|3|node_1}}<BR>t<sub>0,1,2,3,4,6</sub>{4,3,3,3,3,3}||[[Hexisteriruncicantitruncated 7-cube]] (Pugacasa)|||(0,1,2,3,4,4,5)√2 + (1,1,1,1,1,1,1)|||||| || || ||1290240||322560
| |
| |- style="text-align:center; background:#e0e0f0;"
| |
| !126
| |
| |<!-- [o3x3x3x3x3x4x] -->{{CDD|node_1|4|node_1|3|node_1|3|node_1|3|node_1|3|node_1|3|node}}<BR>t<sub>0,1,2,3,4,5</sub>{4,3,3,3,3,3}||[[Pentisteriruncicantitruncated 7-cube]] (Gotesa)|||(0,1,2,3,4,5,5)√2 + (1,1,1,1,1,1,1)|||||| || || ||1128960||322560
| |
| |- style="text-align:center; background:#e0f0e0;"
| |
| !127
| |
| |<!-- [x3x3x3x3x3x4x] -->{{CDD|node_1|4|node_1|3|node_1|3|node_1|3|node_1|3|node_1|3|node_1}}<BR>t<sub>0,1,2,3,4,5,6</sub>{4,3,3,3,3,3}||[[Omnitruncated 7-cube]] (Guposaz)|||(0,1,2,3,4,5,6)√2 + (1,1,1,1,1,1,1)|| || || || || ||2257920||645120
| |
| |}
| |
| | |
| == The D<sub>7</sub> family ==
| |
| | |
| The D<sub>7</sub> family has symmetry of order 322560 (7 [[factorial]] x 2<sup>6</sup>).
| |
| | |
| This family has 3×32−1=95 Wythoffian uniform polytopes, generated by marking one or more nodes of the D<sub>7</sub> [[Coxeter-Dynkin diagram]]. Of these, 63 (2×32−1) are repeated from the B<sub>7</sub> family and 32 are unique to this family, listed below. Bowers names and acronym are given for cross-referencing.
| |
| | |
| See also [[list of D7 polytopes]] for Coxeter plane graphs of these polytopes.
| |
| {| class="wikitable"
| |
| !rowspan=2|#
| |
| !rowspan=2|[[Coxeter diagram]]
| |
| !rowspan=2|Names
| |
| !rowspan=2|Base point<BR>(Alternately signed)
| |
| !colspan=7|Element counts
| |
| |-
| |
| !6||5||4||3||2||1||0
| |
| |- align=center
| |
| !1
| |
| ||{{CDD|nodes_10ru|split2|node|3|node|3|node|3|node|3|node}} = {{CDD|node_h1|4|node|3|node|3|node|3|node|3|node|3|node}}||[[7-demicube]]<BR>Demihepteract (Hesa)||(1,1,1,1,1,1,1)||78||532||1624||2800||2240||672||64
| |
| |- align=center
| |
| !2
| |
| ||{{CDD|nodes_10ru|split2|node_1|3|node|3|node|3|node|3|node}} = {{CDD|node_h1|4|node|3|node_1|3|node|3|node|3|node|3|node}}||[[Truncated 7-demicube]]<BR>Truncated demihepteract (Thesa)||(1,1,3,3,3,3,3)||142||1428||5656||11760||13440||7392||1344
| |
| |- align=center
| |
| !3
| |
| ||{{CDD|nodes_10ru|split2|node|3|node_1|3|node|3|node|3|node}} = {{CDD|node_h1|4|node|3|node|3|node_1|3|node|3|node|3|node}}||[[Cantellated 7-demicube]]<BR>Small rhombated demihepteract (Sirhesa)||(1,1,1,3,3,3,3)|| || || || || ||16800||2240
| |
| |- align=center
| |
| !4
| |
| ||{{CDD|nodes_10ru|split2|node|3|node|3|node_1|3|node|3|node}} = {{CDD|node_h1|4|node|3|node|3|node|3|node_1|3|node|3|node}}||[[Runcinated 7-demicube]]<BR>Small prismated demihepteract (Sphosa)||(1,1,1,1,3,3,3)|| || || || || ||20160||2240
| |
| |- align=center
| |
| !5
| |
| ||{{CDD|nodes_10ru|split2|node|3|node|3|node|3|node_1|3|node}} = {{CDD|node_h1|4|node|3|node|3|node|3|node|3|node_1|3|node}}||[[Stericated 7-demicube]]<BR>Small cellated demihepteract (Sochesa)||(1,1,1,1,1,3,3)|| || || || || ||13440||1344
| |
| |- align=center
| |
| !6
| |
| ||{{CDD|nodes_10ru|split2|node|3|node|3|node|3|node|3|node_1}} = {{CDD|node_h1|4|node|3|node|3|node|3|node|3|node|3|node_1}}||[[Pentellated 7-demicube]]<BR>Small terated demihepteract (Suthesa)||(1,1,1,1,1,1,3)|| || || || || ||4704||448
| |
| |- align=center
| |
| !7
| |
| ||{{CDD|nodes_10ru|split2|node_1|3|node_1|3|node|3|node|3|node}} = {{CDD|node_h1|4|node|3|node_1|3|node_1|3|node|3|node|3|node}}||[[Cantitruncated 7-demicube]]<BR>Great rhombated demihepteract (Girhesa)||(1,1,3,5,5,5,5)|| || || || || ||23520||6720
| |
| |- align=center
| |
| !8
| |
| ||{{CDD|nodes_10ru|split2|node_1|3|node|3|node_1|3|node|3|node}} = {{CDD|node_h1|4|node|3|node_1|3|node|3|node_1|3|node|3|node}}||[[Runcitruncated 7-demicube]]<BR>Prismatotruncated demihepteract (Pothesa)||(1,1,3,3,5,5,5)|| || || || || ||73920||13440
| |
| |- align=center
| |
| !9
| |
| ||{{CDD|nodes_10ru|split2|node|3|node_1|3|node_1|3|node|3|node}} = {{CDD|node_h1|4|node|3|node|3|node_1|3|node_1|3|node|3|node}}||[[Runcicantellated 7-demicube]]<BR>Prismatorhomated demihepteract (Prohesa)||(1,1,1,3,5,5,5)|| || || || || ||40320||8960
| |
| |- align=center
| |
| !10
| |
| ||{{CDD|nodes_10ru|split2|node_1|3|node|3|node|3|node_1|3|node}} = {{CDD|node_h1|4|node|3|node_1|3|node|3|node|3|node_1|3|node}}||[[Steritruncated 7-demicube]]<BR>Cellitruncated demihepteract (Cothesa)||(1,1,3,3,3,5,5)|| || || || || ||87360||13440
| |
| |- align=center
| |
| !11
| |
| ||{{CDD|nodes_10ru|split2|node|3|node_1|3|node|3|node_1|3|node}} = {{CDD|node_h1|4|node|3|node|3|node_1|3|node|3|node_1|3|node}}||[[Stericantellated 7-demicube]]<BR>Cellirhombated demihepteract (Crohesa)||(1,1,1,3,3,5,5)|| || || || || ||87360||13440
| |
| |- align=center
| |
| !12
| |
| ||{{CDD|nodes_10ru|split2|node|3|node|3|node_1|3|node_1|3|node}} = {{CDD|node_h1|4|node|3|node|3|node|3|node_1|3|node_1|3|node}}||[[Steriruncinated 7-demicube]]<BR>Celliprismated demihepteract (Caphesa)||(1,1,1,1,3,5,5)|| || || || || ||40320||6720
| |
| |- align=center
| |
| !13
| |
| ||{{CDD|nodes_10ru|split2|node_1|3|node|3|node|3|node|3|node_1}} = {{CDD|node_h1|4|node|3|node_1|3|node|3|node|3|node|3|node_1}}||[[Pentitruncated 7-demicube]]<BR>Teritruncated demihepteract (Tuthesa)||(1,1,3,3,3,3,5)|| || || || || ||43680||6720
| |
| |- align=center
| |
| !14
| |
| ||{{CDD|nodes_10ru|split2|node|3|node_1|3|node|3|node|3|node_1}} = {{CDD|node_h1|4|node|3|node|3|node_1|3|node|3|node|3|node_1}}||[[Penticantellated 7-demicube]]<BR>Terirhombated demihepteract (Turhesa)||(1,1,1,3,3,3,5)|| || || || || ||67200||8960
| |
| |- align=center
| |
| !15
| |
| ||{{CDD|nodes_10ru|split2|node|3|node|3|node_1|3|node|3|node_1}} = {{CDD|node_h1|4|node|3|node|3|node|3|node_1|3|node|3|node_1}}||[[Pentiruncinated 7-demicube]]<BR>Teriprismated demihepteract (Tuphesa)||(1,1,1,1,3,3,5)|| || || || || ||53760||6720
| |
| |- align=center
| |
| !16
| |
| ||{{CDD|nodes_10ru|split2|node|3|node|3|node|3|node_1|3|node_1}} = {{CDD|node_h1|4|node|3|node|3|node|3|node|3|node_1|3|node_1}}||[[Pentistericated 7-demicube]]<BR>Tericellated demihepteract (Tuchesa)||(1,1,1,1,1,3,5)|| || || || || ||21504||2688
| |
| |- align=center
| |
| !17
| |
| ||{{CDD|nodes_10ru|split2|node_1|3|node_1|3|node_1|3|node|3|node}} = {{CDD|node_h1|4|node|3|node_1|3|node_1|3|node_1|3|node|3|node}}||[[Runcicantitruncated 7-demicube]]<BR>Great prismated demihepteract (Gephosa)||(1,1,3,5,7,7,7)|| || || || || ||94080||26880
| |
| |- align=center
| |
| !18
| |
| ||{{CDD|nodes_10ru|split2|node_1|3|node_1|3|node|3|node_1|3|node}} = {{CDD|node_h1|4|node|3|node_1|3|node_1|3|node|3|node_1|3|node}}||[[Stericantitruncated 7-demicube]]<BR>Celligreatorhombated demihepteract (Cagrohesa)||(1,1,3,5,5,7,7)|| || || || || ||181440||40320
| |
| |- align=center
| |
| !19
| |
| ||{{CDD|nodes_10ru|split2|node_1|3|node|3|node_1|3|node_1|3|node}} = {{CDD|node_h1|4|node|3|node_1|3|node|3|node_1|3|node_1|3|node}}||[[Steriruncitruncated 7-demicube]]<BR>Celliprismatotruncated demihepteract (Capthesa)||(1,1,3,3,5,7,7)|| || || || || ||181440||40320
| |
| |- align=center
| |
| !20
| |
| ||{{CDD|nodes_10ru|split2|node|3|node_1|3|node_1|3|node_1|3|node}} = {{CDD|node_h1|4|node|3|node|3|node_1|3|node_1|3|node_1|3|node}}||[[Steriruncicantellated 7-demicube]]<BR>Celliprismatorhombated demihepteract (Coprahesa)||(1,1,1,3,5,7,7)|| || || || || ||120960||26880
| |
| |- align=center
| |
| !21
| |
| ||{{CDD|nodes_10ru|split2|node_1|3|node_1|3|node|3|node|3|node_1}} = {{CDD|node_h1|4|node|3|node_1|3|node_1|3|node|3|node|3|node_1}}||[[Penticantitruncated 7-demicube]]<BR>Terigreatorhombated demihepteract (Tugrohesa)||(1,1,3,5,5,5,7)|| || || || || ||120960||26880
| |
| |- align=center
| |
| !22
| |
| ||{{CDD|nodes_10ru|split2|node_1|3|node|3|node_1|3|node|3|node_1}} = {{CDD|node_h1|4|node|3|node_1|3|node|3|node_1|3|node|3|node_1}}||[[Pentiruncitruncated 7-demicube]]<BR>Teriprismatotruncated demihepteract (Tupthesa)||(1,1,3,3,5,5,7)|| || || || || ||221760||40320
| |
| |- align=center
| |
| !23
| |
| ||{{CDD|nodes_10ru|split2|node|3|node_1|3|node_1|3|node|3|node_1}} = {{CDD|node_h1|4|node|3|node|3|node_1|3|node_1|3|node|3|node_1}}||[[Pentiruncicantellated 7-demicube]]<BR>Teriprismatorhombated demihepteract (Tuprohesa)||(1,1,1,3,5,5,7)|| || || || || ||134400||26880
| |
| |- align=center
| |
| !24
| |
| ||{{CDD|nodes_10ru|split2|node_1|3|node|3|node|3|node_1|3|node_1}} = {{CDD|node_h1|4|node|3|node_1|3|node|3|node|3|node_1|3|node_1}}||[[Pentisteritruncated 7-demicube]]<BR>Tericellitruncated demihepteract (Tucothesa)||(1,1,3,3,3,5,7)|| || || || || ||147840||26880
| |
| |- align=center
| |
| !25
| |
| ||{{CDD|nodes_10ru|split2|node|3|node_1|3|node|3|node_1|3|node_1}} = {{CDD|node_h1|4|node|3|node|3|node_1|3|node|3|node_1|3|node_1}}||[[Pentistericantellated 7-demicube]]<BR>Tericellirhombated demihepteract (Tucrohesa)||(1,1,1,3,3,5,7)|| || || || || ||161280||26880
| |
| |- align=center
| |
| !26
| |
| ||{{CDD|nodes_10ru|split2|node|3|node|3|node_1|3|node_1|3|node_1}} = {{CDD|node_h1|4|node|3|node|3|node|3|node_1|3|node_1|3|node_1}}||[[Pentisteriruncinated 7-demicube]]<BR>Tericelliprismated demihepteract (Tucophesa)||(1,1,1,1,3,5,7)|| || || || || ||80640||13440
| |
| |- align=center
| |
| !27
| |
| ||{{CDD|nodes_10ru|split2|node_1|3|node_1|3|node_1|3|node_1|3|node}} = {{CDD|node_h1|4|node|3|node_1|3|node_1|3|node_1|3|node_1|3|node}}||[[Steriruncicantitruncated 7-demicube]]<BR>Great cellated demihepteract (Gochesa)||(1,1,3,5,7,9,9)|| || || || || ||282240||80640
| |
| |- align=center
| |
| !28
| |
| ||{{CDD|nodes_10ru|split2|node_1|3|node_1|3|node_1|3|node|3|node_1}} = {{CDD|node_h1|4|node|3|node_1|3|node_1|3|node_1|3|node|3|node_1}}||[[Pentiruncicantitruncated 7-demicube]]<BR>Terigreatoprimated demihepteract (Tugphesa)||(1,1,3,5,7,7,9)|| || || || || ||322560||80640
| |
| |- align=center
| |
| !29
| |
| ||{{CDD|nodes_10ru|split2|node_1|3|node_1|3|node|3|node_1|3|node_1}} = {{CDD|node_h1|4|node|3|node_1|3|node_1|3|node|3|node_1|3|node_1}}||[[Pentistericantitruncated 7-demicube]]<BR>Tericelligreatorhombated demihepteract (Tucagrohesa)||(1,1,3,5,5,7,9)|| || || || || ||322560||80640
| |
| |- align=center
| |
| !30
| |
| ||{{CDD|nodes_10ru|split2|node_1|3|node|3|node_1|3|node_1|3|node_1}} = {{CDD|node_h1|4|node|3|node_1|3|node|3|node_1|3|node_1|3|node_1}}||[[Pentisteriruncitruncated 7-demicube]]<BR>Tericelliprismatotruncated demihepteract (Tucpathesa)||(1,1,3,3,5,7,9)|| || || || || ||362880||80640
| |
| |- align=center
| |
| !31
| |
| ||{{CDD|nodes_10ru|split2|node|3|node_1|3|node_1|3|node_1|3|node_1}} = {{CDD|node_h1|4|node|3|node|3|node_1|3|node_1|3|node_1|3|node_1}}||[[Pentisteriruncicantellated 7-demicube]]<BR>Tericellprismatorhombated demihepteract (Tucprohesa)||(1,1,1,3,5,7,9)|| || || || || ||241920||53760
| |
| |- align=center
| |
| !32
| |
| ||{{CDD|nodes_10ru|split2|node_1|3|node_1|3|node_1|3|node_1|3|node_1}} = {{CDD|node_h1|4|node|3|node_1|3|node_1|3|node_1|3|node_1|3|node_1}}||[[Pentisteriruncicantitruncated 7-demicube]]<BR>Great terated demihepteract (Guthesa)||(1,1,3,5,7,9,11)|| || || || || ||564480||161280
| |
| |}
| |
| | |
| == The E<sub>7</sub> family ==
| |
| | |
| The E<sub>7</sub> [[Coxeter group]] has order 2,903,040.
| |
| | |
| There are 127 forms based on all permutations of the [[Coxeter-Dynkin diagram]]s with one or more rings.
| |
| | |
| See also a [[list of E7 polytopes]] for symmetric Coxeter plane graphs of these polytopes.
| |
| | |
| {| class="wikitable"
| |
| |-
| |
| !rowspan=2|#
| |
| !rowspan=2|[[Coxeter-Dynkin diagram]]<br />[[Schläfli symbol]]
| |
| !rowspan=2|Names
| |
| !colspan=7|Element counts
| |
| |-
| |
| ! 6|| 5|| 4|| 3|| 2|| 1|| 0
| |
| | |
| |- style="text-align:center;"
| |
| |1||{{CDD|nodea|3a|nodea|3a|nodea|3a|branch|3a|nodea|3a|nodea_1}}||[[Gosset 2 31 polytope|2<sub>31</sub>]] (laq)||632||4788||16128||20160||10080||2016||126
| |
| |- style="text-align:center;"
| |
| |2||{{CDD|nodea|3a|nodea|3a|nodea|3a|branch|3a|nodea_1|3a|nodea}}||[[Rectified 2 31 polytope|Rectified 2<sub>31</sub>]] (rolaq)||758||10332||47880||100800||90720||30240||2016
| |
| |- style="text-align:center;"
| |
| |3||{{CDD|nodea|3a|nodea|3a|nodea|3a|branch_10|3a|nodea|3a|nodea}}||[[Rectified 1 32 polytope|Rectified 1<sub>32</sub>]] (rolin)||758||12348||72072||191520||241920||120960||10080
| |
| |- style="text-align:center;"
| |
| |4||{{CDD|nodea|3a|nodea|3a|nodea|3a|branch_01lr|3a|nodea|3a|nodea}}||[[1 32 polytope|1<sub>32</sub>]] (lin)||182||4284||23688||50400||40320||10080||576
| |
| |- style="text-align:center;"
| |
| |5||{{CDD|nodea|3a|nodea|3a|nodea_1|3a|branch|3a|nodea|3a|nodea}}||[[Birectified 3 21 polytope|Birectified 3<sub>21</sub>]] (branq)||758||12348||68040||161280||161280||60480||4032
| |
| |- style="text-align:center;"
| |
| |6||{{CDD|nodea|3a|nodea_1|3a|nodea|3a|branch|3a|nodea|3a|nodea}}||[[Rectified 3 21 polytope|Rectified 3<sub>21</sub>]] (ranq)||758||44352||70560||48384||11592||12096||756
| |
| |- style="text-align:center;"
| |
| |7||{{CDD|nodea_1|3a|nodea|3a|nodea|3a|branch|3a|nodea|3a|nodea}}||[[Gosset 3 21 polytope|3<sub>21</sub>]] (naq)||702||6048||12096||10080||4032||756||56
| |
| |- align=center
| |
| |8||{{CDD|nodea|3a|nodea|3a|nodea|3a|branch|3a|nodea_1|3a|nodea_1}}||[[Truncated 2 31 polytope|Truncated 2<sub>31</sub>]] (talq)||758||10332||47880||100800||90720||32256||4032
| |
| |- align=center
| |
| |9||{{CDD|nodea|3a|nodea|3a|nodea|3a|branch_10|3a|nodea|3a|nodea_1}}||[[Cantellated 2 31 polytope|Cantellated 2<sub>31</sub>]] (sirlaq)|| || || || || ||131040||20160
| |
| |- align=center
| |
| |10||{{CDD|nodea|3a|nodea|3a|nodea|3a|branch_10|3a|nodea_1|3a|nodea}}||Bitruncated 2<sub>31</sub> (botlaq)||||||||||||||30240
| |
| |- align=center
| |
| |11||{{CDD|nodea|3a|nodea|3a|nodea|3a|branch_01lr|3a|nodea|3a|nodea_1}}||small demified 2<sub>31</sub> (shilq)||2774||22428||78120||151200||131040||42336||4032
| |
| |- align=center
| |
| |12||{{CDD|nodea|3a|nodea|3a|nodea|3a|branch_01lr|3a|nodea_1|3a|nodea}}||demirectified 2<sub>31</sub> (hirlaq)||||||||||||||12096
| |
| |- align=center
| |
| |13||{{CDD|nodea|3a|nodea|3a|nodea|3a|branch_11|3a|nodea|3a|nodea}}||truncated 1<sub>32</sub> (tolin)||||||||||||||20160
| |
| |- align=center
| |
| |14||{{CDD|nodea|3a|nodea|3a|nodea_1|3a|branch|3a|nodea|3a|nodea_1}}||small demiprismated 2<sub>31</sub> (shiplaq)||||||||||||||20160
| |
| |- align=center
| |
| |15||{{CDD|nodea|3a|nodea|3a|nodea_1|3a|branch|3a|nodea_1|3a|nodea}}||birectified 1<sub>32</sub> (berlin)||758||22428||142632||403200||544320||302400||40320
| |
| |- align=center
| |
| |16||{{CDD|nodea|3a|nodea|3a|nodea_1|3a|branch_10|3a|nodea|3a|nodea}}||tritruncated 3<sub>21</sub> (totanq)||||||||||||||40320
| |
| |- align=center
| |
| |17||{{CDD|nodea|3a|nodea|3a|nodea_1|3a|branch_01lr|3a|nodea|3a|nodea}}||demibirectified 3<sub>21</sub> (hobranq)||||||||||||||20160
| |
| |- align=center
| |
| |18||{{CDD|nodea|3a|nodea_1|3a|nodea|3a|branch|3a|nodea|3a|nodea_1}}||small cellated 2<sub>31</sub> (scalq)||||||||||||||7560
| |
| |- align=center
| |
| |19||{{CDD|nodea|3a|nodea_1|3a|nodea|3a|branch|3a|nodea_1|3a|nodea}}||small biprismated 2<sub>31</sub> (sobpalq)||||||||||||||30240
| |
| |- align=center
| |
| |20||{{CDD|nodea|3a|nodea_1|3a|nodea|3a|branch_10|3a|nodea|3a|nodea}}||small birhombated 3<sub>21</sub> (sabranq)||||||||||||||60480
| |
| |- align=center
| |
| |21||{{CDD|nodea|3a|nodea_1|3a|nodea|3a|branch_01lr|3a|nodea|3a|nodea}}||demirectified 3<sub>21</sub> (harnaq)||||||||||||||12096
| |
| |- align=center
| |
| |22||{{CDD|nodea|3a|nodea_1|3a|nodea_1|3a|branch|3a|nodea|3a|nodea}}||bitruncated 3<sub>21</sub> (botnaq)||||||||||||||12096
| |
| |- align=center
| |
| |23||{{CDD|nodea_1|3a|nodea|3a|nodea|3a|branch|3a|nodea|3a|nodea_1}}||small terated 3<sub>21</sub> (stanq)||||||||||||||1512
| |
| |- align=center
| |
| |24||{{CDD|nodea_1|3a|nodea|3a|nodea|3a|branch|3a|nodea_1|3a|nodea}}||small demicellated 3<sub>21</sub> (shocanq)||||||||||||||12096
| |
| |- align=center
| |
| |25||{{CDD|nodea_1|3a|nodea|3a|nodea|3a|branch_10|3a|nodea|3a|nodea}}||small prismated 3<sub>21</sub> (spanq)||||||||||||||40320
| |
| |- align=center
| |
| |26||{{CDD|nodea_1|3a|nodea|3a|nodea|3a|branch_01lr|3a|nodea|3a|nodea}}||small demified 3<sub>21</sub> (shanq)||||||||||||||4032
| |
| |- align=center
| |
| |27||{{CDD|nodea_1|3a|nodea|3a|nodea_1|3a|branch|3a|nodea|3a|nodea}}||small rhombated 3<sub>21</sub> (sranq)||||||||||||||12096
| |
| |- align=center
| |
| |28||{{CDD|nodea_1|3a|nodea_1|3a|nodea|3a|branch|3a|nodea|3a|nodea}}||[[Truncated 3 21 polytope|Truncated 3<sub>21</sub>]] (tanq)||758||11592||48384||70560||44352||12852||1512
| |
| |- align=center
| |
| |29||{{CDD|nodea|3a|nodea|3a|nodea|3a|branch_10|3a|nodea_1|3a|nodea_1}}||great rhombated 2<sub>31</sub> (girlaq)||||||||||||||60480
| |
| |- align=center
| |
| |30||{{CDD|nodea|3a|nodea|3a|nodea|3a|branch_01lr|3a|nodea_1|3a|nodea_1}}||demitruncated 2<sub>31</sub> (hotlaq)||||||||||||||24192
| |
| |- align=center
| |
| |31||{{CDD|nodea|3a|nodea|3a|nodea|3a|branch_11|3a|nodea|3a|nodea_1}}||small demirhombated 2<sub>31</sub> (sherlaq)||||||||||||||60480
| |
| |- align=center
| |
| |32||{{CDD|nodea|3a|nodea|3a|nodea|3a|branch_11|3a|nodea_1|3a|nodea}}||demibitruncated 2<sub>31</sub> (hobtalq)||||||||||||||60480
| |
| |- align=center
| |
| |33||{{CDD|nodea|3a|nodea|3a|nodea_1|3a|branch|3a|nodea_1|3a|nodea_1}}||demiprismated 2<sub>31</sub> (hiptalq)||||||||||||||80640
| |
| |- align=center
| |
| |34||{{CDD|nodea|3a|nodea|3a|nodea_1|3a|branch_10|3a|nodea|3a|nodea_1}}||demiprismatorhombated 2<sub>31</sub> (hiprolaq)||||||||||||||120960
| |
| |- align=center
| |
| |35||{{CDD|nodea|3a|nodea|3a|nodea_1|3a|branch_10|3a|nodea_1|3a|nodea}}||bitruncated 1<sub>32</sub> (batlin)||||||||||||||120960
| |
| |- align=center
| |
| |36||{{CDD|nodea|3a|nodea|3a|nodea_1|3a|branch_01lr|3a|nodea|3a|nodea_1}}||small prismated 2<sub>31</sub> (spalq)||||||||||||||80640
| |
| |- align=center
| |
| |37||{{CDD|nodea|3a|nodea|3a|nodea_1|3a|branch_01lr|3a|nodea_1|3a|nodea}}||small rhombated 1<sub>32</sub> (sirlin)||||||||||||||120960
| |
| |- align=center
| |
| |38||{{CDD|nodea|3a|nodea|3a|nodea_1|3a|branch_11|3a|nodea|3a|nodea}}||tritruncated 2<sub>31</sub> (tatilq)||||||||||||||80640
| |
| |- align=center
| |
| |39||{{CDD|nodea|3a|nodea_1|3a|nodea|3a|branch|3a|nodea_1|3a|nodea_1}}||cellitruncated 2<sub>31</sub> (catalaq)||||||||||||||60480
| |
| |- align=center
| |
| |40||{{CDD|nodea|3a|nodea_1|3a|nodea|3a|branch_10|3a|nodea|3a|nodea_1}}||cellirhombated 2<sub>31</sub> (crilq)||||||||||||||362880
| |
| |- align=center
| |
| |41||{{CDD|nodea|3a|nodea_1|3a|nodea|3a|branch_10|3a|nodea_1|3a|nodea}}||biprismatotruncated 2<sub>31</sub> (biptalq)||||||||||||||181440
| |
| |- align=center
| |
| |42||{{CDD|nodea|3a|nodea_1|3a|nodea|3a|branch_01lr|3a|nodea|3a|nodea_1}}||small prismated 1<sub>32</sub> (seplin)||||||||||||||60480
| |
| |- align=center
| |
| |43||{{CDD|nodea|3a|nodea_1|3a|nodea|3a|branch_01lr|3a|nodea_1|3a|nodea}}||small biprismated 3<sub>21</sub> (sabipnaq)||||||||||||||120960
| |
| |- align=center
| |
| |44||{{CDD|nodea|3a|nodea_1|3a|nodea|3a|branch_11|3a|nodea|3a|nodea}}||small demibirhombated 3<sub>21</sub> (shobranq)||||||||||||||120960
| |
| |- align=center
| |
| |45||{{CDD|nodea|3a|nodea_1|3a|nodea_1|3a|branch|3a|nodea|3a|nodea_1}}||cellidemiprismated 2<sub>31</sub> (chaplaq)||||||||||||||60480
| |
| |- align=center
| |
| |46||{{CDD|nodea|3a|nodea_1|3a|nodea_1|3a|branch|3a|nodea_1|3a|nodea}}||demibiprismatotruncated 3<sub>21</sub> (hobpotanq)||||||||||||||120960
| |
| |- align=center
| |
| |47||{{CDD|nodea|3a|nodea_1|3a|nodea_1|3a|branch_10|3a|nodea|3a|nodea}}||great birhombated 3<sub>21</sub> (gobranq)||||||||||||||120960
| |
| |- align=center
| |
| |48||{{CDD|nodea|3a|nodea_1|3a|nodea_1|3a|branch_01lr|3a|nodea|3a|nodea}}||demibitruncated 3<sub>21</sub> (hobtanq)||||||||||||||60480
| |
| |- align=center
| |
| |49||{{CDD|nodea_1|3a|nodea|3a|nodea|3a|branch|3a|nodea_1|3a|nodea_1}}||teritruncated 2<sub>31</sub> (totalq)||||||||||||||24192
| |
| |- align=center
| |
| |50||{{CDD|nodea_1|3a|nodea|3a|nodea|3a|branch_10|3a|nodea|3a|nodea_1}}||terirhombated 2<sub>31</sub> (trilq)||||||||||||||120960
| |
| |- align=center
| |
| |51||{{CDD|nodea_1|3a|nodea|3a|nodea|3a|branch_10|3a|nodea_1|3a|nodea}}||demicelliprismated 3<sub>21</sub> (hicpanq)||||||||||||||120960
| |
| |- align=center
| |
| |52||{{CDD|nodea_1|3a|nodea|3a|nodea|3a|branch_01lr|3a|nodea|3a|nodea_1}}||small teridemified 2<sub>31</sub> (sethalq)||||||||||||||24192
| |
| |- align=center
| |
| |53||{{CDD|nodea_1|3a|nodea|3a|nodea|3a|branch_01lr|3a|nodea_1|3a|nodea}}||small cellated 3<sub>21</sub> (scanq)||||||||||||||60480
| |
| |- align=center
| |
| |54||{{CDD|nodea_1|3a|nodea|3a|nodea|3a|branch_11|3a|nodea|3a|nodea}}||demiprismated 3<sub>21</sub> (hipnaq)||||||||||||||80640
| |
| |- align=center
| |
| |55||{{CDD|nodea_1|3a|nodea|3a|nodea_1|3a|branch|3a|nodea|3a|nodea_1}}||terirhombated 3<sub>21</sub> (tranq)||||||||||||||60480
| |
| |- align=center
| |
| |56||{{CDD|nodea_1|3a|nodea|3a|nodea_1|3a|branch|3a|nodea_1|3a|nodea}}||demicellirhombated 3<sub>21</sub> (hocranq)||||||||||||||120960
| |
| |- align=center
| |
| |57||{{CDD|nodea_1|3a|nodea|3a|nodea_1|3a|branch_10|3a|nodea|3a|nodea}}||prismatorhombated 3<sub>21</sub> (pranq)||||||||||||||120960
| |
| |- align=center
| |
| |58||{{CDD|nodea_1|3a|nodea|3a|nodea_1|3a|branch_01lr|3a|nodea|3a|nodea}}||small demirhombated 3<sub>21</sub> (sharnaq)||||||||||||||60480
| |
| |- align=center
| |
| |59||{{CDD|nodea_1|3a|nodea_1|3a|nodea|3a|branch|3a|nodea|3a|nodea_1}}||teritruncated 3<sub>21</sub> (tetanq)||||||||||||||15120
| |
| |- align=center
| |
| |60||{{CDD|nodea_1|3a|nodea_1|3a|nodea|3a|branch|3a|nodea_1|3a|nodea}}||demicellitruncated 3<sub>21</sub> (hictanq)||||||||||||||60480
| |
| |- align=center
| |
| |61||{{CDD|nodea_1|3a|nodea_1|3a|nodea|3a|branch_10|3a|nodea|3a|nodea}}||prismatotruncated 3<sub>21</sub> (potanq)||||||||||||||120960
| |
| |- align=center
| |
| |62||{{CDD|nodea_1|3a|nodea_1|3a|nodea|3a|branch_01lr|3a|nodea|3a|nodea}}||demitruncated 3<sub>21</sub> (hotnaq)||||||||||||||24192
| |
| |- align=center
| |
| |63||{{CDD|nodea_1|3a|nodea_1|3a|nodea_1|3a|branch|3a|nodea|3a|nodea}}||great rhombated 3<sub>21</sub> (granq)||||||||||||||24192
| |
| |- align=center
| |
| |64||{{CDD|nodea|3a|nodea|3a|nodea|3a|branch_11|3a|nodea_1|3a|nodea_1}}||great demified 2<sub>31</sub> (gahlaq)||||||||||||||120960
| |
| |- align=center
| |
| |65||{{CDD|nodea|3a|nodea|3a|nodea_1|3a|branch_10|3a|nodea_1|3a|nodea_1}}||great demiprismated 2<sub>31</sub> (gahplaq)||||||||||||||241920
| |
| |- align=center
| |
| |66||{{CDD|nodea|3a|nodea|3a|nodea_1|3a|branch_01lr|3a|nodea_1|3a|nodea_1}}||prismatotruncated 2<sub>31</sub> (potlaq)||||||||||||||241920
| |
| |- align=center
| |
| |67||{{CDD|nodea|3a|nodea|3a|nodea_1|3a|branch_11|3a|nodea|3a|nodea_1}}||prismatorhombated 2<sub>31</sub> (prolaq)||||||||||||||241920
| |
| |- align=center
| |
| |68||{{CDD|nodea|3a|nodea|3a|nodea_1|3a|branch_11|3a|nodea_1|3a|nodea}}||great rhombated 1<sub>32</sub> (girlin)||||||||||||||241920
| |
| |- align=center
| |
| |69||{{CDD|nodea|3a|nodea_1|3a|nodea|3a|branch_10|3a|nodea_1|3a|nodea_1}}||celligreatorhombated 2<sub>31</sub> (cagrilq)||||||||||||||362880
| |
| |- align=center
| |
| |70||{{CDD|nodea|3a|nodea_1|3a|nodea|3a|branch_01lr|3a|nodea_1|3a|nodea_1}}||cellidemitruncated 2<sub>31</sub> (chotalq)||||||||||||||241920
| |
| |- align=center
| |
| |71||{{CDD|nodea|3a|nodea_1|3a|nodea|3a|branch_11|3a|nodea|3a|nodea_1}}||prismatotruncated 1<sub>32</sub> (patlin)||||||||||||||362880
| |
| |- align=center
| |
| |72||{{CDD|nodea|3a|nodea_1|3a|nodea|3a|branch_11|3a|nodea_1|3a|nodea}}||biprismatorhombated 3<sub>21</sub> (bipirnaq)||||||||||||||362880
| |
| |- align=center
| |
| |73||{{CDD|nodea|3a|nodea_1|3a|nodea_1|3a|branch|3a|nodea_1|3a|nodea_1}}||tritruncated 1<sub>32</sub> (tatlin)||||||||||||||241920
| |
| |- align=center
| |
| |74||{{CDD|nodea|3a|nodea_1|3a|nodea_1|3a|branch_10|3a|nodea|3a|nodea_1}}||cellidemiprismatorhombated 2<sub>31</sub> (chopralq)||||||||||||||362880
| |
| |- align=center
| |
| |75||{{CDD|nodea|3a|nodea_1|3a|nodea_1|3a|branch_10|3a|nodea_1|3a|nodea}}||great demibiprismated 3<sub>21</sub> (ghobipnaq)||||||||||||||362880
| |
| |- align=center
| |
| |76||{{CDD|nodea|3a|nodea_1|3a|nodea_1|3a|branch_01lr|3a|nodea|3a|nodea_1}}||celliprismated 2<sub>31</sub> (caplaq)||||||||||||||241920
| |
| |- align=center
| |
| |77||{{CDD|nodea|3a|nodea_1|3a|nodea_1|3a|branch_01lr|3a|nodea_1|3a|nodea}}||biprismatotruncated 3<sub>21</sub> (boptanq)||||||||||||||362880
| |
| |- align=center
| |
| |78||{{CDD|nodea|3a|nodea_1|3a|nodea_1|3a|branch_11|3a|nodea|3a|nodea}}||great trirhombated 2<sub>31</sub> (gatralaq)||||||||||||||241920
| |
| |- align=center
| |
| |79||{{CDD|nodea_1|3a|nodea|3a|nodea|3a|branch_10|3a|nodea_1|3a|nodea_1}}||terigreatorhombated 2<sub>31</sub> (togrilq)||||||||||||||241920
| |
| |- align=center
| |
| |80||{{CDD|nodea_1|3a|nodea|3a|nodea|3a|branch_01lr|3a|nodea_1|3a|nodea_1}}||teridemitruncated 2<sub>31</sub> (thotalq)||||||||||||||120960
| |
| |- align=center
| |
| |81||{{CDD|nodea_1|3a|nodea|3a|nodea|3a|branch_11|3a|nodea|3a|nodea_1}}||teridemirhombated 2<sub>31</sub> (thorlaq)||||||||||||||241920
| |
| |- align=center
| |
| |82||{{CDD|nodea_1|3a|nodea|3a|nodea|3a|branch_11|3a|nodea_1|3a|nodea}}||celliprismated 3<sub>21</sub> (capnaq)||||||||||||||241920
| |
| |- align=center
| |
| |83||{{CDD|nodea_1|3a|nodea|3a|nodea_1|3a|branch|3a|nodea_1|3a|nodea_1}}||teridemiprismatotruncated 2<sub>31</sub> (thoptalq)||||||||||||||241920
| |
| |- align=center
| |
| |84||{{CDD|nodea_1|3a|nodea|3a|nodea_1|3a|branch_10|3a|nodea|3a|nodea_1}}||teriprismatorhombated 3<sub>21</sub> (tapronaq)||||||||||||||362880
| |
| |- align=center
| |
| |85||{{CDD|nodea_1|3a|nodea|3a|nodea_1|3a|branch_10|3a|nodea_1|3a|nodea}}||demicelliprismatorhombated 3<sub>21</sub> (hacpranq)||||||||||||||362880
| |
| |- align=center
| |
| |86||{{CDD|nodea_1|3a|nodea|3a|nodea_1|3a|branch_01lr|3a|nodea|3a|nodea_1}}||teriprismated 2<sub>31</sub> (toplaq)||||||||||||||241920
| |
| |- align=center
| |
| |87||{{CDD|nodea_1|3a|nodea|3a|nodea_1|3a|branch_01lr|3a|nodea_1|3a|nodea}}||cellirhombated 3<sub>21</sub> (cranq)||||||||||||||362880
| |
| |- align=center
| |
| |88||{{CDD|nodea_1|3a|nodea|3a|nodea_1|3a|branch_11|3a|nodea|3a|nodea}}||demiprismatorhombated 3<sub>21</sub> (hapranq)||||||||||||||241920
| |
| |- align=center
| |
| |89||{{CDD|nodea_1|3a|nodea_1|3a|nodea|3a|branch|3a|nodea_1|3a|nodea_1}}||tericellitruncated 2<sub>31</sub> (tectalq)||||||||||||||120960
| |
| |- align=center
| |
| |90||{{CDD|nodea_1|3a|nodea_1|3a|nodea|3a|branch_10|3a|nodea|3a|nodea_1}}||teriprismatotruncated 3<sub>21</sub> (toptanq)||||||||||||||362880
| |
| |- align=center
| |
| |91||{{CDD|nodea_1|3a|nodea_1|3a|nodea|3a|branch_10|3a|nodea_1|3a|nodea}}||demicelliprismatotruncated 3<sub>21</sub> (hecpotanq)||||||||||||||362880
| |
| |- align=center
| |
| |92||{{CDD|nodea_1|3a|nodea_1|3a|nodea|3a|branch_01lr|3a|nodea|3a|nodea_1}}||teridemitruncated 3<sub>21</sub> (thotanq)||||||||||||||120960
| |
| |- align=center
| |
| |93||{{CDD|nodea_1|3a|nodea_1|3a|nodea|3a|branch_01lr|3a|nodea_1|3a|nodea}}||cellitruncated 3<sub>21</sub> (catnaq)||||||||||||||241920
| |
| |- align=center
| |
| |94||{{CDD|nodea_1|3a|nodea_1|3a|nodea|3a|branch_11|3a|nodea|3a|nodea}}||demiprismatotruncated 3<sub>21</sub> (hiptanq)||||||||||||||241920
| |
| |- align=center
| |
| |95||{{CDD|nodea_1|3a|nodea_1|3a|nodea_1|3a|branch|3a|nodea|3a|nodea_1}}||terigreatorhombated 3<sub>21</sub> (tagranq)||||||||||||||120960
| |
| |- align=center
| |
| |96||{{CDD|nodea_1|3a|nodea_1|3a|nodea_1|3a|branch|3a|nodea_1|3a|nodea}}||demicelligreatorhombated 3<sub>21</sub> (hicgarnq)||||||||||||||241920
| |
| |- align=center
| |
| |97||{{CDD|nodea_1|3a|nodea_1|3a|nodea_1|3a|branch_10|3a|nodea|3a|nodea}}||great prismated 3<sub>21</sub> (gopanq)||||||||||||||241920
| |
| |- align=center
| |
| |98||{{CDD|nodea_1|3a|nodea_1|3a|nodea_1|3a|branch_01lr|3a|nodea|3a|nodea}}||great demirhombated 3<sub>21</sub> (gahranq)||||||||||||||120960
| |
| |- align=center
| |
| |99||{{CDD|nodea|3a|nodea|3a|nodea_1|3a|branch_11|3a|nodea_1|3a|nodea_1}}||great prismated 2<sub>31</sub> (gopalq)||||||||||||||483840
| |
| |- align=center
| |
| |100||{{CDD|nodea|3a|nodea_1|3a|nodea|3a|branch_11|3a|nodea_1|3a|nodea_1}}||great cellidemified 2<sub>31</sub> (gechalq)||||||||||||||725760
| |
| |- align=center
| |
| |101||{{CDD|nodea|3a|nodea_1|3a|nodea_1|3a|branch_10|3a|nodea_1|3a|nodea_1}}||great birhombated 1<sub>32</sub> (gebrolin)||||||||||||||725760
| |
| |- align=center
| |
| |102||{{CDD|nodea|3a|nodea_1|3a|nodea_1|3a|branch_01lr|3a|nodea_1|3a|nodea_1}}||prismatorhombated 1<sub>32</sub> (prolin)||||||||||||||725760
| |
| |- align=center
| |
| |103||{{CDD|nodea|3a|nodea_1|3a|nodea_1|3a|branch_11|3a|nodea|3a|nodea_1}}||celliprismatorhombated 2<sub>31</sub> (caprolaq)||||||||||||||725760
| |
| |- align=center
| |
| |104||{{CDD|nodea|3a|nodea_1|3a|nodea_1|3a|branch_11|3a|nodea_1|3a|nodea}}||great biprismated 2<sub>31</sub> (gobpalq)||||||||||||||725760
| |
| |- align=center
| |
| |105||{{CDD|nodea_1|3a|nodea|3a|nodea|3a|branch_11|3a|nodea_1|3a|nodea_1}}||tericelliprismated 3<sub>21</sub> (ticpanq)||||||||||||||483840
| |
| |- align=center
| |
| |106||{{CDD|nodea_1|3a|nodea|3a|nodea_1|3a|branch_10|3a|nodea_1|3a|nodea_1}}||teridemigreatoprismated 2<sub>31</sub> (thegpalq)||||||||||||||725760
| |
| |- align=center
| |
| |107||{{CDD|nodea_1|3a|nodea|3a|nodea_1|3a|branch_01lr|3a|nodea_1|3a|nodea_1}}||teriprismatotruncated 2<sub>31</sub> (teptalq)||||||||||||||725760
| |
| |- align=center
| |
| |108||{{CDD|nodea_1|3a|nodea|3a|nodea_1|3a|branch_11|3a|nodea|3a|nodea_1}}||teriprismatorhombated 2<sub>31</sub> (topralq)||||||||||||||725760
| |
| |- align=center
| |
| |109||{{CDD|nodea_1|3a|nodea|3a|nodea_1|3a|branch_11|3a|nodea_1|3a|nodea}}||cellipriemsatorhombated 3<sub>21</sub> (copranq)||||||||||||||725760
| |
| |- align=center
| |
| |110||{{CDD|nodea_1|3a|nodea_1|3a|nodea|3a|branch_10|3a|nodea_1|3a|nodea_1}}||tericelligreatorhombated 2<sub>31</sub> (tecgrolaq)||||||||||||||725760
| |
| |- align=center
| |
| |111||{{CDD|nodea_1|3a|nodea_1|3a|nodea|3a|branch_01lr|3a|nodea_1|3a|nodea_1}}||tericellitruncated 3<sub>21</sub> (tectanq)||||||||||||||483840
| |
| |- align=center
| |
| |112||{{CDD|nodea_1|3a|nodea_1|3a|nodea|3a|branch_11|3a|nodea|3a|nodea_1}}||teridemiprismatotruncated 3<sub>21</sub> (thoptanq)||||||||||||||725760
| |
| |- align=center
| |
| |113||{{CDD|nodea_1|3a|nodea_1|3a|nodea|3a|branch_11|3a|nodea_1|3a|nodea}}||celliprismatotruncated 3<sub>21</sub> (coptanq)||||||||||||||725760
| |
| |- align=center
| |
| |114||{{CDD|nodea_1|3a|nodea_1|3a|nodea_1|3a|branch|3a|nodea_1|3a|nodea_1}}||teridemicelligreatorhombated 3<sub>21</sub> (thocgranq)||||||||||||||483840
| |
| |- align=center
| |
| |115||{{CDD|nodea_1|3a|nodea_1|3a|nodea_1|3a|branch_10|3a|nodea|3a|nodea_1}}||terigreatoprismated 3<sub>21</sub> (tagpanq)||||||||||||||725760
| |
| |- align=center
| |
| |116||{{CDD|nodea_1|3a|nodea_1|3a|nodea_1|3a|branch_10|3a|nodea_1|3a|nodea}}||great demicellated 3<sub>21</sub> (gahcnaq)||||||||||||||725760
| |
| |- align=center
| |
| |117||{{CDD|nodea_1|3a|nodea_1|3a|nodea_1|3a|branch_01lr|3a|nodea|3a|nodea_1}}||tericelliprismated laq (tecpalq)||||||||||||||483840
| |
| |- align=center
| |
| |118||{{CDD|nodea_1|3a|nodea_1|3a|nodea_1|3a|branch_01lr|3a|nodea_1|3a|nodea}}||celligreatorhombated 3<sub>21</sub> (cogranq)||||||||||||||725760
| |
| |- align=center
| |
| |119||{{CDD|nodea_1|3a|nodea_1|3a|nodea_1|3a|branch_11|3a|nodea|3a|nodea}}||great demified 3<sub>21</sub> (gahnq)||||||||||||||483840
| |
| |- align=center
| |
| |120||{{CDD|nodea|3a|nodea_1|3a|nodea_1|3a|branch_11|3a|nodea_1|3a|nodea_1}}||great cellated 2<sub>31</sub> (gocalq)||||||||||||||1451520
| |
| |- align=center
| |
| |121||{{CDD|nodea_1|3a|nodea|3a|nodea_1|3a|branch_11|3a|nodea_1|3a|nodea_1}}||terigreatoprismated 2<sub>31</sub> (tegpalq)||||||||||||||1451520
| |
| |- align=center
| |
| |122||{{CDD|nodea_1|3a|nodea_1|3a|nodea|3a|branch_11|3a|nodea_1|3a|nodea_1}}||tericelliprismatotruncated 3<sub>21</sub> (tecpotniq)||||||||||||||1451520
| |
| |- align=center
| |
| |123||{{CDD|nodea_1|3a|nodea_1|3a|nodea_1|3a|branch_10|3a|nodea_1|3a|nodea_1}}||tericellidemigreatoprismated 2<sub>31</sub> (techogaplaq)||||||||||||||1451520
| |
| |- align=center
| |
| |124||{{CDD|nodea_1|3a|nodea_1|3a|nodea_1|3a|branch_01lr|3a|nodea_1|3a|nodea_1}}||tericelligreatorhombated 3<sub>21</sub> (tacgarnq)||||||||||||||1451520
| |
| |- align=center
| |
| |125||{{CDD|nodea_1|3a|nodea_1|3a|nodea_1|3a|branch_11|3a|nodea|3a|nodea_1}}||tericelliprismatorhombated 2<sub>31</sub> (tecprolaq)||||||||||||||1451520
| |
| |- align=center
| |
| |126||{{CDD|nodea_1|3a|nodea_1|3a|nodea_1|3a|branch_11|3a|nodea_1|3a|nodea}}||great cellated 3<sub>21</sub> (gocanq)||||||||||||||1451520
| |
| |- align=center
| |
| |127||{{CDD|nodea_1|3a|nodea_1|3a|nodea_1|3a|branch_11|3a|nodea_1|3a|nodea_1}}||great terated 3<sub>21</sub> (gotanq)||||||||||||||2903040
| |
| |}
| |
| | |
| == Regular and uniform honeycombs ==
| |
| [[File:Coxeter diagram affine rank7 correspondence.png|518px|thumb|Coxeter-Dynkin diagram correspondences between families and higher symmetry within diagrams. Nodes of the same color in each row represent identical mirrors. Black nodes are not active in the correspondence.]]
| |
| There are five fundamental affine [[Coxeter groups]] and sixteen prismatic groups that generate regular and uniform tessellations in 6-space:
| |
| {| class="wikitable"
| |
| |-
| |
| !#
| |
| !colspan=2|[[Coxeter group]]
| |
| ![[Coxeter diagram]]
| |
| !Forms
| |
| |- align=center
| |
| |1||<math>{\tilde{A}}_6</math>||[3<sup>[7]</sup>]||{{CDD|branch|3ab|nodes|3ab|nodes|split2|node}}||17
| |
| |- align=center
| |
| |2||<math>{\tilde{C}}_6</math>||[4,3<sup>4</sup>,4]||{{CDD|node|4|node|3|node|3|node|3|node|3|node|4|node}}||71
| |
| |- align=center
| |
| |3||<math>{\tilde{B}}_6</math>||h[4,3<sup>4</sup>,4]<br />[4,3<sup>3</sup>,3<sup>1,1</sup>]||{{CDD|nodes|split2|node|3|node|3|node|3|node|4|node}}||95 (32 new)
| |
| |- align=center
| |
| |4||<math>{\tilde{D}}_6</math>||q[4,3<sup>4</sup>,4]<br />[3<sup>1,1</sup>,3<sup>2</sup>,3<sup>1,1</sup>]||{{CDD|nodes|split2|node|3|node|3|node|split1|nodes}}|| 41 (6 new)
| |
| |- align=center
| |
| |5||<math>{\tilde{E}}_6</math>||[3<sup>2,2,2</sup>]||{{CDD|nodes|3ab|nodes|split2|node|3|node|3|node}}||39
| |
| |}
| |
| | |
| Regular and uniform tessellations include:
| |
| * <math>{\tilde{A}}_6</math>, 17 forms
| |
| ** Uniform [[6-simplex honeycomb]]: {3<sup>[7]</sup>} {{CDD|node_1|split1|nodes|3ab|nodes|3ab|nodes|3ab|branch}}
| |
| * <math>{\tilde{C}}_6</math>, [4,3<sup>4</sup>,4], 71 forms
| |
| ** Regular [[6-cube honeycomb]], represented by symbols {4,3<sup>4</sup>,4}, {{CDD|node_1|4|node|3|node|3|node|3|node|3|node|4|node}}
| |
| * <math>{\tilde{B}}_6</math>, [3<sup>1,1</sup>,3<sup>3</sup>,4], 95 forms, 64 shared with <math>{\tilde{C}}_6</math>, 32 new
| |
| ** Uniform [[6-demicube honeycomb]], represented by symbols h{4,3<sup>4</sup>,4} = {3<sup>1,1</sup>,3<sup>3</sup>,4}, {{CDD|node_h1|4|node|3|node|3|node|3|node|3|node|4|node}} = {{CDD|nodes_10ru|split2|node|3|node|3|node|3|node|4|node}}
| |
| * <math>{\tilde{D}}_6</math>, [3<sup>1,1</sup>,3<sup>2</sup>,3<sup>1,1</sup>], 41 unique ringed permuations, most shared with <math>{\tilde{B}}_6</math> and <math>{\tilde{C}}_6</math>, and 6 are new. Coxeter calls the first one a [[quarter 6-cubic honeycomb]].
| |
| ** {{CDD|nodes_10ru|split2|node|3|node|3|node|split1|nodes_10lu}}, {{CDD|nodes_10ru|split2|node_1|3|node|3|node|split1|nodes_10lu}}, {{CDD|nodes_10ru|split2|node|3|node_1|3|node|split1|nodes_10lu}}, {{CDD|nodes_10ru|split2|node_1|3|node_1|3|node|split1|nodes_10lu}}, {{CDD|nodes_10ru|split2|node_1|3|node|3|node_1|split1|nodes_10lu}}, {{CDD|nodes_10ru|split2|node_1|3|node_1|3|node_1|split1|nodes_10lu}}
| |
| * <math>{\tilde{E}}_6</math>: [3<sup>2,2,2</sup>], 39 forms
| |
| ** Uniform [[Gosset 2 22 honeycomb|2<sub>22</sub> honeycomb]]: represented by symbols {3<sup>2,2,2</sup>}, {{CDD|nodes|3ab|nodes|split2|node|3|node|3|node_1}}
| |
| | |
| {| class=wikitable
| |
| |+ Prismatic groups
| |
| |-
| |
| !#
| |
| !colspan=2|[[Coxeter group]]
| |
| ![[Coxeter-Dynkin diagram]]
| |
| |-
| |
| |1||<math>{\tilde{A}}_5</math>x<math>{\tilde{I}}_1</math>||[3<sup>[6]</sup>,2,∞]||{{CDD|node|split1|nodes|3ab|nodes|split2|node|2|node|infin|node}}
| |
| |-
| |
| |2||<math>{\tilde{B}}_5</math>x<math>{\tilde{I}}_1</math>||[4,3,3<sup>1,1</sup>,2,∞]||{{CDD|node|4|node|3|node|3|node|3|node|4|node|2|node|infin|node}}
| |
| |-
| |
| |3||<math>{\tilde{C}}_5</math>x<math>{\tilde{I}}_1</math>||[4,3<sup>3</sup>,4,2,∞]||{{CDD|nodes|split2|node|3|node|3|node|4|node|2|node|infin|node}}
| |
| |-
| |
| |4||<math>{\tilde{D}}_5</math>x<math>{\tilde{I}}_1</math>||[3<sup>1,1</sup>,3,3<sup>1,1</sup>,2,∞]||{{CDD|nodes|split2|node|3|node|split1|nodes|2|node|infin|node}}
| |
| |-
| |
| |5||<math>{\tilde{A}}_4</math>x<math>{\tilde{I}}_1</math>x<math>{\tilde{I}}_1</math>||[3<sup>[5]</sup>,2,∞,2,∞,2,∞]||{{CDD|branch|3ab|nodes|split2|node|2|node|infin|node|2|node|infin|node}}
| |
| |-
| |
| |6||<math>{\tilde{B}}_4</math>x<math>{\tilde{I}}_1</math>x<math>{\tilde{I}}_1</math>||[4,3,3<sup>1,1</sup>,2,∞,2,∞]||{{CDD|nodes|split2|node|3|node|4|node|2|node|infin|node|2|node|infin|node}}
| |
| |-
| |
| |7||<math>{\tilde{C}}_4</math>x<math>{\tilde{I}}_1</math>x<math>{\tilde{I}}_1</math>||[4,3,3,4,2,∞,2,∞]||{{CDD|node|4|node|3|node|3|node|4|node|2|node|infin|node|2|node|infin|node}}
| |
| |-
| |
| |8||<math>{\tilde{D}}_4</math>x<math>{\tilde{I}}_1</math>x<math>{\tilde{I}}_1</math>||[3<sup>1,1,1,1</sup>,2,∞,2,∞]||{{CDD|nodes|split2|node|split1|nodes|2|node|infin|node|2|node|infin|node}}
| |
| |-
| |
| |9||<math>{\tilde{F}}_4</math>x<math>{\tilde{I}}_1</math>x<math>{\tilde{I}}_1</math>||[3,4,3,3,2,∞,2,∞]||{{CDD|node|3|node|4|node|3|node|3|node|2|node|infin|node|2|node|infin|node}}
| |
| |-
| |
| |10||<math>{\tilde{C}}_3</math>x<math>{\tilde{I}}_1</math>x<math>{\tilde{I}}_1</math>x<math>{\tilde{I}}_1</math>||[4,3,4,2,∞,2,∞,2,∞]||{{CDD|node|4|node|3|node|4|node|2|node|infin|node|2|node|infin|node|2|node|infin|node}}
| |
| |-
| |
| |11||<math>{\tilde{B}}_3</math>x<math>{\tilde{I}}_1</math>x<math>{\tilde{I}}_1</math>x<math>{\tilde{I}}_1</math>||[4,3<sup>1,1</sup>,2,∞,2,∞,2,∞]||{{CDD|nodes|split2|node|4|node|2|node|infin|node|2|node|infin|node|2|node|infin|node}}
| |
| |-
| |
| |12||<math>{\tilde{A}}_3</math>x<math>{\tilde{I}}_1</math>x<math>{\tilde{I}}_1</math>x<math>{\tilde{I}}_1</math>||[3<sup>[4]</sup>,2,∞,2,∞,2,∞]||{{CDD|branch|3ab|branch|2|node|infin|node|2|node|infin|node|2|node|infin|node}}
| |
| |-
| |
| |13||<math>{\tilde{C}}_2</math>x<math>{\tilde{I}}_1</math>x<math>{\tilde{I}}_1</math>x<math>{\tilde{I}}_1</math>x<math>{\tilde{I}}_1</math>||[4,4,2,∞,2,∞,2,∞,2,∞]||{{CDD|node|4|node|4|node|2|node|infin|node|2|node|infin|node|2|node|infin|node|2|node|infin|node}}
| |
| |-
| |
| |14||<math>{\tilde{H}}_2</math>x<math>{\tilde{I}}_1</math>x<math>{\tilde{I}}_1</math>x<math>{\tilde{I}}_1</math>x<math>{\tilde{I}}_1</math>||[6,3,2,∞,2,∞,2,∞,2,∞]||{{CDD|node|6|node|3|node|2|node|infin|node|2|node|infin|node|2|node|infin|node|2|node|infin|node}}
| |
| |-
| |
| |15||<math>{\tilde{A}}_2</math>x<math>{\tilde{I}}_1</math>x<math>{\tilde{I}}_1</math>x<math>{\tilde{I}}_1</math>x<math>{\tilde{I}}_1</math>||[3<sup>[3]</sup>,2,∞,2,∞,2,∞,2,∞]||{{CDD|node|split1|branch|2|node|infin|node|2|node|infin|node|2|node|infin|node|2|node|infin|node}}
| |
| |-
| |
| |16||<math>{\tilde{I}}_1</math>x<math>{\tilde{I}}_1</math>x<math>{\tilde{I}}_1</math>x<math>{\tilde{I}}_1</math>x<math>{\tilde{I}}_1</math>x<math>{\tilde{I}}_1</math>||[∞,2,∞,2,∞,2,∞,2,∞]||{{CDD|node|infin|node|2|node|infin|node|2|node|infin|node|2|node|infin|node|2|node|infin|node|2|node|infin|node}}
| |
| |}
| |
| | |
| === Regular and uniform hyperbolic honeycombs ===
| |
| | |
| There are no compact hyperbolic Coxeter groups of rank 7, groups that can generate honeycombs with all finite facets, and a finite [[vertex figure]]. However there are [[Coxeter-Dynkin_diagram#Rank_4_to_10|3 noncompact hyperbolic Coxeter groups]] of rank 7, each generating uniform honeycombs in 6-space as permutations of rings of the Coxeter diagrams.
| |
| {| class=wikitable
| |
| |align=right|<math>{\bar{P}}_6</math> = [3,3<sup>[6]</sup>]:<BR>{{CDD|node|split1|nodes|3ab|nodes|split2|node|3|node}}
| |
| |align=right|<math>{\bar{Q}}_6</math> = [3<sup>1,1</sup>,3,3<sup>2,1</sup>]:<BR>{{CDD|nodea|3a|branch|3a|branch|3a|nodea|3a|nodea}}
| |
| | |
| |align=right|<math>{\bar{S}}_6</math> = [4,3,3,3<sup>2,1</sup>]:<BR>{{CDD|nodea|3a|nodea|3a|branch|3a|nodea|3a|nodea|4a|nodea}}
| |
| |}
| |
| | |
| == Notes on the Wythoff construction for the uniform 7-polytopes ==
| |
| | |
| The reflective 7-dimensional [[uniform polytope]]s are constructed through a [[Wythoff construction]] process, and represented by a [[Coxeter-Dynkin diagram]], where each node represents a mirror. An active mirror is represented by a ringed node. Each combination of active mirrors generates a unique uniform polytope. Uniform polytopes are named in relation to the [[regular polytope]]s in each family. Some families have two regular constructors and thus may be named in two equally valid ways.
| |
| | |
| Here are the primary operators available for constructing and naming the uniform 7-polytopes. | |
| | |
| The prismatic forms and bifurcating graphs can use the same truncation indexing notation, but require an explicit numbering system on the nodes for clarity.
| |
| | |
| {|class="wikitable"
| |
| |-
| |
| !Operation
| |
| !Extended<br/>[[Schläfli symbol]]
| |
| !width=110|[[Coxeter-Dynkin diagram|Coxeter-<br/>Dynkin<br/>diagram]]
| |
| !Description
| |
| |-
| |
| ! Parent
| |
| |width=70| t<sub>0</sub>{p,q,r,s,t,u}
| |
| |{{CDD|node_1|p|node|q|node|r|node|s|node|t|node|u|node}}
| |
| | Any regular 7-polytope
| |
| |-
| |
| ! [[Rectification (geometry)|Rectified]]
| |
| | t<sub>1</sub>{p,q,r,s,t,u}
| |
| |{{CDD|node|p|node_1|q|node|r|node|s|node|t|node|u|node}}
| |
| |The edges are fully truncated into single points. The 7-polytope now has the combined faces of the parent and dual.
| |
| |-
| |
| ! Birectified
| |
| | t<sub>2</sub>{p,q,r,s,t,u}
| |
| |{{CDD|node|p|node|q|node_1|r|node|s|node|t|node|u|node}}
| |
| |Birectification reduces [[Cell (geometry)|cells]] to their [[Dual polytope|duals]].
| |
| |-
| |
| ![[Truncation (geometry)|Truncated]]
| |
| | t<sub>0,1</sub>{p,q,r,s,t,u}
| |
| |{{CDD|node_1|p|node_1|q|node|r|node|s|node|t|node|u|node}}
| |
| |Each original vertex is cut off, with a new face filling the gap. Truncation has a degree of freedom, which has one solution that creates a uniform truncated 7-polytope. The 7-polytope has its original faces doubled in sides, and contains the faces of the dual.<br/>[[File:Cube truncation sequence.svg|400px]]
| |
| |-
| |
| ![[Bitruncated]]
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| | t<sub>1,2</sub>{p,q,r,s,t,u}
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| |{{CDD|node|p|node_1|q|node_1|r|node|s|node|t|node|u|node}}
| |
| |Bitrunction transforms cells to their dual truncation.
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| |-
| |
| !Tritruncated
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| | t<sub>2,3</sub>{p,q,r,s,t,u}
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| |{{CDD|node|p|node|q|node_1|r|node_1|s|node|t|node|u|node}}
| |
| |Tritruncation transforms 4-faces to their dual truncation.
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| |-
| |
| ! [[Cantellation (geometry)|Cantellated]]
| |
| | t<sub>0,2</sub>{p,q,r,s,t,u}
| |
| |{{CDD|node_1|p|node|q|node_1|r|node|s|node|t|node|u|node}}
| |
| |In addition to vertex truncation, each original edge is ''beveled'' with new rectangular faces appearing in their place. A uniform cantellation is half way between both the parent and dual forms.<br/>[[File:Cube cantellation sequence.svg|400px]]
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| |-
| |
| ! Bicantellated
| |
| | t<sub>1,3</sub>{p,q,r,s,t,u}
| |
| |{{CDD|node|p|node_1|q|node|r|node_1|s|node|t|node|u|node}}
| |
| |In addition to vertex truncation, each original edge is ''beveled'' with new rectangular faces appearing in their place. A uniform cantellation is half way between both the parent and dual forms.
| |
| |-
| |
| ! [[Runcination (geometry)|Runcinated]]
| |
| | t<sub>0,3</sub>{p,q,r,s,t,u}
| |
| |{{CDD|node_1|p|node|q|node|r|node_1|s|node|t|node|u|node}}
| |
| |Runcination reduces cells and creates new cells at the vertices and edges.
| |
| |-
| |
| ! Biruncinated
| |
| | t<sub>1,4</sub>{p,q,r,s,t,u}
| |
| |{{CDD|node|p|node_1|q|node|r|node|s|node_1|t|node|u|node}}
| |
| |Runcination reduces cells and creates new cells at the vertices and edges.
| |
| |-
| |
| ! [[Sterication|Stericated]]
| |
| | t<sub>0,4</sub>{p,q,r,s,t,u}
| |
| |{{CDD|node_1|p|node|q|node|r|node|s|node_1|t|node|u|node}}
| |
| |Sterication reduces 4-faces and creates new 4-faces at the vertices, edges, and faces in the gaps.
| |
| |-
| |
| ! Pentellated
| |
| | t<sub>0,5</sub>{p,q,r,s,t,u}
| |
| |{{CDD|node_1|p|node|q|node|r|node|s|node|t|node_1|u|node}}
| |
| |Pentellation reduces 5-faces and creates new 5-faces at the vertices, edges, faces, and cells in the gaps.
| |
| |-
| |
| ! Hexicated
| |
| | t<sub>0,6</sub>{p,q,r,s,t,u}
| |
| |{{CDD|node_1|p|node|q|node|r|node|s|node|t|node|u|node_1}}
| |
| |Hexication reduces 6-faces and creates new 6-faces at the vertices, edges, faces, cells, and 4-faces in the gaps. ([[Expansion (geometry)|expansion]] operation for 7-polytopes)
| |
| |-
| |
| ![[Omnitruncation (geometry)|Omnitruncated]]
| |
| | t<sub>0,1,2,3,4,5,6</sub>{p,q,r,s,t,u}
| |
| |{{CDD|node_1|p|node_1|q|node_1|r|node_1|s|node_1|t|node_1|u|node_1}}
| |
| |All six operators, truncation, cantellation, runcination, sterication, pentellation, and hexication are applied.
| |
| |}
| |
| | |
| == References ==
| |
| | |
| * [[Thorold Gosset|T. Gosset]]: ''On the Regular and Semi-Regular Figures in Space of n Dimensions'', [[Messenger of Mathematics]], Macmillan, 1900
| |
| * [[Alicia Boole Stott|A. Boole Stott]]: ''Geometrical deduction of semiregular from regular polytopes and space fillings'', Verhandelingen of the Koninklijke academy van Wetenschappen width unit Amsterdam, Eerste Sectie 11,1, Amsterdam, 1910
| |
| * [[Harold Scott MacDonald Coxeter|H.S.M. Coxeter]]:
| |
| ** H.S.M. Coxeter, M.S. Longuet-Higgins und J.C.P. Miller: ''Uniform Polyhedra'', Philosophical Transactions of the Royal Society of London, Londne, 1954
| |
| ** H.S.M. Coxeter, ''Regular Polytopes'', 3rd Edition, Dover New York, 1973
| |
| * '''Kaleidoscopes: Selected Writings of H.S.M. Coxeter''', editied 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]
| |
| * [[Norman Johnson (mathematician)|N.W. Johnson]]: ''The Theory of Uniform Polytopes and Honeycombs'', Ph.D. Dissertation, University of Toronto, 1966
| |
| * {{KlitzingPolytopes|polyexa.htm|7D|uniform polytopes (polyexa)}}
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| | |
| == External links ==
| |
| * [http://www.steelpillow.com/polyhedra/ditela.html Polytope names]
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| * [http://www.polytope.net/hedrondude/topes.htm Polytopes of Various Dimensions]
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| * [http://tetraspace.alkaline.org/glossary.htm Multi-dimensional Glossary]
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| * {{PolyCell | urlname = glossary.html| title = Glossary for hyperspace}}
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| {{Polytopes}}
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| [[Category:7-polytopes]]
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