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| | Hi there, I am Felicidad Oquendo. One of my favorite hobbies is tenting and now I'm attempting to earn cash with it. Alabama has usually been his home and his family enjoys it. Managing individuals is what I do in my day job.<br><br>Also visit my website :: [http://schnitzls-superdudes.de/index/users/view/id/18715 schnitzls-superdudes.de] |
| |+ Graphs of three [[List of regular polytopes#Eight Dimensions|regular]] and related [[uniform polytope]]s.
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| |- valign=top align=center
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| |colspan=4|[[File:8-simplex t0.svg|100px]]<br/>[[8-simplex]]
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| |colspan=4|[[File:8-simplex t1.svg|100px]]<br/>[[Rectified 8-simplex]]
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| |colspan=4|[[File:8-simplex t01.svg|100px]]<br/>[[Truncated 8-simplex]]
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| |- valign=top align=center
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| |colspan=4|[[File:8-simplex t02.svg|100px]]<br/>[[Cantellated 8-simplex]]
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| |colspan=4|[[File:8-simplex t03.svg|100px]]<br/>[[Runcinated 8-simplex]]
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| |colspan=4|[[File:8-simplex t04.svg|100px]]<br/>[[Stericated 8-simplex]]
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| |- valign=top align=center
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| |colspan=4|[[File:8-simplex t05.svg|100px]]<br/>[[Pentellated 8-simplex]]
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| |colspan=4|[[File:8-simplex t06.svg|100px]]<br/>[[Hexicated 8-simplex]]
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| |colspan=4|[[File:8-simplex t07.svg|100px]]<br/>[[Heptellated 8-simplex]]
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| |- valign=top align=center
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| |colspan=4|[[File:8-cube t7.svg|100px]]<br/>[[8-orthoplex]]
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| |colspan=4|[[File:8-cube t6.svg|100px]]<br/>[[Rectified 8-orthoplex]]
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| |colspan=4|[[File:8-cube t67.svg|100px]]<br/>[[Truncated 8-orthoplex]]
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| |- valign=top align=center
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| |colspan=6|[[File:8-cube t57.svg|150px]]<br/>[[Cantellated 8-orthoplex]]
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| |colspan=6|[[File:8-cube t47.svg|150px]]<br/>[[Runcinated 8-orthoplex]]
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| <!--|colspan=4|[[File:8-cube_t37.svg|100px]]<br/>[[Stericated 8-orthoplex]]-->
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| |- valign=top align=center
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| <!--|colspan=4|[[File:8-cube_t27.svg|100px]]<br/>[[Pentellated 8-orthoplex]]-->
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| |colspan=6|[[File:8-cube t17.svg|150px]]<br/>[[Hexicated 8-orthoplex]]
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| |colspan=6|[[File:8-cube t02.svg|150px]]<br/>[[Cantellated 8-cube]]
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| |- valign=top align=center
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| |colspan=4|[[File:8-cube t03.svg|100px]]<br/>[[Runcinated 8-cube]]
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| |colspan=4|[[File:8-cube t04.svg|100px]]<br/>[[Stericated 8-cube]]
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| |colspan=4|[[File:8-cube t05.svg|100px]]<br/>[[Pentellated 8-cube]]
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| |- valign=top align=center
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| |colspan=6|[[File:8-cube t06.svg|150px]]<br/>[[Hexicated 8-cube]]
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| |colspan=6|[[File:8-cube t07.svg|150px]]<br/>[[Heptellated 8-cube]]
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| |- valign=top align=center
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| |colspan=4|[[File:8-cube t0.svg|100px]]<br/>[[8-cube]]
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| |colspan=4|[[File:8-cube t1.svg|100px]]<br/>[[Rectified 8-cube]]
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| |colspan=4|[[File:8-cube t01.svg|100px]]<br/>[[Truncated 8-cube]]
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| |- valign=top align=center
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| |colspan=4|[[File:8-demicube t0 D7.svg|100px]]<br/>[[8-demicube]]
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| |colspan=4|[[File:8-demicube t01 D7.svg|100px]]<br/>[[Truncated 8-demicube]]
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| |colspan=4|[[File:8-demicube t02 D7.svg|100px]]<br/>[[Cantellated 8-demicube]]
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| |- valign=top align=center
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| |colspan=6|[[File:8-demicube t03 D7.svg|150px]]<br/>[[Runcinated 8-demicube]]
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| |colspan=6|[[File:8-demicube t04 D7.svg|150px]]<br/>[[Stericated 8-demicube]]
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| |- valign=top align=center
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| |colspan=6|[[File:8-demicube t05 D7.svg|150px]]<br/>[[Pentellated 8-demicube]]
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| |colspan=6|[[File:8-demicube t06 D7.svg|150px]]<br/>[[Hexicated 8-demicube]]
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| |- valign=top align=center
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| |colspan=4|[[File:Gosset 4 21 polytope petrie.svg|100px]]<br/>[[4 21 polytope|4<sub>21</sub>]]
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| |colspan=4|[[File:Gosset 1 42 polytope petrie.svg|100px]]<br/>[[1 42 polytope|1<sub>42</sub>]]
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| |colspan=4|[[File:2 41 polytope petrie.svg|100px]]<br/>[[2 41 polytope|2<sub>41</sub>]]
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| |}
| |
| In [[Eight-dimensional space|eight-dimensional]] [[geometry]], a '''polyzetton'''<ref>A proposed name for 8-polytope is '''polyzetton''' (plural: '''polyzetta'''), created from ''poly-'', and ''[[zetta|zetta-]]'' (following the [[International System of Units|SI prefix]] as a variation on [[Numerical prefix|hepta]], meaning seven) and ''-on''.</ref> (or '''8-polytope''') is a [[polytope]] contained by 7-polytope facets. Each [[6-polytope]] [[Ridge (geometry)|ridge]] being shared by exactly two [[7-polytope]] [[Facet (mathematics)|facets]].
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| | |
| A '''uniform polyzetton''' is one which is [[vertex-transitive]], and constructed from [[uniform polyexon|uniform]] (7-polytope) facets.
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| | |
| == Regular 8-polytopes ==
| |
| | |
| Regular polyzetta can be represented by the [[Schläfli symbol]] {p,q,r,s,t,u,v}, with '''v''' {p,q,r,s,t,u} 7-polytope [[Facet (mathematics)|facets]] around each [[Peak (geometry)|peak]].
| |
| | |
| There are exactly three such [[List of regular polytopes#Convex 4|convex regular 8-polytopes]]:
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| # {3,3,3,3,3,3,3} - [[8-simplex]]
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| # {4,3,3,3,3,3,3} - [[8-cube]]
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| # {3,3,3,3,3,3,4} - [[8-orthoplex]]
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| | |
| There are no nonconvex regular 8-polytopes.
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| | |
| == Euler characteristic ==
| |
| | |
| The [[Euler characteristic]] for 8-polytopes that are topological [[7-sphere]]s (including all convex 8-polytopes) is zero. χ=V-E+F-C+f<sub>4</sub>-f<sub>5</sub>+f<sub>6</sub>-f<sub>7</sub>=0.
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| | |
| == Uniform 8-polytopes by fundamental Coxeter groups ==
| |
| | |
| Uniform 8-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
| |
| |-
| |
| !#
| |
| !colspan=2|[[Coxeter group]]
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| ![[Coxeter-Dynkin diagram]]
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| !Forms
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| |-
| |
| |1||A<sub>8</sub>|| [3<sup>7</sup>]||{{CDD|node|3|node|3|node|3|node|3|node|3|node|3|node|3|node}}||135
| |
| |-
| |
| |2||BC<sub>8</sub>||[4,3<sup>6</sup>]||{{CDD|node|4|node|3|node|3|node|3|node|3|node|3|node|3|node}}||255
| |
| |-
| |
| |3||D<sub>8</sub>||[3<sup>5,1,1</sup>]||{{CDD|nodes|split2|node|3|node|3|node|3|node|3|node|3|node}}||191 (64 unique)
| |
| |-
| |
| |4||[[E8 (mathematics)|E<sub>8</sub>]]||[3<sup>4,2,1</sup>]||{{CDD|nodea|3a|nodea|3a|branch|3a|nodea|3a|nodea|3a|nodea|3a|nodea}}||255
| |
| |}
| |
| Selected regular and uniform 8-polytopes from each family include:
| |
| # [[Simplex]] family: A<sub>8</sub> [3<sup>7</sup>] - {{CDD|node|3|node|3|node|3|node|3|node|3|node|3|node|3|node}}
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| #* 135 uniform 8-polytopes as permutations of rings in the group diagram, including one regular:
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| #*# {3<sup>7</sup>} - [[8-simplex]] or ennea-9-tope or enneazetton - {{CDD|node_1|3|node|3|node|3|node|3|node|3|node|3|node|3|node}}
| |
| # [[Hypercube]]/[[orthoplex]] family: B<sub>8</sub> [4,3<sup>6</sup>] - {{CDD|node|4|node|3|node|3|node|3|node|3|node|3|node|3|node}}
| |
| #* 255 uniform 8-polytopes as permutations of rings in the group diagram, including two regular ones:
| |
| #*# {4,3<sup>6</sup>} - [[8-cube]] or '''octeract'''- {{CDD|node_1|4|node|3|node|3|node|3|node|3|node|3|node|3|node}}
| |
| #*# {3<sup>6</sup>,4} - [[8-orthoplex]] or '''octacross''' - {{CDD|node_1|3|node|3|node|3|node|3|node|3|node|3|node|4|node}}
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| # [[Demihypercube]] D<sub>8</sub> family: [3<sup>5,1,1</sup>] - {{CDD|nodea|3a|branch|3a|nodea|3a|nodea|3a|nodea|3a|nodea|3a|nodea}}
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| #* 191 uniform 8-polytopes as permutations of rings in the group diagram, including:
| |
| #*# {3<sup>1,5,1</sup>} - [[8-demicube]] or '''demiocteract''', '''1<sub>51</sub>''' - {{CDD|nodea_1|3a|branch|3a|nodea|3a|nodea|3a|nodea|3a|nodea|3a|nodea}}; also as h{4,3<sup>6</sup>} {{CDD|node_h|4|node|3|node|3|node|3|node|3|node|3|node|3|node}}.
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| #*# {3<sup>5,1,1</sup>} - [[8-orthoplex]], '''5<sub>11</sub>''' - {{CDD|nodea|3a|branch|3a|nodea|3a|nodea|3a|nodea|3a|nodea|3a|nodea_1}}
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| # [[Semiregular E-polytope|E-polytope family]] E<sub>8</sub> family: [3<sup>4,1,1</sup>] - {{CDD|nodea|3a|nodea|3a|branch|3a|nodea|3a|nodea|3a|nodea|3a|nodea}}
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| #* 255 uniform 8-polytopes as permutations of rings in the group diagram, including:
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| #*# {3<sup>4,2,1</sup>} - [[Thorold Gosset]]'s semiregular '''[[Gosset 4 21 polytope|4<sub>21</sub>]]''', {{CDD|nodea|3a|nodea|3a|branch|3a|nodea|3a|nodea|3a|nodea|3a|nodea_1}}
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| #*# {3<sup>1,4,2</sup>} - the uniform '''[[Gosset 1 42 polytope|1<sub>42</sub>]]''', {{CDD|nodea|3a|nodea|3a|branch_01lr|3a|nodea|3a|nodea|3a|nodea|3a|nodea}},
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| #*# {3<sup>2,4,1</sup>} - the uniform '''[[Gosset 2 41 polytope|2<sub>41</sub>]]''', {{CDD|nodea_1|3a|nodea|3a|branch|3a|nodea|3a|nodea|3a|nodea|3a|nodea}}
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| | |
| === Uniform prismatic forms ===
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| There are many [[Uniform polytope|uniform]] [[Prismatic polytope|prismatic]] families, including:
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| {| class=wikitable
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| |-
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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|7+1
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| |-
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| |1||A<sub>7</sub>×A<sub>1</sub>|| [3,3,3,3,3,3]×[ ]||{{CDD|node|3|node|3|node|3|node|3|node|3|node|3|node|2|node}}
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| |-
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| |2||BC<sub>7</sub>×A<sub>1</sub>||[4,3,3,3,3,3]×[ ]||{{CDD|node|4|node|3|node|3|node|3|node|3|node|3|node|2|node}}
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| |-
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| |3||D<sub>7</sub>×A<sub>1</sub>||[3<sup>4,1,1</sup>]×[ ]||{{CDD|nodes|split2|node|3|node|3|node|3|node|3|node|2|node}}
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| |-
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| |4||[[E7 (mathematics)|E<sub>7</sub>]]×A<sub>1</sub>||[3<sup>3,2,1</sup>]×[ ]||{{CDD|nodea|3a|nodea|3a|branch|3a|nodea|3a|nodea|3a|nodea|2|nodea}}
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| |-
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| !colspan=4|6+2
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| |-
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| |1||A<sub>6</sub>×I<sub>2</sub>(p) ||[3,3,3,3,3]×[p] ||{{CDD|node|3|node|3|node|3|node|3|node|3|node|2|node|p|node}}
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| |-
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| |2||BC<sub>6</sub>×I<sub>2</sub>(p) ||[4,3,3,3,3]×[p] ||{{CDD|node|4|node|3|node|3|node|3|node|3|node|2|node|p|node}}
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| |-
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| |3||D<sub>6</sub>×I<sub>2</sub>(p) ||[3<sup>3,1,1</sup>]×[p] ||{{CDD|nodes|split2|node|3|node|3|node|3|node|2|node|p|node}}
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| |-
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| |4||E<sub>6</sub>×I<sub>2</sub>(p) ||[3,3,3,3,3]×[p] ||{{CDD|node|3|node|3|node|3|node|3|node|3|node|2|node|p|node}}
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| |-
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| !colspan=4|6+1+1
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| |-
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| |1||A<sub>6</sub>×A<sub>1</sub>×A<sub>1</sub> ||[3,3,3,3,3]×[ ]x[ ] ||{{CDD|node|3|node|3|node|3|node|3|node|3|node|2|node|2|node}}
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| |-
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| |2||BC<sub>6</sub>×A<sub>1</sub>×A<sub>1</sub> ||[4,3,3,3,3]×[ ]x[ ] ||{{CDD|node|4|node|3|node|3|node|3|node|3|node|2|node|2|node}}
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| |-
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| |3||D<sub>6</sub>×A<sub>1</sub>×A<sub>1</sub> ||[3<sup>3,1,1</sup>]×[ ]x[ ] ||{{CDD|nodes|split2|node|3|node|3|node|3|node|2|node|2|node}}
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| |-
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| |4||E<sub>6</sub>×A<sub>1</sub>×A<sub>1</sub> ||[3,3,3,3,3]×[ ]x[ ] ||{{CDD|node|3|node|3|node|3|node|3|node|3|node|2|node|2|node}}
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| |-
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| !colspan=4|5+3
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| |-
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| |1||A<sub>5</sub>×A<sub>3</sub>|| [3<sup>4</sup>]×[3,3]||{{CDD|node|3|node|3|node|3|node|3|node|2|node|3|node|3|node}}
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| |-
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| |2||BC<sub>5</sub>×A<sub>3</sub>||[4,3<sup>3</sup>]×[3,3]||{{CDD|node|4|node|3|node|3|node|3|node|2|node|3|node|3|node}}
| |
| |-
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| |3||D<sub>5</sub>×A<sub>3</sub>||[3<sup>2,1,1</sup>]×[3,3]||{{CDD|nodes|split2|node|3|node|3|node|2|node|3|node|3|node}}
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| |-
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| |4||A<sub>5</sub>×BC<sub>3</sub>|| [3<sup>4</sup>]×[4,3]||{{CDD|node|3|node|3|node|3|node|3|node|2|node|4|node|3|node}}
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| |-
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| |5||BC<sub>5</sub>×BC<sub>3</sub>||[4,3<sup>3</sup>]×[4,3]||{{CDD|node|4|node|3|node|3|node|3|node|2|node|4|node|3|node}}
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| |-
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| |6||D<sub>5</sub>×BC<sub>3</sub>||[3<sup>2,1,1</sup>]×[4,3]||{{CDD|nodes|split2|node|3|node|3|node|2|node|4|node|3|node}}
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| |-
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| |7||A<sub>5</sub>×H<sub>3</sub>|| [3<sup>4</sup>]×[5,3]||{{CDD|node|3|node|3|node|3|node|3|node|2|node|5|node|3|node}}
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| |-
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| |8||BC<sub>5</sub>×H<sub>3</sub>||[4,3<sup>3</sup>]×[5,3]||{{CDD|node|4|node|3|node|3|node|3|node|2|node|5|node|3|node}}
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| |-
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| |9||D<sub>5</sub>×H<sub>3</sub>||[3<sup>2,1,1</sup>]×[5,3]||{{CDD|nodes|split2|node|3|node|3|node|2|node|5|node|3|node}}
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| |-
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| !colspan=4|5+2+1
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| |-
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| |1 ||A<sub>5</sub>×I<sub>2</sub>(p)×A<sub>1</sub>|| [3,3,3]×[p]×[ ]|| {{CDD|node|3|node|3|node|3|node|3|node|2|node|p|node|2|node}}
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| |-
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| |2 ||BC<sub>5</sub>×I<sub>2</sub>(p)×A<sub>1</sub>|| [4,3,3]×[p]×[ ]|| {{CDD|node|4|node|3|node|3|node|3|node|2|node|p|node|2|node}}
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| |-
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| |3 ||D<sub>5</sub>×I<sub>2</sub>(p)×A<sub>1</sub>|| [3<sup>2,1,1</sup>]×[p]×[ ]|| {{CDD|nodes|split2|node|3|node|3|node|2|node|p|node|2|node}}
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| |-
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| !colspan=4|5+1+1+1
| |
| |-
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| |1 ||A<sub>5</sub>×A<sub>1</sub>×A<sub>1</sub>×A<sub>1</sub>|| [3,3,3]×[ ]×[ ]×[ ]|| {{CDD|node|3|node|3|node|3|node|3|node|2|node|2|node|2|node}}
| |
| |-
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| |2 ||BC<sub>5</sub>×A<sub>1</sub>×A<sub>1</sub>×A<sub>1</sub>|| [4,3,3]×[ ]×[ ]×[ ]|| {{CDD|node|4|node|3|node|3|node|3|node|2|node|2|node|2|node}}
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| |-
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| |3 ||D<sub>5</sub>×A<sub>1</sub>×A<sub>1</sub>×A<sub>1</sub>|| [3<sup>2,1,1</sup>]×[ ]×[ ]×[ ]|| {{CDD|nodes|split2|node|3|node|3|node|2|node|2|node|2|node}}
| |
| |-
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| !colspan=4|4+4
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| |-
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| |1||A<sub>4</sub>×A<sub>4</sub>||[3,3,3]×[3,3,3]||{{CDD|node|3|node|3|node|3|node|2|node|3|node|3|node|3|node}}
| |
| |-
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| |2|| BC<sub>4</sub>×A<sub>4</sub>||[4,3,3]×[3,3,3]||{{CDD|node|4|node|3|node|3|node|2|node|3|node|3|node|3|node}}
| |
| |-
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| |3||D<sub>4</sub>×A<sub>4</sub>||[3<sup>1,1,1</sup>]×[3,3,3]||{{CDD|nodes|split2|node|3|node|2|node|3|node|3|node|3|node}}
| |
| |-
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| |4|| F<sub>4</sub>×A<sub>4</sub>||[3,4,3]×[3,3,3]||{{CDD|node|3|node|4|node|3|node|2|node|3|node|3|node|3|node}}
| |
| |-
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| |5|| H<sub>4</sub>×A<sub>4</sub>||[5,3,3]×[3,3,3]||{{CDD|node|5|node|3|node|3|node|2|node|3|node|3|node|3|node}}
| |
| |-
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| |6|| BC<sub>4</sub>×BC<sub>4</sub>||[4,3,3]×[4,3,3]||{{CDD|node|4|node|3|node|3|node|2|node|4|node|3|node|3|node}}
| |
| |-
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| |7||D<sub>4</sub>×BC<sub>4</sub>||[3<sup>1,1,1</sup>]×[4,3,3]||{{CDD|nodes|split2|node|3|node|2|node|4|node|3|node|3|node}}
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| |-
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| |8|| F<sub>4</sub>×BC<sub>4</sub>||[3,4,3]×[4,3,3]||{{CDD|node|3|node|4|node|3|node|2|node|4|node|3|node|3|node}}
| |
| |-
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| |9|| H<sub>4</sub>×BC<sub>4</sub>||[5,3,3]×[4,3,3]||{{CDD|node|5|node|3|node|3|node|2|node|4|node|3|node|3|node}}
| |
| |-
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| |10||D<sub>4</sub>×D<sub>4</sub>||[3<sup>1,1,1</sup>]×[3<sup>1,1,1</sup>]||{{CDD|nodes|split2|node|3|node|2|nodes|split2|node|3|node}}
| |
| |-
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| |11|| F<sub>4</sub>×D<sub>4</sub>||[3,4,3]×[3<sup>1,1,1</sup>]||{{CDD|node|3|node|4|node|3|node|2|nodes|split2|node|3|node}}
| |
| |-
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| |12|| H<sub>4</sub>×D<sub>4</sub>||[5,3,3]×[3<sup>1,1,1</sup>]||{{CDD|node|5|node|3|node|3|node|2|nodes|split2|node|3|node}}
| |
| |-
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| |13|| F<sub>4</sub>×F<sub>4</sub>||[3,4,3]×[3,4,3]||{{CDD|node|3|node|4|node|3|node|2|node|3|node|4|node|3|node}}
| |
| |-
| |
| |14|| H<sub>4</sub>×F<sub>4</sub>||[5,3,3]×[3,4,3]||{{CDD|node|5|node|3|node|3|node|2|node|3|node|4|node|3|node}}
| |
| |-
| |
| |15|| H<sub>4</sub>×H<sub>4</sub>||[5,3,3]×[5,3,3]||{{CDD|node|5|node|3|node|3|node|2|node|5|node|3|node|3|node}}
| |
| |-
| |
| !colspan=4|4+3+1
| |
| |-
| |
| |1 ||A<sub>4</sub>×A<sub>3</sub>×A<sub>1</sub>|| [3,3,3]×[3,3]×[ ]|| {{CDD|node|3|node|3|node|3|node|2|node|3|node|3|node|2|node}}
| |
| |-
| |
| |2 ||A<sub>4</sub>×BC<sub>3</sub>×A<sub>1</sub>|| [3,3,3]×[4,3]×[ ]|| {{CDD|node|3|node|3|node|3|node|2|node|4|node|3|node|2|node}}
| |
| |-
| |
| |3 ||A<sub>4</sub>×H<sub>3</sub>×A<sub>1</sub>|| [3,3,3]×[5,3]×[ ]|| {{CDD|node|3|node|3|node|3|node|2|node|5|node|3|node|2|node}}
| |
| |-
| |
| |4 ||BC<sub>4</sub>×A<sub>3</sub>×A<sub>1</sub>|| [4,3,3]×[3,3]×[ ]|| {{CDD|node|4|node|3|node|3|node|2|node|3|node|3|node|2|node}}
| |
| |-
| |
| |5 ||BC<sub>4</sub>×BC<sub>3</sub>×A<sub>1</sub>|| [4,3,3]×[4,3]×[ ]|| {{CDD|node|4|node|3|node|3|node|2|node|4|node|3|node|2|node}}
| |
| |-
| |
| |6 ||BC<sub>4</sub>×H<sub>3</sub>×A<sub>1</sub>|| [4,3,3]×[5,3]×[ ]|| {{CDD|node|4|node|3|node|3|node|2|node|5|node|3|node|2|node}}
| |
| |-
| |
| |7 ||H<sub>4</sub>×A<sub>3</sub>×A<sub>1</sub>|| [5,3,3]×[3,3]×[ ]|| {{CDD|node|5|node|3|node|3|node|2|node|3|node|3|node|2|node}}
| |
| |-
| |
| |8 ||H<sub>4</sub>×BC<sub>3</sub>×A<sub>1</sub>|| [5,3,3]×[4,3]×[ ]|| {{CDD|node|5|node|3|node|3|node|2|node|4|node|3|node|2|node}}
| |
| |-
| |
| |9 ||H<sub>4</sub>×H<sub>3</sub>×A<sub>1</sub>|| [5,3,3]×[5,3]×[ ]|| {{CDD|node|5|node|3|node|3|node|2|node|5|node|3|node|2|node}}
| |
| |-
| |
| |10 ||F<sub>4</sub>×A<sub>3</sub>×A<sub>1</sub>|| [3,4,3]×[3,3]×[ ]|| {{CDD|node|3|node|4|node|3|node|2|node|3|node|3|node|2|node}}
| |
| |-
| |
| |11 ||F<sub>4</sub>×BC<sub>3</sub>×A<sub>1</sub>|| [3,4,3]×[4,3]×[ ]|| {{CDD|node|3|node|4|node|3|node|2|node|4|node|3|node|2|node}}
| |
| |-
| |
| |12 ||F<sub>4</sub>×H<sub>3</sub>×A<sub>1</sub>|| [3,4,3]×[5,3]×[ ]|| {{CDD|node|3|node|4|node|3|node|2|node|5|node|3|node|2|node}}
| |
| |-
| |
| |13 ||D<sub>4</sub>×A<sub>3</sub>×A<sub>1</sub>|| [3<sup>1,1,1</sup>]×[3,3]×[ ]|| {{CDD|nodes|split2|node|3|node|2|node|3|node|3|node|2|node}}
| |
| |-
| |
| |14 ||D<sub>4</sub>×BC<sub>3</sub>×A<sub>1</sub>|| [3<sup>1,1,1</sup>]×[4,3]×[ ]|| {{CDD|nodes|split2|node|3|node|2|node|4|node|3|node|2|node}}
| |
| |-
| |
| |15 ||D<sub>4</sub>×H<sub>3</sub>×A<sub>1</sub>|| [3<sup>1,1,1</sup>]×[5,3]×[ ]|| {{CDD|nodes|split2|node|3|node|2|node|5|node|3|node|2|node}}
| |
| |-
| |
| !colspan=4|4+2+2
| |
| |-
| |
| |...
| |
| |-
| |
| !colspan=4|4+2+1+1
| |
| |-
| |
| |...
| |
| |-
| |
| !colspan=4|4+1+1+1+1
| |
| |-
| |
| |...
| |
| |-
| |
| !colspan=4|3+3+2
| |
| |-
| |
| !1
| |
| || A<sub>3</sub>×A<sub>3</sub>×I<sub>2</sub>(p)||[3,3]×[3,3]×[p]||{{CDD|node|3|node|3|node|2|node|3|node|3|node|2|node|p|node}}
| |
| |-
| |
| !2
| |
| || BC<sub>3</sub>×A<sub>3</sub>×I<sub>2</sub>(p)||[4,3]×[3,3]×[p]||{{CDD|node|4|node|3|node|2|node|3|node|3|node|2|node|p|node}}
| |
| |-
| |
| !3
| |
| ||H<sub>3</sub>×A<sub>3</sub>×I<sub>2</sub>(p)||[5,3]×[3,3]×[p]||{{CDD|node|5|node|3|node|2|node|3|node|3|node|2|node|p|node}}
| |
| |-
| |
| !4
| |
| || BC<sub>3</sub>×BC<sub>3</sub>×I<sub>2</sub>(p)||[4,3]×[4,3]×[p]||{{CDD|node|4|node|3|node|2|node|4|node|3|node|2|node|p|node}}
| |
| |-
| |
| !5
| |
| ||H<sub>3</sub>×BC<sub>3</sub>×I<sub>2</sub>(p)||[5,3]×[4,3]×[p]||{{CDD|node|5|node|3|node|2|node|4|node|3|node|2|node|p|node}}
| |
| |-
| |
| !6
| |
| ||H<sub>3</sub>×H<sub>3</sub>×I<sub>2</sub>(p)||[5,3]×[5,3]×[p]||{{CDD|node|5|node|3|node|2|node|5|node|3|node|2|node|p|node}}
| |
| |-
| |
| !colspan=4|3+3+1+1
| |
| |-
| |
| !1
| |
| || A<sub>3</sub>×A<sub>3</sub>×A<sub>1</sub>×A<sub>1</sub>||[3,3]×[3,3]×[ ]×[ ]||{{CDD|node|3|node|3|node|2|node|3|node|3|node|2|node|2|node}}
| |
| |-
| |
| !2
| |
| || BC<sub>3</sub>×A<sub>3</sub>×A<sub>1</sub>×A<sub>1</sub>||[4,3]×[3,3]×[ ]×[ ]||{{CDD|node|4|node|3|node|2|node|3|node|3|node|2|node|2|node}}
| |
| |-
| |
| !3
| |
| ||H<sub>3</sub>×A<sub>3</sub>×A<sub>1</sub>×A<sub>1</sub>||[5,3]×[3,3]×[ ]×[ ]||{{CDD|node|5|node|3|node|2|node|3|node|3|node|2|node|2|node}}
| |
| |-
| |
| !4
| |
| || BC<sub>3</sub>×BC<sub>3</sub>×A<sub>1</sub>×A<sub>1</sub>||[4,3]×[4,3]×[ ]×[ ]||{{CDD|node|4|node|3|node|2|node|4|node|3|node|2|node|2|node}}
| |
| |-
| |
| !5
| |
| ||H<sub>3</sub>×BC<sub>3</sub>×A<sub>1</sub>×A<sub>1</sub>||[5,3]×[4,3]×[ ]×[ ]||{{CDD|node|5|node|3|node|2|node|4|node|3|node|2|node|2|node}}
| |
| |-
| |
| !6
| |
| ||H<sub>3</sub>×H<sub>3</sub>×A<sub>1</sub>×A<sub>1</sub>||[5,3]×[5,3]×[ ]×[ ]||{{CDD|node|5|node|3|node|2|node|5|node|3|node|2|node|2|node}}
| |
| |-
| |
| !colspan=4|3+2+2+1
| |
| |-
| |
| |1 ||A<sub>3</sub>×I<sub>2</sub>(p)×I<sub>2</sub>(q)×A<sub>1</sub>|| [3,3]×[p]×[q]×[ ]|| {{CDD|node|3|node|3|node|2|node|p|node|2|node|q|node|2|node}}
| |
| |-
| |
| |2 ||BC<sub>3</sub>×I<sub>2</sub>(p)×I<sub>2</sub>(q)×A<sub>1</sub>|| [4,3]×[p]×[q]×[ ]|| {{CDD|node|4|node|3|node|2|node|p|node|2|node|q|node|2|node}}
| |
| |-
| |
| |3 ||H<sub>3</sub>×I<sub>2</sub>(p)×I<sub>2</sub>(q)×A<sub>1</sub>|| [5,3]×[p]×[q]×[ ]|| {{CDD|node|5|node|3|node|2|node|p|node|2|node|q|node|2|node}}
| |
| |-
| |
| !colspan=4|3+2+1+1+1
| |
| |-
| |
| |1 ||A<sub>3</sub>×I<sub>2</sub>(p)×A<sub>1</sub>×A<sub>1</sub>×A<sub>1</sub>|| [3,3]×[p]×[ ]x[ ]×[ ]|| {{CDD|node|3|node|3|node|2|node|p|node|2|node|2|node|2|node}}
| |
| |-
| |
| |2 ||BC<sub>3</sub>×I<sub>2</sub>(p)×A<sub>1</sub>×A<sub>1</sub>×A<sub>1</sub>|| [4,3]×[p]×[ ]x[ ]×[ ]|| {{CDD|node|4|node|3|node|2|node|p|node|2|node|2|node|2|node}}
| |
| |-
| |
| |3 ||H<sub>3</sub>×I<sub>2</sub>(p)×A<sub>1</sub>×A<sub>1</sub>×A<sub>1</sub>|| [5,3]×[p]×[ ]x[ ]×[ ]|| {{CDD|node|5|node|3|node|2|node|p|node|2|node|2|node|2|node}}
| |
| |-
| |
| !colspan=4|3+1+1+1+1+1
| |
| |-
| |
| |1 ||A<sub>3</sub>×A<sub>1</sub>×A<sub>1</sub>×A<sub>1</sub>×A<sub>1</sub>×A<sub>1</sub>|| [3,3]×[ ]x[ ]×[ ]x[ ]×[ ]|| {{CDD|node|3|node|3|node|2|node|2|node|2|node|2|node|2|node}}
| |
| |-
| |
| |2 ||BC<sub>3</sub>×A<sub>1</sub>×A<sub>1</sub>×A<sub>1</sub>×A<sub>1</sub>×A<sub>1</sub>|| [4,3]×[ ]x[ ]×[ ]x[ ]×[ ]|| {{CDD|node|4|node|3|node|2|node|2|node|2|node|2|node|2|node}}
| |
| |-
| |
| |3 ||H<sub>3</sub>×A<sub>1</sub>×A<sub>1</sub>×A<sub>1</sub>×A<sub>1</sub>×A<sub>1</sub>|| [5,3]×[ ]x[ ]×[ ]x[ ]×[ ]|| {{CDD|node|5|node|3|node|2|node|2|node|2|node|2|node|2|node}}
| |
| |-
| |
| !colspan=4|2+2+2+2
| |
| |-
| |
| |1 ||I<sub>2</sub>(p)×I<sub>2</sub>(q)×I<sub>2</sub>(r)×I<sub>2</sub>(s)|| [p]×[q]×[r]×[s]|| {{CDD|node|p|node|2|node|q|node|2|node|r|node|2|node|s|node}}
| |
| |-
| |
| !colspan=4|2+2+2+1+1
| |
| |-
| |
| |1 ||I<sub>2</sub>(p)×I<sub>2</sub>(q)×I<sub>2</sub>(r)×A<sub>1</sub>×A<sub>1</sub>|| [p]×[q]×[r]×[ ]×[ ]|| {{CDD|node|p|node|2|node|q|node|2|node|r|node|2|node|2|node}}
| |
| |-
| |
| !colspan=4|2+2+1+1+1+1
| |
| |-
| |
| |2 ||I<sub>2</sub>(p)×I<sub>2</sub>(q)×A<sub>1</sub>×A<sub>1</sub>×A<sub>1</sub>×A<sub>1</sub>|| [p]×[q]×[ ]×[ ]×[ ]×[ ]|| {{CDD|node|p|node|2|node|q|node|2|node|2|node|2|node|2|node}}
| |
| |-
| |
| !colspan=4|2+1+1+1+1+1+1
| |
| |-
| |
| |1 ||I<sub>2</sub>(p)×A<sub>1</sub>×A<sub>1</sub>×A<sub>1</sub>×A<sub>1</sub>×A<sub>1</sub>×A<sub>1</sub>|| [p]×[ ]×[ ]×[ ]×[ ]×[ ]×[ ]|| {{CDD|node|p|node|2|node|2|node|2|node|2|node|2|node|2|node}}
| |
| |-
| |
| !colspan=4|1+1+1+1+1+1+1+1
| |
| |-
| |
| |1 ||A<sub>1</sub>×A<sub>1</sub>×A<sub>1</sub>×A<sub>1</sub>×A<sub>1</sub>×A<sub>1</sub>×A<sub>1</sub>×A<sub>1</sub>|| [ ]×[ ]×[ ]×[ ]×[ ]×[ ]×[ ]×[ ]|| {{CDD|node|2|node|2|node|2|node|2|node|2|node|2|node|2|node}}
| |
| |}
| |
| | |
| === The A<sub>8</sub> family ===
| |
| | |
| The A<sub>8</sub> family has symmetry of order 362880 (9 [[factorial]]).
| |
| | |
| There are 135 forms based on all permutations of the [[Coxeter-Dynkin diagram]]s with one or more rings. (128+8-1 cases) These are all enumerated below. Bowers-style acronym names are given in parentheses for cross-referencing.
| |
| | |
| See also a [[list of 8-simplex 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]]
| |
| !rowspan=2|Basepoint
| |
| !colspan=8|Element counts
| |
| |-
| |
| ! 7|| 6|| 5|| 4|| 3|| 2|| 1|| 0
| |
| |-
| |
| |- align=center
| |
| !1
| |
| |
| |
| {{CDD|node|3|node|3|node|3|node|3|node|3|node|3|node|3|node_1}}
| |
| |t<sub>0</sub>
| |
| |[[8-simplex]] (ene)
| |
| |(0,0,0,0,0,0,0,0,1)
| |
| ||9 ||36 ||84 ||126 ||126 ||84 ||36 ||9
| |
| |- align=center
| |
| !2
| |
| |
| |
| {{CDD|node|3|node|3|node|3|node|3|node|3|node|3|node_1|3|node}}
| |
| |t<sub>1</sub>
| |
| |[[Rectified 8-simplex]] (rene)
| |
| |(0,0,0,0,0,0,0,1,1)
| |
| ||18 ||108 ||336 ||630 ||576 ||588 ||252 ||36
| |
| |- align=center
| |
| !3
| |
| |
| |
| {{CDD|node|3|node|3|node|3|node|3|node|3|node_1|3|node|3|node}}
| |
| |t<sub>2</sub>
| |
| |[[Birectified 8-simplex]] (bene)
| |
| |(0,0,0,0,0,0,1,1,1)
| |
| ||18 ||144 ||588 ||1386 ||2016 ||1764 ||756 ||84
| |
| |- align=center
| |
| !4
| |
| |
| |
| {{CDD|node|3|node|3|node|3|node|3|node_1|3|node|3|node|3|node}}
| |
| |t<sub>3</sub>
| |
| |[[Trirectified 8-simplex]] (trene)
| |
| |(0,0,0,0,0,1,1,1,1)
| |
| || || || || || || ||1260 ||126
| |
| |- align=center
| |
| !5
| |
| |
| |
| {{CDD|node|3|node|3|node|3|node|3|node|3|node|3|node_1|3|node_1}}
| |
| |t<sub>0,1</sub>
| |
| |[[Truncated 8-simplex]] (tene)
| |
| |(0,0,0,0,0,0,0,1,2)
| |
| || || || || || || ||288 ||72
| |
| |- align=center
| |
| !6
| |
| |
| |
| {{CDD|node|3|node|3|node|3|node|3|node|3|node_1|3|node|3|node_1}}
| |
| |t<sub>0,2</sub>
| |
| |[[Cantellated 8-simplex]]
| |
| |(0,0,0,0,0,0,1,1,2)
| |
| || || || || || || ||1764 ||252
| |
| |- align=center
| |
| !7
| |
| |
| |
| {{CDD|node|3|node|3|node|3|node|3|node|3|node_1|3|node_1|3|node}}
| |
| |t<sub>1,2</sub>
| |
| |[[Bitruncated 8-simplex]]
| |
| |(0,0,0,0,0,0,1,2,2)
| |
| || || || || || || ||1008 ||252
| |
| |- align=center
| |
| !8
| |
| |
| |
| {{CDD|node|3|node|3|node|3|node|3|node_1|3|node|3|node|3|node_1}}
| |
| |t<sub>0,3</sub>
| |
| |[[Runcinated 8-simplex]]
| |
| |(0,0,0,0,0,1,1,1,2)
| |
| || || || || || || ||4536 ||504
| |
| |- align=center
| |
| !9
| |
| |
| |
| {{CDD|node|3|node|3|node|3|node|3|node_1|3|node|3|node_1|3|node}}
| |
| |t<sub>1,3</sub>
| |
| |[[Bicantellated 8-simplex]]
| |
| |(0,0,0,0,0,1,1,2,2)
| |
| || || || || || || ||5292 ||756
| |
| |- align=center
| |
| !10
| |
| |
| |
| {{CDD|node|3|node|3|node|3|node|3|node_1|3|node_1|3|node|3|node}}
| |
| |t<sub>2,3</sub>
| |
| |[[Tritruncated 8-simplex]]
| |
| |(0,0,0,0,0,1,2,2,2)
| |
| || || || || || || ||2016 ||504
| |
| |- align=center
| |
| !11
| |
| |
| |
| {{CDD|node|3|node|3|node|3|node_1|3|node|3|node|3|node|3|node_1}}
| |
| |t<sub>0,4</sub>
| |
| |[[Stericated 8-simplex]]
| |
| |(0,0,0,0,1,1,1,1,2)
| |
| || || || || || || ||6300 ||630
| |
| |- align=center
| |
| !12
| |
| |
| |
| {{CDD|node|3|node|3|node|3|node_1|3|node|3|node|3|node_1|3|node}}
| |
| |t<sub>1,4</sub>
| |
| |[[Biruncinated 8-simplex]]
| |
| |(0,0,0,0,1,1,1,2,2)
| |
| || || || || || || ||11340 ||1260
| |
| |- align=center
| |
| !13
| |
| |
| |
| {{CDD|node|3|node|3|node|3|node_1|3|node|3|node_1|3|node|3|node}}
| |
| |t<sub>2,4</sub>
| |
| |[[Tricantellated 8-simplex]]
| |
| |(0,0,0,0,1,1,2,2,2)
| |
| || || || || || || ||8820 ||1260
| |
| |- align=center BGCOLOR="#e0f0e0"
| |
| !14
| |
| |
| |
| {{CDD|node|3|node|3|node|3|node_1|3|node_1|3|node|3|node|3|node}}
| |
| |t<sub>3,4</sub>
| |
| |[[Quadritruncated 8-simplex]]
| |
| |(0,0,0,0,1,2,2,2,2)
| |
| || || || || || || ||2520 ||630
| |
| |- align=center
| |
| !15
| |
| |
| |
| {{CDD|node|3|node|3|node_1|3|node|3|node|3|node|3|node|3|node_1}}
| |
| |t<sub>0,5</sub>
| |
| |[[Pentellated 8-simplex]]
| |
| |(0,0,0,1,1,1,1,1,2)
| |
| || || || || || || ||5040 ||504
| |
| |- align=center
| |
| !16
| |
| |
| |
| {{CDD|node|3|node|3|node_1|3|node|3|node|3|node|3|node_1|3|node}}
| |
| |t<sub>1,5</sub>
| |
| |[[Bistericated 8-simplex]]
| |
| |(0,0,0,1,1,1,1,2,2)
| |
| || || || || || || ||12600 ||1260
| |
| |- align=center BGCOLOR="#e0f0e0"
| |
| !17
| |
| |
| |
| {{CDD|node|3|node|3|node_1|3|node|3|node|3|node_1|3|node|3|node}}
| |
| |t<sub>2,5</sub>
| |
| |[[Triruncinated 8-simplex]]
| |
| |(0,0,0,1,1,1,2,2,2)
| |
| || || || || || || ||15120 ||1680
| |
| |- align=center
| |
| !18
| |
| |
| |
| {{CDD|node|3|node_1|3|node|3|node|3|node|3|node|3|node|3|node_1}}
| |
| |t<sub>0,6</sub>
| |
| |[[Hexicated 8-simplex]]
| |
| |(0,0,1,1,1,1,1,1,2)
| |
| || || || || || || ||2268 ||252
| |
| |- align=center BGCOLOR="#e0f0e0"
| |
| !19
| |
| |
| |
| {{CDD|node|3|node_1|3|node|3|node|3|node|3|node|3|node_1|3|node}}
| |
| |t<sub>1,6</sub>
| |
| |[[Bipentellated 8-simplex]]
| |
| |(0,0,1,1,1,1,1,2,2)
| |
| || || || || || || ||7560 ||756
| |
| |- align=center BGCOLOR="#e0f0e0"
| |
| !20
| |
| |
| |
| {{CDD|node_1|3|node|3|node|3|node|3|node|3|node|3|node|3|node_1}}
| |
| |t<sub>0,7</sub>
| |
| |[[Heptellated 8-simplex]]
| |
| |(0,1,1,1,1,1,1,1,2)
| |
| || || || || || || ||504 ||72
| |
| |- align=center
| |
| !21
| |
| |
| |
| {{CDD|node|3|node|3|node|3|node|3|node|3|node_1|3|node_1|3|node_1}}
| |
| |t<sub>0,1,2</sub>
| |
| |[[Cantitruncated 8-simplex]]
| |
| |(0,0,0,0,0,0,1,2,3)
| |
| || || || || || || ||2016 ||504
| |
| |- align=center
| |
| !22
| |
| |
| |
| {{CDD|node|3|node|3|node|3|node|3|node_1|3|node|3|node_1|3|node_1}}
| |
| |t<sub>0,1,3</sub>
| |
| |[[Runcitruncated 8-simplex]]
| |
| |(0,0,0,0,0,1,1,2,3)
| |
| || || || || || || ||9828 ||1512
| |
| |- align=center
| |
| !23
| |
| |
| |
| {{CDD|node|3|node|3|node|3|node|3|node_1|3|node_1|3|node|3|node_1}}
| |
| |t<sub>0,2,3</sub>
| |
| |[[Runcicantellated 8-simplex]]
| |
| |(0,0,0,0,0,1,2,2,3)
| |
| || || || || || || ||6804 ||1512
| |
| |- align=center
| |
| !24
| |
| |
| |
| {{CDD|node|3|node|3|node|3|node|3|node_1|3|node_1|3|node_1|3|node}}
| |
| |t<sub>1,2,3</sub>
| |
| |[[Bicantitruncated 8-simplex]]
| |
| |(0,0,0,0,0,1,2,3,3)
| |
| || || || || || || ||6048 ||1512
| |
| |- align=center
| |
| !25
| |
| |
| |
| {{CDD|node|3|node|3|node|3|node_1|3|node|3|node|3|node_1|3|node_1}}
| |
| |t<sub>0,1,4</sub>
| |
| |[[Steritruncated 8-simplex]]
| |
| |(0,0,0,0,1,1,1,2,3)
| |
| || || || || || || ||20160 ||2520
| |
| |- align=center
| |
| !26
| |
| |
| |
| {{CDD|node|3|node|3|node|3|node_1|3|node|3|node_1|3|node|3|node_1}}
| |
| |t<sub>0,2,4</sub>
| |
| |[[Stericantellated 8-simplex]]
| |
| |(0,0,0,0,1,1,2,2,3)
| |
| || || || || || || ||26460 ||3780
| |
| |- align=center
| |
| !27
| |
| |
| |
| {{CDD|node|3|node|3|node|3|node_1|3|node|3|node_1|3|node_1|3|node}}
| |
| |t<sub>1,2,4</sub>
| |
| |[[Biruncitruncated 8-simplex]]
| |
| |(0,0,0,0,1,1,2,3,3)
| |
| || || || || || || ||22680 ||3780
| |
| |- align=center
| |
| !28
| |
| |
| |
| {{CDD|node|3|node|3|node|3|node_1|3|node_1|3|node|3|node|3|node_1}}
| |
| |t<sub>0,3,4</sub>
| |
| |[[Steriruncinated 8-simplex]]
| |
| |(0,0,0,0,1,2,2,2,3)
| |
| || || || || || || ||12600 ||2520
| |
| |- align=center
| |
| !29
| |
| |
| |
| {{CDD|node|3|node|3|node|3|node_1|3|node_1|3|node|3|node_1|3|node}}
| |
| |t<sub>1,3,4</sub>
| |
| |[[Biruncicantellated 8-simplex]]
| |
| |(0,0,0,0,1,2,2,3,3)
| |
| || || || || || || ||18900 ||3780
| |
| |- align=center
| |
| !30
| |
| |
| |
| {{CDD|node|3|node|3|node|3|node_1|3|node_1|3|node_1|3|node|3|node}}
| |
| |t<sub>2,3,4</sub>
| |
| |[[Tricantitruncated 8-simplex]]
| |
| |(0,0,0,0,1,2,3,3,3)
| |
| || || || || || || ||10080 ||2520
| |
| |- align=center
| |
| !31
| |
| |
| |
| {{CDD|node|3|node|3|node_1|3|node|3|node|3|node|3|node_1|3|node_1}}
| |
| |t<sub>0,1,5</sub>
| |
| |[[Pentitruncated 8-simplex]]
| |
| |(0,0,0,1,1,1,1,2,3)
| |
| || || || || || || ||21420 ||2520
| |
| |- align=center
| |
| !32
| |
| |
| |
| {{CDD|node|3|node|3|node_1|3|node|3|node|3|node_1|3|node|3|node_1}}
| |
| |t<sub>0,2,5</sub>
| |
| |[[Penticantellated 8-simplex]]
| |
| |(0,0,0,1,1,1,2,2,3)
| |
| || || || || || || ||42840 ||5040
| |
| |- align=center
| |
| !33
| |
| |
| |
| {{CDD|node|3|node|3|node_1|3|node|3|node|3|node_1|3|node_1|3|node}}
| |
| |t<sub>1,2,5</sub>
| |
| |[[Bisteritruncated 8-simplex]]
| |
| |(0,0,0,1,1,1,2,3,3)
| |
| || || || || || || ||35280 ||5040
| |
| |- align=center
| |
| !34
| |
| |
| |
| {{CDD|node|3|node|3|node_1|3|node|3|node_1|3|node|3|node|3|node_1}}
| |
| |t<sub>0,3,5</sub>
| |
| |[[Pentiruncinated 8-simplex]]
| |
| |(0,0,0,1,1,2,2,2,3)
| |
| || || || || || || ||37800 ||5040
| |
| |- align=center
| |
| !35
| |
| |
| |
| {{CDD|node|3|node|3|node_1|3|node|3|node_1|3|node|3|node_1|3|node}}
| |
| |t<sub>1,3,5</sub>
| |
| |[[Bistericantellated 8-simplex]]
| |
| |(0,0,0,1,1,2,2,3,3)
| |
| || || || || || || ||52920 ||7560
| |
| |- align=center
| |
| !36
| |
| |
| |
| {{CDD|node|3|node|3|node_1|3|node|3|node_1|3|node_1|3|node|3|node}}
| |
| |t<sub>2,3,5</sub>
| |
| |[[Triruncitruncated 8-simplex]]
| |
| |(0,0,0,1,1,2,3,3,3)
| |
| || || || || || || ||27720 ||5040
| |
| |- align=center
| |
| !37
| |
| |
| |
| {{CDD|node|3|node|3|node_1|3|node_1|3|node|3|node|3|node|3|node_1}}
| |
| |t<sub>0,4,5</sub>
| |
| |[[Pentistericated 8-simplex]]
| |
| |(0,0,0,1,2,2,2,2,3)
| |
| || || || || || || ||13860 ||2520
| |
| |- align=center
| |
| !38
| |
| |
| |
| {{CDD|node|3|node|3|node_1|3|node_1|3|node|3|node|3|node_1|3|node}}
| |
| |t<sub>1,4,5</sub>
| |
| |[[Bisteriruncinated 8-simplex]]
| |
| |(0,0,0,1,2,2,2,3,3)
| |
| || || || || || || ||30240 ||5040
| |
| |- align=center
| |
| !39
| |
| |
| |
| {{CDD|node|3|node_1|3|node|3|node|3|node|3|node|3|node_1|3|node_1}}
| |
| |t<sub>0,1,6</sub>
| |
| |[[Hexitruncated 8-simplex]]
| |
| |(0,0,1,1,1,1,1,2,3)
| |
| || || || || || || ||12096 ||1512
| |
| |- align=center
| |
| !40
| |
| |
| |
| {{CDD|node|3|node_1|3|node|3|node|3|node|3|node_1|3|node|3|node_1}}
| |
| |t<sub>0,2,6</sub>
| |
| |[[Hexicantellated 8-simplex]]
| |
| |(0,0,1,1,1,1,2,2,3)
| |
| || || || || || || ||34020 ||3780
| |
| |- align=center
| |
| !41
| |
| |
| |
| {{CDD|node|3|node_1|3|node|3|node|3|node|3|node_1|3|node_1|3|node}}
| |
| |t<sub>1,2,6</sub>
| |
| |[[Bipentitruncated 8-simplex]]
| |
| |(0,0,1,1,1,1,2,3,3)
| |
| || || || || || || ||26460 ||3780
| |
| |- align=center
| |
| !42
| |
| |
| |
| {{CDD|node|3|node_1|3|node|3|node|3|node_1|3|node|3|node|3|node_1}}
| |
| |t<sub>0,3,6</sub>
| |
| |[[Hexiruncinated 8-simplex]]
| |
| |(0,0,1,1,1,2,2,2,3)
| |
| || || || || || || ||45360 ||5040
| |
| |- align=center
| |
| !43
| |
| |
| |
| {{CDD|node|3|node_1|3|node|3|node|3|node_1|3|node|3|node_1|3|node}}
| |
| |t<sub>1,3,6</sub>
| |
| |[[Bipenticantellated 8-simplex]]
| |
| |(0,0,1,1,1,2,2,3,3)
| |
| || || || || || || ||60480 ||7560
| |
| |- align=center
| |
| !44
| |
| |
| |
| {{CDD|node|3|node_1|3|node|3|node_1|3|node|3|node|3|node|3|node_1}}
| |
| |t<sub>0,4,6</sub>
| |
| |[[Hexistericated 8-simplex]]
| |
| |(0,0,1,1,2,2,2,2,3)
| |
| || || || || || || ||30240 ||3780
| |
| |- align=center
| |
| !45
| |
| |
| |
| {{CDD|node|3|node_1|3|node_1|3|node|3|node|3|node|3|node|3|node_1}}
| |
| |t<sub>0,5,6</sub>
| |
| |[[Hexipentellated 8-simplex]]
| |
| |(0,0,1,2,2,2,2,2,3)
| |
| || || || || || || ||9072 ||1512
| |
| |- align=center
| |
| !46
| |
| |
| |
| {{CDD|node_1|3|node|3|node|3|node|3|node|3|node|3|node_1|3|node_1}}
| |
| |t<sub>0,1,7</sub>
| |
| |[[Heptitruncated 8-simplex]]
| |
| |(0,1,1,1,1,1,1,2,3)
| |
| || || || || || || ||3276 ||504
| |
| |- align=center
| |
| !47
| |
| |
| |
| {{CDD|node_1|3|node|3|node|3|node|3|node|3|node_1|3|node|3|node_1}}
| |
| |t<sub>0,2,7</sub>
| |
| |[[Hepticantellated 8-simplex]]
| |
| |(0,1,1,1,1,1,2,2,3)
| |
| || || || || || || ||12852 ||1512
| |
| |- align=center
| |
| !48
| |
| |
| |
| {{CDD|node_1|3|node|3|node|3|node|3|node_1|3|node|3|node|3|node_1}}
| |
| |t<sub>0,3,7</sub>
| |
| |[[Heptiruncinated 8-simplex]]
| |
| |(0,1,1,1,1,2,2,2,3)
| |
| || || || || || || ||23940 ||2520
| |
| |- align=center
| |
| !49
| |
| |
| |
| {{CDD|node|3|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 8-simplex]]
| |
| |(0,0,0,0,0,1,2,3,4)
| |
| || || || || || || ||12096 ||3024
| |
| |- align=center
| |
| !50
| |
| |
| |
| {{CDD|node|3|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 8-simplex]]
| |
| |(0,0,0,0,1,1,2,3,4)
| |
| || || || || || || ||45360 ||7560
| |
| |- align=center
| |
| !51
| |
| |
| |
| {{CDD|node|3|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 8-simplex]]
| |
| |(0,0,0,0,1,2,2,3,4)
| |
| || || || || || || ||34020 ||7560
| |
| |- align=center
| |
| !52
| |
| |
| |
| {{CDD|node|3|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 8-simplex]]
| |
| |(0,0,0,0,1,2,3,3,4)
| |
| || || || || || || ||34020 ||7560
| |
| |- align=center
| |
| !53
| |
| |
| |
| {{CDD|node|3|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 8-simplex]]
| |
| |(0,0,0,0,1,2,3,4,4)
| |
| || || || || || || ||30240 ||7560
| |
| |- align=center
| |
| !54
| |
| |
| |
| {{CDD|node|3|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 8-simplex]]
| |
| |(0,0,0,1,1,1,2,3,4)
| |
| || || || || || || ||70560 ||10080
| |
| |- align=center
| |
| !55
| |
| |
| |
| {{CDD|node|3|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 8-simplex]]
| |
| |(0,0,0,1,1,2,2,3,4)
| |
| || || || || || || ||98280 ||15120
| |
| |- align=center
| |
| !56
| |
| |
| |
| {{CDD|node|3|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 8-simplex]]
| |
| |(0,0,0,1,1,2,3,3,4)
| |
| || || || || || || ||90720 ||15120
| |
| |- align=center
| |
| !57
| |
| |
| |
| {{CDD|node|3|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 8-simplex]]
| |
| |(0,0,0,1,1,2,3,4,4)
| |
| || || || || || || ||83160 ||15120
| |
| |- align=center
| |
| !58
| |
| |
| |
| {{CDD|node|3|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 8-simplex]]
| |
| |(0,0,0,1,2,2,2,3,4)
| |
| || || || || || || ||50400 ||10080
| |
| |- align=center
| |
| !59
| |
| |
| |
| {{CDD|node|3|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 8-simplex]]
| |
| |(0,0,0,1,2,2,3,3,4)
| |
| || || || || || || ||83160 ||15120
| |
| |- align=center
| |
| !60
| |
| |
| |
| {{CDD|node|3|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 8-simplex]]
| |
| |(0,0,0,1,2,2,3,4,4)
| |
| || || || || || || ||68040 ||15120
| |
| |- align=center
| |
| !61
| |
| |
| |
| {{CDD|node|3|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 8-simplex]]
| |
| |(0,0,0,1,2,3,3,3,4)
| |
| || || || || || || ||50400 ||10080
| |
| |- align=center
| |
| !62
| |
| |
| |
| {{CDD|node|3|node|3|node_1|3|node_1|3|node_1|3|node|3|node_1|3|node}}
| |
| |t<sub>1,3,4,5</sub>
| |
| |[[Bisteriruncicantellated 8-simplex]]
| |
| |(0,0,0,1,2,3,3,4,4)
| |
| || || || || || || ||75600 ||15120
| |
| |- align=center BGCOLOR="#e0f0e0"
| |
| !63
| |
| |
| |
| {{CDD|node|3|node|3|node_1|3|node_1|3|node_1|3|node_1|3|node|3|node}}
| |
| |t<sub>2,3,4,5</sub>
| |
| |[[Triruncicantitruncated 8-simplex]]
| |
| |(0,0,0,1,2,3,4,4,4)
| |
| || || || || || || ||40320 ||10080
| |
| |- align=center
| |
| !64
| |
| |
| |
| {{CDD|node|3|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 8-simplex]]
| |
| |(0,0,1,1,1,1,2,3,4)
| |
| || || || || || || ||52920 ||7560
| |
| |- align=center
| |
| !65
| |
| |
| |
| {{CDD|node|3|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 8-simplex]]
| |
| |(0,0,1,1,1,2,2,3,4)
| |
| || || || || || || ||113400 ||15120
| |
| |- align=center
| |
| !66
| |
| |
| |
| {{CDD|node|3|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 8-simplex]]
| |
| |(0,0,1,1,1,2,3,3,4)
| |
| || || || || || || ||98280 ||15120
| |
| |- align=center
| |
| !67
| |
| |
| |
| {{CDD|node|3|node_1|3|node|3|node|3|node_1|3|node_1|3|node_1|3|node}}
| |
| |t<sub>1,2,3,6</sub>
| |
| |[[Bipenticantitruncated 8-simplex]]
| |
| |(0,0,1,1,1,2,3,4,4)
| |
| || || || || || || ||90720 ||15120
| |
| |- align=center
| |
| !68
| |
| |
| |
| {{CDD|node|3|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 8-simplex]]
| |
| |(0,0,1,1,2,2,2,3,4)
| |
| || || || || || || ||105840 ||15120
| |
| |- align=center
| |
| !69
| |
| |
| |
| {{CDD|node|3|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 8-simplex]]
| |
| |(0,0,1,1,2,2,3,3,4)
| |
| || || || || || || ||158760 ||22680
| |
| |- align=center
| |
| !70
| |
| |
| |
| {{CDD|node|3|node_1|3|node|3|node_1|3|node|3|node_1|3|node_1|3|node}}
| |
| |t<sub>1,2,4,6</sub>
| |
| |[[Bipentiruncitruncated 8-simplex]]
| |
| |(0,0,1,1,2,2,3,4,4)
| |
| || || || || || || ||136080 ||22680
| |
| |- align=center
| |
| !71
| |
| |
| |
| {{CDD|node|3|node_1|3|node|3|node_1|3|node_1|3|node|3|node|3|node_1}}
| |
| |t<sub>0,3,4,6</sub>
| |
| |[[Hexisteriruncinated 8-simplex]]
| |
| |(0,0,1,1,2,3,3,3,4)
| |
| || || || || || || ||90720 ||15120
| |
| |- align=center BGCOLOR="#e0f0e0"
| |
| !72
| |
| |
| |
| {{CDD|node|3|node_1|3|node|3|node_1|3|node_1|3|node|3|node_1|3|node}}
| |
| |t<sub>1,3,4,6</sub>
| |
| |[[Bipentiruncicantellated 8-simplex]]
| |
| |(0,0,1,1,2,3,3,4,4)
| |
| || || || || || || ||136080 ||22680
| |
| |- align=center
| |
| !73
| |
| |
| |
| {{CDD|node|3|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 8-simplex]]
| |
| |(0,0,1,2,2,2,2,3,4)
| |
| || || || || || || ||41580 ||7560
| |
| |- align=center
| |
| !74
| |
| |
| |
| {{CDD|node|3|node_1|3|node_1|3|node|3|node|3|node_1|3|node|3|node_1}}
| |
| |t<sub>0,2,5,6</sub>
| |
| |[[Hexipenticantellated 8-simplex]]
| |
| |(0,0,1,2,2,2,3,3,4)
| |
| || || || || || || ||98280 ||15120
| |
| |- align=center BGCOLOR="#e0f0e0"
| |
| !75
| |
| |
| |
| {{CDD|node|3|node_1|3|node_1|3|node|3|node|3|node_1|3|node_1|3|node}}
| |
| |t<sub>1,2,5,6</sub>
| |
| |[[Bipentisteritruncated 8-simplex]]
| |
| |(0,0,1,2,2,2,3,4,4)
| |
| || || || || || || ||75600 ||15120
| |
| |- align=center
| |
| !76
| |
| |
| |
| {{CDD|node|3|node_1|3|node_1|3|node|3|node_1|3|node|3|node|3|node_1}}
| |
| |t<sub>0,3,5,6</sub>
| |
| |[[Hexipentiruncinated 8-simplex]]
| |
| |(0,0,1,2,2,3,3,3,4)
| |
| || || || || || || ||98280 ||15120
| |
| |- align=center
| |
| !77
| |
| |
| |
| {{CDD|node|3|node_1|3|node_1|3|node_1|3|node|3|node|3|node|3|node_1}}
| |
| |t<sub>0,4,5,6</sub>
| |
| |[[Hexipentistericated 8-simplex]]
| |
| |(0,0,1,2,3,3,3,3,4)
| |
| || || || || || || ||41580 ||7560
| |
| |- align=center
| |
| !78
| |
| |
| |
| {{CDD|node_1|3|node|3|node|3|node|3|node|3|node_1|3|node_1|3|node_1}}
| |
| |t<sub>0,1,2,7</sub>
| |
| |[[Hepticantitruncated 8-simplex]]
| |
| |(0,1,1,1,1,1,2,3,4)
| |
| || || || || || || ||18144 ||3024
| |
| |- align=center
| |
| !79
| |
| |
| |
| {{CDD|node_1|3|node|3|node|3|node|3|node_1|3|node|3|node_1|3|node_1}}
| |
| |t<sub>0,1,3,7</sub>
| |
| |[[Heptiruncitruncated 8-simplex]]
| |
| |(0,1,1,1,1,2,2,3,4)
| |
| || || || || || || ||56700 ||7560
| |
| |- align=center
| |
| !80
| |
| |
| |
| {{CDD|node_1|3|node|3|node|3|node|3|node_1|3|node_1|3|node|3|node_1}}
| |
| |t<sub>0,2,3,7</sub>
| |
| |[[Heptiruncicantellated 8-simplex]]
| |
| |(0,1,1,1,1,2,3,3,4)
| |
| || || || || || || ||45360 ||7560
| |
| |- align=center
| |
| !81
| |
| |
| |
| {{CDD|node_1|3|node|3|node|3|node_1|3|node|3|node|3|node_1|3|node_1}}
| |
| |t<sub>0,1,4,7</sub>
| |
| |[[Heptisteritruncated 8-simplex]]
| |
| |(0,1,1,1,2,2,2,3,4)
| |
| || || || || || || ||80640 ||10080
| |
| |- align=center
| |
| !82
| |
| |
| |
| {{CDD|node_1|3|node|3|node|3|node_1|3|node|3|node_1|3|node|3|node_1}}
| |
| |t<sub>0,2,4,7</sub>
| |
| |[[Heptistericantellated 8-simplex]]
| |
| |(0,1,1,1,2,2,3,3,4)
| |
| || || || || || || ||113400 ||15120
| |
| |- align=center BGCOLOR="#e0f0e0"
| |
| !83
| |
| |
| |
| {{CDD|node_1|3|node|3|node|3|node_1|3|node_1|3|node|3|node|3|node_1}}
| |
| |t<sub>0,3,4,7</sub>
| |
| |[[Heptisteriruncinated 8-simplex]]
| |
| |(0,1,1,1,2,3,3,3,4)
| |
| || || || || || || ||60480 ||10080
| |
| |- align=center
| |
| !84
| |
| |
| |
| {{CDD|node_1|3|node|3|node_1|3|node|3|node|3|node|3|node_1|3|node_1}}
| |
| |t<sub>0,1,5,7</sub>
| |
| |[[Heptipentitruncated 8-simplex]]
| |
| |(0,1,1,2,2,2,2,3,4)
| |
| || || || || || || ||56700 ||7560
| |
| |- align=center BGCOLOR="#e0f0e0"
| |
| !85
| |
| |
| |
| {{CDD|node_1|3|node|3|node_1|3|node|3|node|3|node_1|3|node|3|node_1}}
| |
| |t<sub>0,2,5,7</sub>
| |
| |[[Heptipenticantellated 8-simplex]]
| |
| |(0,1,1,2,2,2,3,3,4)
| |
| || || || || || || ||120960 ||15120
| |
| |- align=center BGCOLOR="#e0f0e0"
| |
| !86
| |
| |
| |
| {{CDD|node_1|3|node_1|3|node|3|node|3|node|3|node|3|node_1|3|node_1}}
| |
| |t<sub>0,1,6,7</sub>
| |
| |[[Heptihexitruncated 8-simplex]]
| |
| |(0,1,2,2,2,2,2,3,4)
| |
| || || || || || || ||18144 ||3024
| |
| |- align=center
| |
| !87
| |
| |
| |
| {{CDD|node|3|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 8-simplex]]
| |
| |(0,0,0,0,1,2,3,4,5)
| |
| || || || || || || ||60480 ||15120
| |
| |- align=center
| |
| !88
| |
| |
| |
| {{CDD|node|3|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 8-simplex]]
| |
| |(0,0,0,1,1,2,3,4,5)
| |
| || || || || || || ||166320 ||30240
| |
| |- align=center
| |
| !89
| |
| |
| |
| {{CDD|node|3|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 8-simplex]]
| |
| |(0,0,0,1,2,2,3,4,5)
| |
| || || || || || || ||136080 ||30240
| |
| |- align=center
| |
| !90
| |
| |
| |
| {{CDD|node|3|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 8-simplex]]
| |
| |(0,0,0,1,2,3,3,4,5)
| |
| || || || || || || ||136080 ||30240
| |
| |- align=center
| |
| !91
| |
| |
| |
| {{CDD|node|3|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 8-simplex]]
| |
| |(0,0,0,1,2,3,4,4,5)
| |
| || || || || || || ||136080 ||30240
| |
| |- align=center
| |
| !92
| |
| |
| |
| {{CDD|node|3|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 8-simplex]]
| |
| |(0,0,0,1,2,3,4,5,5)
| |
| || || || || || || ||120960 ||30240
| |
| |- align=center
| |
| !93
| |
| |
| |
| {{CDD|node|3|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 8-simplex]]
| |
| |(0,0,1,1,1,2,3,4,5)
| |
| || || || || || || ||181440 ||30240
| |
| |- align=center
| |
| !94
| |
| |
| |
| {{CDD|node|3|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 8-simplex]]
| |
| |(0,0,1,1,2,2,3,4,5)
| |
| || || || || || || ||272160 ||45360
| |
| |- align=center
| |
| !95
| |
| |
| |
| {{CDD|node|3|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 8-simplex]]
| |
| |(0,0,1,1,2,3,3,4,5)
| |
| || || || || || || ||249480 ||45360
| |
| |- align=center
| |
| !96
| |
| |
| |
| {{CDD|node|3|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 8-simplex]]
| |
| |(0,0,1,1,2,3,4,4,5)
| |
| || || || || || || ||249480 ||45360
| |
| |- align=center
| |
| !97
| |
| |
| |
| {{CDD|node|3|node_1|3|node|3|node_1|3|node_1|3|node_1|3|node_1|3|node}}
| |
| |t<sub>1,2,3,4,6</sub>
| |
| |[[Bipentiruncicantitruncated 8-simplex]]
| |
| |(0,0,1,1,2,3,4,5,5)
| |
| || || || || || || ||226800 ||45360
| |
| |- align=center
| |
| !98
| |
| |
| |
| {{CDD|node|3|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 8-simplex]]
| |
| |(0,0,1,2,2,2,3,4,5)
| |
| || || || || || || ||151200 ||30240
| |
| |- align=center
| |
| !99
| |
| |
| |
| {{CDD|node|3|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 8-simplex]]
| |
| |(0,0,1,2,2,3,3,4,5)
| |
| || || || || || || ||249480 ||45360
| |
| |- align=center
| |
| !100
| |
| |
| |
| {{CDD|node|3|node_1|3|node_1|3|node|3|node_1|3|node_1|3|node|3|node_1}}
| |
| |t<sub>0,2,3,5,6</sub>
| |
| |[[Hexipentiruncicantellated 8-simplex]]
| |
| |(0,0,1,2,2,3,4,4,5)
| |
| || || || || || || ||226800 ||45360
| |
| |- align=center
| |
| !101
| |
| |
| |
| {{CDD|node|3|node_1|3|node_1|3|node|3|node_1|3|node_1|3|node_1|3|node}}
| |
| |t<sub>1,2,3,5,6</sub>
| |
| |[[Bipentistericantitruncated 8-simplex]]
| |
| |(0,0,1,2,2,3,4,5,5)
| |
| || || || || || || ||204120 ||45360
| |
| |- align=center
| |
| !102
| |
| |
| |
| {{CDD|node|3|node_1|3|node_1|3|node_1|3|node|3|node|3|node_1|3|node_1}}
| |
| |t<sub>0,1,4,5,6</sub>
| |
| |[[Hexipentisteritruncated 8-simplex]]
| |
| |(0,0,1,2,3,3,3,4,5)
| |
| || || || || || || ||151200 ||30240
| |
| |- align=center
| |
| !103
| |
| |
| |
| {{CDD|node|3|node_1|3|node_1|3|node_1|3|node|3|node_1|3|node|3|node_1}}
| |
| |t<sub>0,2,4,5,6</sub>
| |
| |[[Hexipentistericantellated 8-simplex]]
| |
| |(0,0,1,2,3,3,4,4,5)
| |
| || || || || || || ||249480 ||45360
| |
| |- align=center
| |
| !104
| |
| |
| |
| {{CDD|node|3|node_1|3|node_1|3|node_1|3|node_1|3|node|3|node|3|node_1}}
| |
| |t<sub>0,3,4,5,6</sub>
| |
| |[[Hexipentisteriruncinated 8-simplex]]
| |
| |(0,0,1,2,3,4,4,4,5)
| |
| || || || || || || ||151200 ||30240
| |
| |- align=center
| |
| !105
| |
| |
| |
| {{CDD|node_1|3|node|3|node|3|node|3|node_1|3|node_1|3|node_1|3|node_1}}
| |
| |t<sub>0,1,2,3,7</sub>
| |
| |[[Heptiruncicantitruncated 8-simplex]]
| |
| |(0,1,1,1,1,2,3,4,5)
| |
| || || || || || || ||83160 ||15120
| |
| |- align=center
| |
| !106
| |
| |
| |
| {{CDD|node_1|3|node|3|node|3|node_1|3|node|3|node_1|3|node_1|3|node_1}}
| |
| |t<sub>0,1,2,4,7</sub>
| |
| |[[Heptistericantitruncated 8-simplex]]
| |
| |(0,1,1,1,2,2,3,4,5)
| |
| || || || || || || ||196560 ||30240
| |
| |- align=center
| |
| !107
| |
| |
| |
| {{CDD|node_1|3|node|3|node|3|node_1|3|node_1|3|node|3|node_1|3|node_1}}
| |
| |t<sub>0,1,3,4,7</sub>
| |
| |[[Heptisteriruncitruncated 8-simplex]]
| |
| |(0,1,1,1,2,3,3,4,5)
| |
| || || || || || || ||166320 ||30240
| |
| |- align=center
| |
| !108
| |
| |
| |
| {{CDD|node_1|3|node|3|node|3|node_1|3|node_1|3|node_1|3|node|3|node_1}}
| |
| |t<sub>0,2,3,4,7</sub>
| |
| |[[Heptisteriruncicantellated 8-simplex]]
| |
| |(0,1,1,1,2,3,4,4,5)
| |
| || || || || || || ||166320 ||30240
| |
| |- align=center
| |
| !109
| |
| |
| |
| {{CDD|node_1|3|node|3|node_1|3|node|3|node|3|node_1|3|node_1|3|node_1}}
| |
| |t<sub>0,1,2,5,7</sub>
| |
| |[[Heptipenticantitruncated 8-simplex]]
| |
| |(0,1,1,2,2,2,3,4,5)
| |
| || || || || || || ||196560 ||30240
| |
| |- align=center
| |
| !110
| |
| |
| |
| {{CDD|node_1|3|node|3|node_1|3|node|3|node_1|3|node|3|node_1|3|node_1}}
| |
| |t<sub>0,1,3,5,7</sub>
| |
| |[[Heptipentiruncitruncated 8-simplex]]
| |
| |(0,1,1,2,2,3,3,4,5)
| |
| || || || || || || ||294840 ||45360
| |
| |- align=center
| |
| !111
| |
| |
| |
| {{CDD|node_1|3|node|3|node_1|3|node|3|node_1|3|node_1|3|node|3|node_1}}
| |
| |t<sub>0,2,3,5,7</sub>
| |
| |[[Heptipentiruncicantellated 8-simplex]]
| |
| |(0,1,1,2,2,3,4,4,5)
| |
| || || || || || || ||272160 ||45360
| |
| |- align=center
| |
| !112
| |
| |
| |
| {{CDD|node_1|3|node|3|node_1|3|node_1|3|node|3|node|3|node_1|3|node_1}}
| |
| |t<sub>0,1,4,5,7</sub>
| |
| |[[Heptipentisteritruncated 8-simplex]]
| |
| |(0,1,1,2,3,3,3,4,5)
| |
| || || || || || || ||166320 ||30240
| |
| |- align=center
| |
| !113
| |
| |
| |
| {{CDD|node_1|3|node_1|3|node|3|node|3|node|3|node_1|3|node_1|3|node_1}}
| |
| |t<sub>0,1,2,6,7</sub>
| |
| |[[Heptihexicantitruncated 8-simplex]]
| |
| |(0,1,2,2,2,2,3,4,5)
| |
| || || || || || || ||83160 ||15120
| |
| |- align=center
| |
| !114
| |
| |
| |
| {{CDD|node_1|3|node_1|3|node|3|node|3|node_1|3|node|3|node_1|3|node_1}}
| |
| |t<sub>0,1,3,6,7</sub>
| |
| |[[Heptihexiruncitruncated 8-simplex]]
| |
| |(0,1,2,2,2,3,3,4,5)
| |
| || || || || || || ||196560 ||30240
| |
| |- align=center
| |
| !115
| |
| |
| |
| {{CDD|node|3|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 8-simplex]]
| |
| |(0,0,0,1,2,3,4,5,6)
| |
| || || || || || || ||241920 ||60480
| |
| |- align=center
| |
| !116
| |
| |
| |
| {{CDD|node|3|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 8-simplex]]
| |
| |(0,0,1,1,2,3,4,5,6)
| |
| || || || || || || ||453600 ||90720
| |
| |- align=center
| |
| !117
| |
| |
| |
| {{CDD|node|3|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 8-simplex]]
| |
| |(0,0,1,2,2,3,4,5,6)
| |
| || || || || || || ||408240 ||90720
| |
| |- align=center
| |
| !118
| |
| |
| |
| {{CDD|node|3|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 8-simplex]]
| |
| |(0,0,1,2,3,3,4,5,6)
| |
| || || || || || || ||408240 ||90720
| |
| |- align=center
| |
| !119
| |
| |
| |
| {{CDD|node|3|node_1|3|node_1|3|node_1|3|node_1|3|node|3|node_1|3|node_1}}
| |
| |t<sub>0,1,3,4,5,6</sub>
| |
| |[[Hexipentisteriruncitruncated 8-simplex]]
| |
| |(0,0,1,2,3,4,4,5,6)
| |
| || || || || || || ||408240 ||90720
| |
| |- align=center
| |
| !120
| |
| |
| |
| {{CDD|node|3|node_1|3|node_1|3|node_1|3|node_1|3|node_1|3|node|3|node_1}}
| |
| |t<sub>0,2,3,4,5,6</sub>
| |
| |[[Hexipentisteriruncicantellated 8-simplex]]
| |
| |(0,0,1,2,3,4,5,5,6)
| |
| || || || || || || ||408240 ||90720
| |
| |- align=center BGCOLOR="#e0f0e0"
| |
| !121
| |
| |
| |
| {{CDD|node|3|node_1|3|node_1|3|node_1|3|node_1|3|node_1|3|node_1|3|node}}
| |
| |t<sub>1,2,3,4,5,6</sub>
| |
| |[[Bipentisteriruncicantitruncated 8-simplex]]
| |
| |(0,0,1,2,3,4,5,6,6)
| |
| || || || || || || ||362880 ||90720
| |
| |- align=center
| |
| !122
| |
| |
| |
| {{CDD|node_1|3|node|3|node|3|node_1|3|node_1|3|node_1|3|node_1|3|node_1}}
| |
| |t<sub>0,1,2,3,4,7</sub>
| |
| |[[Heptisteriruncicantitruncated 8-simplex]]
| |
| |(0,1,1,1,2,3,4,5,6)
| |
| || || || || || || ||302400 ||60480
| |
| |- align=center
| |
| !123
| |
| |
| |
| {{CDD|node_1|3|node|3|node_1|3|node|3|node_1|3|node_1|3|node_1|3|node_1}}
| |
| |t<sub>0,1,2,3,5,7</sub>
| |
| |[[Heptipentiruncicantitruncated 8-simplex]]
| |
| |(0,1,1,2,2,3,4,5,6)
| |
| || || || || || || ||498960 ||90720
| |
| |- align=center
| |
| !124
| |
| |
| |
| {{CDD|node_1|3|node|3|node_1|3|node_1|3|node|3|node_1|3|node_1|3|node_1}}
| |
| |t<sub>0,1,2,4,5,7</sub>
| |
| |[[Heptipentistericantitruncated 8-simplex]]
| |
| |(0,1,1,2,3,3,4,5,6)
| |
| || || || || || || ||453600 ||90720
| |
| |- align=center
| |
| !125
| |
| |
| |
| {{CDD|node_1|3|node|3|node_1|3|node_1|3|node_1|3|node|3|node_1|3|node_1}}
| |
| |t<sub>0,1,3,4,5,7</sub>
| |
| |[[Heptipentisteriruncitruncated 8-simplex]]
| |
| |(0,1,1,2,3,4,4,5,6)
| |
| || || || || || || ||453600 ||90720
| |
| |- align=center BGCOLOR="#e0f0e0"
| |
| !126
| |
| |
| |
| {{CDD|node_1|3|node|3|node_1|3|node_1|3|node_1|3|node_1|3|node|3|node_1}}
| |
| |t<sub>0,2,3,4,5,7</sub>
| |
| |[[Heptipentisteriruncicantellated 8-simplex]]
| |
| |(0,1,1,2,3,4,5,5,6)
| |
| || || || || || || ||453600 ||90720
| |
| |- align=center
| |
| !127
| |
| |
| |
| {{CDD|node_1|3|node_1|3|node|3|node|3|node_1|3|node_1|3|node_1|3|node_1}}
| |
| |t<sub>0,1,2,3,6,7</sub>
| |
| |[[Heptihexiruncicantitruncated 8-simplex]]
| |
| |(0,1,2,2,2,3,4,5,6)
| |
| || || || || || || ||302400 ||60480
| |
| |- align=center
| |
| !128
| |
| |
| |
| {{CDD|node_1|3|node_1|3|node|3|node_1|3|node|3|node_1|3|node_1|3|node_1}}
| |
| |t<sub>0,1,2,4,6,7</sub>
| |
| |[[Heptihexistericantitruncated 8-simplex]]
| |
| |(0,1,2,2,3,3,4,5,6)
| |
| || || || || || || ||498960 ||90720
| |
| |- align=center BGCOLOR="#e0f0e0"
| |
| !129
| |
| |
| |
| {{CDD|node_1|3|node_1|3|node|3|node_1|3|node_1|3|node|3|node_1|3|node_1}}
| |
| |t<sub>0,1,3,4,6,7</sub>
| |
| |[[Heptihexisteriruncitruncated 8-simplex]]
| |
| |(0,1,2,2,3,4,4,5,6)
| |
| || || || || || || ||453600 ||90720
| |
| |- align=center BGCOLOR="#e0f0e0"
| |
| !130
| |
| |
| |
| {{CDD|node_1|3|node_1|3|node_1|3|node|3|node|3|node_1|3|node_1|3|node_1}}
| |
| |t<sub>0,1,2,5,6,7</sub>
| |
| |[[Heptihexipenticantitruncated 8-simplex]]
| |
| |(0,1,2,3,3,3,4,5,6)
| |
| || || || || || || ||302400 ||60480
| |
| |- align=center
| |
| !131
| |
| |
| |
| {{CDD|node|3|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>
| |
| |[[Hexipentisteriruncicantitruncated 8-simplex]]
| |
| |(0,0,1,2,3,4,5,6,7)
| |
| || || || || || || ||725760 ||181440
| |
| |- align=center
| |
| !132
| |
| |
| |
| {{CDD|node_1|3|node|3|node_1|3|node_1|3|node_1|3|node_1|3|node_1|3|node_1}}
| |
| |t<sub>0,1,2,3,4,5,7</sub>
| |
| |[[Heptipentisteriruncicantitruncated 8-simplex]]
| |
| |(0,1,1,2,3,4,5,6,7)
| |
| || || || || || || ||816480 ||181440
| |
| |- align=center
| |
| !133
| |
| |
| |
| {{CDD|node_1|3|node_1|3|node|3|node_1|3|node_1|3|node_1|3|node_1|3|node_1}}
| |
| |t<sub>0,1,2,3,4,6,7</sub>
| |
| |[[Heptihexisteriruncicantitruncated 8-simplex]]
| |
| |(0,1,2,2,3,4,5,6,7)
| |
| || || || || || || ||816480 ||181440
| |
| |- align=center
| |
| !134
| |
| |
| |
| {{CDD|node_1|3|node_1|3|node_1|3|node|3|node_1|3|node_1|3|node_1|3|node_1}}
| |
| |t<sub>0,1,2,3,5,6,7</sub>
| |
| |[[Heptihexipentiruncicantitruncated 8-simplex]]
| |
| |(0,1,2,3,3,4,5,6,7)
| |
| || || || || || || ||816480 ||181440
| |
| |- align=center BGCOLOR="#e0f0e0"
| |
| !135
| |
| |
| |
| {{CDD|node_1|3|node_1|3|node_1|3|node_1|3|node_1|3|node_1|3|node_1|3|node_1}}
| |
| |t<sub>0,1,2,3,4,5,6,7</sub>
| |
| |[[Omnitruncated 8-simplex]]
| |
| |(0,1,2,3,4,5,6,7,8)
| |
| || || || || || || ||1451520 ||362880
| |
| |}
| |
| | |
| === The B<sub>8</sub> family ===
| |
| | |
| The B<sub>8</sub> family has symmetry of order 10321920 (8 [[factorial]] x 2<sup>8</sup>). There are 255 forms based on all permutations of the [[Coxeter-Dynkin diagram]]s with one or more rings.
| |
| | |
| See also a [[list of B8 polytopes]] for symmetric [[Coxeter plane]] graphs of these polytopes.
| |
| | |
| {| class="wikitable"
| |
| !rowspan=2|#
| |
| !rowspan=2|[[Coxeter-Dynkin diagram]]
| |
| !rowspan=2|[[Schläfli symbol|Schläfli<BR>symbol]]
| |
| !rowspan=2|Name
| |
| !colspan=8|Element counts
| |
| |-
| |
| ! 7|| 6|| 5|| 4|| 3|| 2|| 1|| 0
| |
| |- align=center BGCOLOR="#f0e0e0"
| |
| !1
| |
| |<!-- [x3o3o3o3o3o3o4o] -->{{CDD|node|4|node|3|node|3|node|3|node|3|node|3|node|3|node_1}}||t<sub>0</sub>{3<sup>6</sup>,4}||[[8-orthoplex]]<BR>Diacosipentacontahexazetton (ek)||256||1024||1792||1792||1120||448||112||16
| |
| |- align=center BGCOLOR="#f0e0e0"
| |
| !2
| |
| |<!-- [o3x3o3o3o3o3o4o] -->{{CDD|node|4|node|3|node|3|node|3|node|3|node|3|node_1|3|node}}||t<sub>1</sub>{3<sup>6</sup>,4}||[[Rectified 8-orthoplex]]<BR>Rectified diacosipentacontahexazetton (rek)||272||3072||8960||12544||10080||4928||1344||112
| |
| |- align=center BGCOLOR="#f0e0e0"
| |
| !3
| |
| |<!-- [o3o3x3o3o3o3o4o] -->{{CDD|node|4|node|3|node|3|node|3|node|3|node_1|3|node|3|node}}||t<sub>2</sub>{3<sup>6</sup>,4}||[[Birectified 8-orthoplex]]<BR>Birectified diacosipentacontahexazetton (bark)||272||3184||16128||34048||36960||22400||6720||448
| |
| |- align=center BGCOLOR="#f0e0e0"
| |
| !4
| |
| |<!-- [o3o3o3x3o3o3o4o] -->{{CDD|node|4|node|3|node|3|node|3|node_1|3|node|3|node|3|node}}||t<sub>3</sub>{3<sup>6</sup>,4}||[[Trirectified 8-orthoplex]]<BR>Trirectified diacosipentacontahexazetton (tark)||272||3184||16576||48384||71680||53760||17920||1120
| |
| |- align=center BGCOLOR="#e0e0f0"
| |
| !5
| |
| |<!-- [o3o3o3o3x3o3o4o] -->{{CDD|node|4|node|3|node|3|node_1|3|node|3|node|3|node|3|node}}||t<sub>3</sub>{4,3<sup>6</sup>}||[[Trirectified 8-cube]]<BR>Trirectified octeract (tro)||272||3184||16576||47712||80640||71680||26880||1792
| |
| |- align=center BGCOLOR="#e0e0f0"
| |
| !6
| |
| |<!-- [o3o3o3o3o3x3o4o] -->{{CDD|node|4|node|3|node_1|3|node|3|node|3|node|3|node|3|node}}||t<sub>2</sub>{4,3<sup>6</sup>}||[[Birectified 8-cube]]<BR>Birectified octeract (bro)||272||3184||14784||36960||55552||50176||21504||1792
| |
| |- align=center BGCOLOR="#e0e0f0"
| |
| !7
| |
| |<!-- [o3o3o3o3o3o3x4o] -->{{CDD|node|4|node_1|3|node|3|node|3|node|3|node|3|node|3|node}}||t<sub>1</sub>{4,3<sup>6</sup>}||[[Rectified 8-cube]]<BR>Rectified octeract (recto)||272||2160||7616||15456||19712||16128||7168||1024
| |
| |- align=center BGCOLOR="#e0e0f0"
| |
| !8
| |
| |<!-- [o3o3o3o3o3o3o4x] -->{{CDD|node_1|4|node|3|node|3|node|3|node|3|node|3|node|3|node}}||t<sub>0</sub>{4,3<sup>6</sup>}||[[8-cube]]<BR>Octeract (octo)||16||112||448||1120||1792||1792||1024||256
| |
| |- align=center BGCOLOR="#f0e0e0"
| |
| !9
| |
| |<!-- [x3x3o3o3o3o3o4o] -->{{CDD|node|4|node|3|node|3|node|3|node|3|node|3|node_1|3|node_1}}||t<sub>0,1</sub>{3<sup>6</sup>,4}||[[Truncated 8-orthoplex]]<BR>Truncated diacosipentacontahexazetton (tek)||||||||||||||1456||224
| |
| |- align=center BGCOLOR="#f0e0e0"
| |
| !10
| |
| |<!-- [x3o3x3o3o3o3o4o] -->{{CDD|node|4|node|3|node|3|node|3|node|3|node_1|3|node|3|node_1}}||t<sub>0,2</sub>{3<sup>6</sup>,4}||[[Cantellated 8-orthoplex]]<BR>Small rhombated diacosipentacontahexazetton (srek)||||||||||||||14784||1344
| |
| |- align=center BGCOLOR="#f0e0e0"
| |
| !11
| |
| |<!-- [o3x3x3o3o3o3o4o] -->{{CDD|node|4|node|3|node|3|node|3|node|3|node_1|3|node_1|3|node}}||t<sub>1,2</sub>{3<sup>6</sup>,4}||[[Bitruncated 8-orthoplex]]<BR>Bitruncated diacosipentacontahexazetton (batek)||||||||||||||8064||1344
| |
| |- align=center BGCOLOR="#f0e0e0"
| |
| !12
| |
| |<!-- [x3o3o3x3o3o3o4o] -->{{CDD|node|4|node|3|node|3|node|3|node_1|3|node|3|node|3|node_1}}||t<sub>0,3</sub>{3<sup>6</sup>,4}||[[Runcinated 8-orthoplex]]<BR>Small prismated diacosipentacontahexazetton (spek)||||||||||||||60480||4480
| |
| |- align=center BGCOLOR="#f0e0e0"
| |
| !13
| |
| |<!-- [o3x3o3x3o3o3o4o] -->{{CDD|node|4|node|3|node|3|node|3|node_1|3|node|3|node_1|3|node}}||t<sub>1,3</sub>{3<sup>6</sup>,4}||[[Bicantellated 8-orthoplex]]<BR>Small birhombated diacosipentacontahexazetton (sabork)||||||||||||||67200||6720
| |
| |- align=center BGCOLOR="#f0e0e0"
| |
| !14
| |
| |<!-- [o3o3x3x3o3o3o4o] -->{{CDD|node|4|node|3|node|3|node|3|node_1|3|node_1|3|node|3|node}}||t<sub>2,3</sub>{3<sup>6</sup>,4}||[[Tritruncated 8-orthoplex]]<BR>Tritruncated diacosipentacontahexazetton (tatek)||||||||||||||24640||4480
| |
| |- align=center BGCOLOR="#f0e0e0"
| |
| !15
| |
| |<!-- [x3o3o3o3x3o3o4o] -->{{CDD|node|4|node|3|node|3|node_1|3|node|3|node|3|node|3|node_1}}||t<sub>0,4</sub>{3<sup>6</sup>,4}||[[Stericated 8-orthoplex]]<BR>Small cellated diacosipentacontahexazetton (scak)||||||||||||||125440||8960
| |
| |- align=center BGCOLOR="#f0e0e0"
| |
| !16
| |
| |<!-- [o3x3o3o3x3o3o4o] -->{{CDD|node|4|node|3|node|3|node_1|3|node|3|node|3|node_1|3|node}}||t<sub>1,4</sub>{3<sup>6</sup>,4}||[[Biruncinated 8-orthoplex]]<BR>Small biprismated diacosipentacontahexazetton (sabpek)||||||||||||||215040||17920
| |
| |- align=center BGCOLOR="#f0e0e0"
| |
| !17
| |
| |<!-- [o3o3x3o3x3o3o4o] -->{{CDD|node|4|node|3|node|3|node_1|3|node|3|node_1|3|node|3|node}}||t<sub>2,4</sub>{3<sup>6</sup>,4}||[[Tricantellated 8-orthoplex]]<BR>Small trirhombated diacosipentacontahexazetton (satrek)||||||||||||||161280||17920
| |
| |- align=center BGCOLOR="#e0f0e0"
| |
| !18
| |
| |<!-- [o3o3o3x3x3o3o4o] -->{{CDD|node|4|node|3|node|3|node_1|3|node_1|3|node|3|node|3|node}}||t<sub>3,4</sub>{4,3<sup>6</sup>}||[[Quadritruncated 8-cube]]<BR>Octeractidiacosipentacontahexazetton (oke)||||||||||||||44800||8960
| |
| |- align=center BGCOLOR="#f0e0e0"
| |
| !19
| |
| |<!-- [x3o3o3o3o3x3o4o] -->{{CDD|node|4|node|3|node_1|3|node|3|node|3|node|3|node|3|node_1}}||t<sub>0,5</sub>{3<sup>6</sup>,4}||[[Pentellated 8-orthoplex]]<BR>Small terated diacosipentacontahexazetton (setek)||||||||||||||134400||10752
| |
| |- align=center BGCOLOR="#f0e0e0"
| |
| !20
| |
| |<!-- [o3x3o3o3o3x3o4o] -->{{CDD|node|4|node|3|node_1|3|node|3|node|3|node|3|node_1|3|node}}||t<sub>1,5</sub>{3<sup>6</sup>,4}||[[Bistericated 8-orthoplex]]<BR>Small bicellated diacosipentacontahexazetton (sibcak)||||||||||||||322560||26880
| |
| |- align=center BGCOLOR="#e0f0e0"
| |
| !21
| |
| |<!-- [o3o3x3o3o3x3o4o] -->{{CDD|node|4|node|3|node_1|3|node|3|node|3|node_1|3|node|3|node}}||t<sub>2,5</sub>{4,3<sup>6</sup>}||[[Triruncinated 8-cube]]<BR>Small triprismato-octeractidiacosipentacontahexazetton (sitpoke)||||||||||||||376320||35840
| |
| |- align=center BGCOLOR="#e0e0f0"
| |
| !22
| |
| |<!-- [o3o3o3x3o3x3o4o] -->{{CDD|node|4|node|3|node_1|3|node|3|node_1|3|node|3|node|3|node}}||t<sub>2,4</sub>{4,3<sup>6</sup>}||[[Tricantellated 8-cube]]<BR>Small trirhombated octeract (satro)||||||||||||||215040||26880
| |
| |- align=center BGCOLOR="#e0e0f0"
| |
| !23
| |
| |<!-- [o3o3o3o3x3x3o4o] -->{{CDD|node|4|node|3|node_1|3|node_1|3|node|3|node|3|node|3|node}}||t<sub>2,3</sub>{4,3<sup>6</sup>}||[[Tritruncated 8-cube]]<BR>Tritruncated octeract (tato)||||||||||||||48384||10752
| |
| |- align=center BGCOLOR="#f0e0e0"
| |
| !24
| |
| |<!-- [x3o3o3o3o3o3x4o] -->{{CDD|node|4|node_1|3|node|3|node|3|node|3|node|3|node|3|node_1}}||t<sub>0,6</sub>{3<sup>6</sup>,4}||[[Hexicated 8-orthoplex]]<BR>Small petated diacosipentacontahexazetton (supek)||||||||||||||64512||7168
| |
| |- align=center BGCOLOR="#e0f0e0"
| |
| !25
| |
| |<!-- [o3x3o3o3o3o3x4o] -->{{CDD|node|4|node_1|3|node|3|node|3|node|3|node|3|node_1|3|node}}||t<sub>1,6</sub>{4,3<sup>6</sup>}||[[Bipentellated 8-cube]]<BR>Small biteri-octeractidiacosipentacontahexazetton (sabtoke)||||||||||||||215040||21504
| |
| |- align=center BGCOLOR="#e0e0f0"
| |
| !26
| |
| |<!-- [o3o3x3o3o3o3x4o] -->{{CDD|node|4|node_1|3|node|3|node|3|node|3|node_1|3|node|3|node}}||t<sub>1,5</sub>{4,3<sup>6</sup>}||[[Bistericated 8-cube]]<BR>Small bicellated octeract (sobco)||||||||||||||358400||35840
| |
| |- align=center BGCOLOR="#e0e0f0"
| |
| !27
| |
| |<!-- [o3o3o3x3o3o3x4o] -->{{CDD|node|4|node_1|3|node|3|node|3|node_1|3|node|3|node|3|node}}||t<sub>1,4</sub>{4,3<sup>6</sup>}||[[Biruncinated 8-cube]]<BR>Small biprismated octeract (sabepo)||||||||||||||322560||35840
| |
| |- align=center BGCOLOR="#e0e0f0"
| |
| !28
| |
| |<!-- [o3o3o3o3x3o3x4o] -->{{CDD|node|4|node_1|3|node|3|node_1|3|node|3|node|3|node|3|node}}||t<sub>1,3</sub>{4,3<sup>6</sup>}||[[Bicantellated 8-cube]]<BR>Small birhombated octeract (subro)||||||||||||||150528||21504
| |
| |- align=center BGCOLOR="#e0e0f0"
| |
| !29
| |
| |<!-- [o3o3o3o3o3x3x4o] -->{{CDD|node|4|node_1|3|node_1|3|node|3|node|3|node|3|node|3|node}}||t<sub>1,2</sub>{4,3<sup>6</sup>}||[[Bitruncated 8-cube]]<BR>Bitruncated octeract (bato)||||||||||||||28672||7168
| |
| |- align=center BGCOLOR="#e0f0e0"
| |
| !30
| |
| |<!-- [x3o3o3o3o3o3o4x] -->{{CDD|node_1|4|node|3|node|3|node|3|node|3|node|3|node|3|node_1}}||t<sub>0,7</sub>{4,3<sup>6</sup>}||[[Heptellated 8-cube]]<BR>Small exi-octeractidiacosipentacontahexazetton (saxoke)||||||||||||||14336||2048
| |
| |- align=center BGCOLOR="#e0e0f0"
| |
| !31
| |
| |<!-- [o3x3o3o3o3o3o4x] -->{{CDD|node_1|4|node|3|node|3|node|3|node|3|node|3|node_1|3|node}}||t<sub>0,6</sub>{4,3<sup>6</sup>}||[[Hexicated 8-cube]]<BR>Small petated octeract (supo)||||||||||||||64512||7168
| |
| |- align=center BGCOLOR="#e0e0f0"
| |
| !32
| |
| |<!-- [o3o3x3o3o3o3o4x] -->{{CDD|node_1|4|node|3|node|3|node|3|node|3|node_1|3|node|3|node}}||t<sub>0,5</sub>{4,3<sup>6</sup>}||[[Pentellated 8-cube]]<BR>Small terated octeract (soto)||||||||||||||143360||14336
| |
| |- align=center BGCOLOR="#e0e0f0"
| |
| !33
| |
| |<!-- [o3o3o3x3o3o3o4x] -->{{CDD|node_1|4|node|3|node|3|node|3|node_1|3|node|3|node|3|node}}||t<sub>0,4</sub>{4,3<sup>6</sup>}||[[Stericated 8-cube]]<BR>Small cellated octeract (soco)||||||||||||||179200||17920
| |
| |- align=center BGCOLOR="#e0e0f0"
| |
| !34
| |
| |<!-- [o3o3o3o3x3o3o4x] -->{{CDD|node_1|4|node|3|node|3|node_1|3|node|3|node|3|node|3|node}}||t<sub>0,3</sub>{4,3<sup>6</sup>}||[[Runcinated 8-cube]]<BR>Small prismated octeract (sopo)||||||||||||||129024||14336
| |
| |- align=center BGCOLOR="#e0e0f0"
| |
| !35
| |
| |<!-- [o3o3o3o3o3x3o4x] -->{{CDD|node_1|4|node|3|node_1|3|node|3|node|3|node|3|node|3|node}}||t<sub>0,2</sub>{4,3<sup>6</sup>}||[[Cantellated 8-cube]]<BR>Small rhombated octeract (soro)||||||||||||||50176||7168
| |
| |- align=center BGCOLOR="#e0e0f0"
| |
| !36
| |
| |<!-- [o3o3o3o3o3o3x4x] -->{{CDD|node_1|4|node_1|3|node|3|node|3|node|3|node|3|node|3|node}}||t<sub>0,1</sub>{4,3<sup>6</sup>}||[[Truncated 8-cube]]<BR>Truncated octeract (tocto)||||||||||||||8192||2048
| |
| |- align=center BGCOLOR="#f0e0e0"
| |
| !37
| |
| |<!-- [x3x3x3o3o3o3o4o] -->{{CDD|node|4|node|3|node|3|node|3|node|3|node_1|3|node_1|3|node_1}}||t<sub>0,1,2</sub>{3<sup>6</sup>,4}||[[Cantitruncated 8-orthoplex]]<BR>Great rhombated diacosipentacontahexazetton||||||||||||||16128||2688
| |
| |- align=center BGCOLOR="#f0e0e0"
| |
| !38
| |
| |<!-- [x3x3o3x3o3o3o4o] -->{{CDD|node|4|node|3|node|3|node|3|node_1|3|node|3|node_1|3|node_1}}||t<sub>0,1,3</sub>{3<sup>6</sup>,4}||[[Runcitruncated 8-orthoplex]]<BR>Prismatotruncated diacosipentacontahexazetton||||||||||||||127680||13440
| |
| |- align=center BGCOLOR="#f0e0e0"
| |
| !39
| |
| |<!-- [x3o3x3x3o3o3o4o] -->{{CDD|node|4|node|3|node|3|node|3|node_1|3|node_1|3|node|3|node_1}}||t<sub>0,2,3</sub>{3<sup>6</sup>,4}||[[Runcicantellated 8-orthoplex]]<BR>Prismatorhombated diacosipentacontahexazetton||||||||||||||80640||13440
| |
| |- align=center BGCOLOR="#f0e0e0"
| |
| !40
| |
| |<!-- [o3x3x3x3o3o3o4o] -->{{CDD|node|4|node|3|node|3|node|3|node_1|3|node_1|3|node_1|3|node}}||t<sub>1,2,3</sub>{3<sup>6</sup>,4}||[[Bicantitruncated 8-orthoplex]]<BR>Great birhombated diacosipentacontahexazetton||||||||||||||73920||13440
| |
| |- align=center BGCOLOR="#f0e0e0"
| |
| !41
| |
| |<!-- [x3x3o3o3x3o3o4o] -->{{CDD|node|4|node|3|node|3|node_1|3|node|3|node|3|node_1|3|node_1}}||t<sub>0,1,4</sub>{3<sup>6</sup>,4}||[[Steritruncated 8-orthoplex]]<BR>Cellitruncated diacosipentacontahexazetton||||||||||||||394240||35840
| |
| |- align=center BGCOLOR="#f0e0e0"
| |
| !42
| |
| |<!-- [x3o3x3o3x3o3o4o] -->{{CDD|node|4|node|3|node|3|node_1|3|node|3|node_1|3|node|3|node_1}}||t<sub>0,2,4</sub>{3<sup>6</sup>,4}||[[Stericantellated 8-orthoplex]]<BR>Cellirhombated diacosipentacontahexazetton||||||||||||||483840||53760
| |
| |- align=center BGCOLOR="#f0e0e0"
| |
| !43
| |
| |<!-- [o3x3x3o3x3o3o4o] -->{{CDD|node|4|node|3|node|3|node_1|3|node|3|node_1|3|node_1|3|node}}||t<sub>1,2,4</sub>{3<sup>6</sup>,4}||[[Biruncitruncated 8-orthoplex]]<BR>Biprismatotruncated diacosipentacontahexazetton||||||||||||||430080||53760
| |
| |- align=center BGCOLOR="#f0e0e0"
| |
| !44
| |
| |<!-- [x3o3o3x3x3o3o4o] -->{{CDD|node|4|node|3|node|3|node_1|3|node_1|3|node|3|node|3|node_1}}||t<sub>0,3,4</sub>{3<sup>6</sup>,4}||[[Steriruncinated 8-orthoplex]]<BR>Celliprismated diacosipentacontahexazetton||||||||||||||215040||35840
| |
| |- align=center BGCOLOR="#f0e0e0"
| |
| !45
| |
| |<!-- [o3x3o3x3x3o3o4o] -->{{CDD|node|4|node|3|node|3|node_1|3|node_1|3|node|3|node_1|3|node}}||t<sub>1,3,4</sub>{3<sup>6</sup>,4}||[[Biruncicantellated 8-orthoplex]]<BR>Biprismatorhombated diacosipentacontahexazetton||||||||||||||322560||53760
| |
| |- align=center BGCOLOR="#f0e0e0"
| |
| !46
| |
| |<!-- [o3o3x3x3x3o3o4o] -->{{CDD|node|4|node|3|node|3|node_1|3|node_1|3|node_1|3|node|3|node}}||t<sub>2,3,4</sub>{3<sup>6</sup>,4}||[[Tricantitruncated 8-orthoplex]]<BR>Great trirhombated diacosipentacontahexazetton||||||||||||||179200||35840
| |
| |- align=center BGCOLOR="#f0e0e0"
| |
| !47
| |
| |<!-- [x3x3o3o3o3x3o4o] -->{{CDD|node|4|node|3|node_1|3|node|3|node|3|node|3|node_1|3|node_1}}||t<sub>0,1,5</sub>{3<sup>6</sup>,4}||[[Pentitruncated 8-orthoplex]]<BR>Teritruncated diacosipentacontahexazetton||||||||||||||564480||53760
| |
| |- align=center BGCOLOR="#f0e0e0"
| |
| !48
| |
| |<!-- [x3o3x3o3o3x3o4o] -->{{CDD|node|4|node|3|node_1|3|node|3|node|3|node_1|3|node|3|node_1}}||t<sub>0,2,5</sub>{3<sup>6</sup>,4}||[[Penticantellated 8-orthoplex]]<BR>Terirhombated diacosipentacontahexazetton||||||||||||||1075200||107520
| |
| |- align=center BGCOLOR="#f0e0e0"
| |
| !49
| |
| |<!-- [o3x3x3o3o3x3o4o] -->{{CDD|node|4|node|3|node_1|3|node|3|node|3|node_1|3|node_1|3|node}}||t<sub>1,2,5</sub>{3<sup>6</sup>,4}||[[Bisteritruncated 8-orthoplex]]<BR>Bicellitruncated diacosipentacontahexazetton||||||||||||||913920||107520
| |
| |- align=center BGCOLOR="#f0e0e0"
| |
| !50
| |
| |<!-- [x3o3o3x3o3x3o4o] -->{{CDD|node|4|node|3|node_1|3|node|3|node_1|3|node|3|node|3|node_1}}||t<sub>0,3,5</sub>{3<sup>6</sup>,4}||[[Pentiruncinated 8-orthoplex]]<BR>Teriprismated diacosipentacontahexazetton||||||||||||||913920||107520
| |
| |- align=center BGCOLOR="#f0e0e0"
| |
| !51
| |
| |<!-- [o3x3o3x3o3x3o4o] -->{{CDD|node|4|node|3|node_1|3|node|3|node_1|3|node|3|node_1|3|node}}||t<sub>1,3,5</sub>{3<sup>6</sup>,4}||[[Bistericantellated 8-orthoplex]]<BR>Bicellirhombated diacosipentacontahexazetton||||||||||||||1290240||161280
| |
| |- align=center BGCOLOR="#f0e0e0"
| |
| !52
| |
| |<!-- [o3o3x3x3o3x3o4o] -->{{CDD|node|4|node|3|node_1|3|node|3|node_1|3|node_1|3|node|3|node}}||t<sub>2,3,5</sub>{3<sup>6</sup>,4}||[[Triruncitruncated 8-orthoplex]]<BR>Triprismatotruncated diacosipentacontahexazetton||||||||||||||698880||107520
| |
| |- align=center BGCOLOR="#f0e0e0"
| |
| !53
| |
| |<!-- [x3o3o3o3x3x3o4o] -->{{CDD|node|4|node|3|node_1|3|node_1|3|node|3|node|3|node|3|node_1}}||t<sub>0,4,5</sub>{3<sup>6</sup>,4}||[[Pentistericated 8-orthoplex]]<BR>Tericellated diacosipentacontahexazetton||||||||||||||322560||53760
| |
| |- align=center BGCOLOR="#f0e0e0"
| |
| !54
| |
| |<!-- [o3x3o3o3x3x3o4o] -->{{CDD|node|4|node|3|node_1|3|node_1|3|node|3|node|3|node_1|3|node}}||t<sub>1,4,5</sub>{3<sup>6</sup>,4}||[[Bisteriruncinated 8-orthoplex]]<BR>Bicelliprismated diacosipentacontahexazetton||||||||||||||698880||107520
| |
| |- align=center BGCOLOR="#e0e0f0"
| |
| !55
| |
| |<!-- [o3o3x3o3x3x3o4o] -->{{CDD|node|4|node|3|node_1|3|node_1|3|node|3|node_1|3|node|3|node}}||t<sub>2,3,5</sub>{4,3<sup>6</sup>}||[[Triruncitruncated 8-cube]]<BR>Triprismatotruncated octeract||||||||||||||645120||107520
| |
| |- align=center BGCOLOR="#e0e0f0"
| |
| !56
| |
| |<!-- [o3o3o3x3x3x3o4o] -->{{CDD|node|4|node|3|node_1|3|node_1|3|node_1|3|node|3|node|3|node}}||t<sub>2,3,4</sub>{4,3<sup>6</sup>}||[[Tricantitruncated 8-cube]]<BR>Great trirhombated octeract||||||||||||||241920||53760
| |
| |- align=center BGCOLOR="#f0e0e0"
| |
| !57
| |
| |<!-- [x3x3o3o3o3o3x4o] -->{{CDD|node|4|node_1|3|node|3|node|3|node|3|node|3|node_1|3|node_1}}||t<sub>0,1,6</sub>{3<sup>6</sup>,4}||[[Hexitruncated 8-orthoplex]]<BR>Petitruncated diacosipentacontahexazetton||||||||||||||344064||43008
| |
| |- align=center BGCOLOR="#f0e0e0"
| |
| !58
| |
| |<!-- [x3o3x3o3o3o3x4o] -->{{CDD|node|4|node_1|3|node|3|node|3|node|3|node_1|3|node|3|node_1}}||t<sub>0,2,6</sub>{3<sup>6</sup>,4}||[[Hexicantellated 8-orthoplex]]<BR>Petirhombated diacosipentacontahexazetton||||||||||||||967680||107520
| |
| |- align=center BGCOLOR="#f0e0e0"
| |
| !59
| |
| |<!-- [o3x3x3o3o3o3x4o] -->{{CDD|node|4|node_1|3|node|3|node|3|node|3|node_1|3|node_1|3|node}}||t<sub>1,2,6</sub>{3<sup>6</sup>,4}||[[Bipentitruncated 8-orthoplex]]<BR>Biteritruncated diacosipentacontahexazetton||||||||||||||752640||107520
| |
| |- align=center BGCOLOR="#f0e0e0"
| |
| !60
| |
| |<!-- [x3o3o3x3o3o3x4o] -->{{CDD|node|4|node_1|3|node|3|node|3|node_1|3|node|3|node|3|node_1}}||t<sub>0,3,6</sub>{3<sup>6</sup>,4}||[[Hexiruncinated 8-orthoplex]]<BR>Petiprismated diacosipentacontahexazetton||||||||||||||1290240||143360
| |
| |- align=center BGCOLOR="#f0e0e0"
| |
| !61
| |
| |<!-- [o3x3o3x3o3o3x4o] -->{{CDD|node|4|node_1|3|node|3|node|3|node_1|3|node|3|node_1|3|node}}||t<sub>1,3,6</sub>{3<sup>6</sup>,4}||[[Bipenticantellated 8-orthoplex]]<BR>Biterirhombated diacosipentacontahexazetton||||||||||||||1720320||215040
| |
| |- align=center BGCOLOR="#e0e0f0"
| |
| !62
| |
| |<!-- [o3o3x3x3o3o3x4o] -->{{CDD|node|4|node_1|3|node|3|node|3|node_1|3|node_1|3|node|3|node}}||t<sub>1,4,5</sub>{4,3<sup>6</sup>}||[[Bisteriruncinated 8-cube]]<BR>Bicelliprismated octeract||||||||||||||860160||143360
| |
| |- align=center BGCOLOR="#f0e0e0"
| |
| !63
| |
| |<!-- [x3o3o3o3x3o3x4o] -->{{CDD|node|4|node_1|3|node|3|node_1|3|node|3|node|3|node|3|node_1}}||t<sub>0,4,6</sub>{3<sup>6</sup>,4}||[[Hexistericated 8-orthoplex]]<BR>Peticellated diacosipentacontahexazetton||||||||||||||860160||107520
| |
| |- align=center BGCOLOR="#e0e0f0"
| |
| !64
| |
| |<!-- [o3x3o3o3x3o3x4o] -->{{CDD|node|4|node_1|3|node|3|node_1|3|node|3|node|3|node_1|3|node}}||t<sub>1,3,6</sub>{4,3<sup>6</sup>}||[[Bipenticantellated 8-cube]]<BR>Biterirhombated octeract||||||||||||||1720320||215040
| |
| |- align=center BGCOLOR="#e0e0f0"
| |
| !65
| |
| |<!-- [o3o3x3o3x3o3x4o] -->{{CDD|node|4|node_1|3|node|3|node_1|3|node|3|node_1|3|node|3|node}}||t<sub>1,3,5</sub>{4,3<sup>6</sup>}||[[Bistericantellated 8-cube]]<BR>Bicellirhombated octeract||||||||||||||1505280||215040
| |
| |- align=center BGCOLOR="#e0e0f0"
| |
| !66
| |
| |<!-- [o3o3o3x3x3o3x4o] -->{{CDD|node|4|node_1|3|node|3|node_1|3|node_1|3|node|3|node|3|node}}||t<sub>1,3,4</sub>{4,3<sup>6</sup>}||[[Biruncicantellated 8-cube]]<BR>Biprismatorhombated octeract||||||||||||||537600||107520
| |
| |- align=center BGCOLOR="#f0e0e0"
| |
| !67
| |
| |<!-- [x3o3o3o3o3x3x4o] -->{{CDD|node|4|node_1|3|node_1|3|node|3|node|3|node|3|node|3|node_1}}||t<sub>0,5,6</sub>{3<sup>6</sup>,4}||[[Hexipentellated 8-orthoplex]]<BR>Petiterated diacosipentacontahexazetton||||||||||||||258048||43008
| |
| |- align=center BGCOLOR="#e0e0f0"
| |
| !68
| |
| |<!-- [o3x3o3o3o3x3x4o] -->{{CDD|node|4|node_1|3|node_1|3|node|3|node|3|node|3|node_1|3|node}}||t<sub>1,2,6</sub>{4,3<sup>6</sup>}||[[Bipentitruncated 8-cube]]<BR>Biteritruncated octeract||||||||||||||752640||107520
| |
| |- align=center BGCOLOR="#e0e0f0"
| |
| !69
| |
| |<!-- [o3o3x3o3o3x3x4o] -->{{CDD|node|4|node_1|3|node_1|3|node|3|node|3|node_1|3|node|3|node}}||t<sub>1,2,5</sub>{4,3<sup>6</sup>}||[[Bisteritruncated 8-cube]]<BR>Bicellitruncated octeract||||||||||||||1003520||143360
| |
| |- align=center BGCOLOR="#e0e0f0"
| |
| !70
| |
| |<!-- [o3o3o3x3o3x3x4o] -->{{CDD|node|4|node_1|3|node_1|3|node|3|node_1|3|node|3|node|3|node}}||t<sub>1,2,4</sub>{4,3<sup>6</sup>}||[[Biruncitruncated 8-cube]]<BR>Biprismatotruncated octeract||||||||||||||645120||107520
| |
| |- align=center BGCOLOR="#e0e0f0"
| |
| !71
| |
| |<!-- [o3o3o3o3x3x3x4o] -->{{CDD|node|4|node_1|3|node_1|3|node_1|3|node|3|node|3|node|3|node}}||t<sub>1,2,3</sub>{4,3<sup>6</sup>}||[[Bicantitruncated 8-cube]]<BR>Great birhombated octeract||||||||||||||172032||43008
| |
| |- align=center BGCOLOR="#f0e0e0"
| |
| !72
| |
| |<!-- [x3x3o3o3o3o3o4x] -->{{CDD|node_1|4|node|3|node|3|node|3|node|3|node|3|node_1|3|node_1}}||t<sub>0,1,7</sub>{3<sup>6</sup>,4}||[[Heptitruncated 8-orthoplex]]<BR>Exitruncated diacosipentacontahexazetton||||||||||||||93184||14336
| |
| |- align=center BGCOLOR="#f0e0e0"
| |
| !73
| |
| |<!-- [x3o3x3o3o3o3o4x] -->{{CDD|node_1|4|node|3|node|3|node|3|node|3|node_1|3|node|3|node_1}}||t<sub>0,2,7</sub>{3<sup>6</sup>,4}||[[Hepticantellated 8-orthoplex]]<BR>Exirhombated diacosipentacontahexazetton||||||||||||||365568||43008
| |
| |- align=center BGCOLOR="#e0e0f0"
| |
| !74
| |
| |<!-- [o3x3x3o3o3o3o4x] -->{{CDD|node_1|4|node|3|node|3|node|3|node|3|node_1|3|node_1|3|node}}||t<sub>0,5,6</sub>{4,3<sup>6</sup>}||[[Hexipentellated 8-cube]]<BR>Petiterated octeract||||||||||||||258048||43008
| |
| |- align=center BGCOLOR="#f0e0e0"
| |
| !75
| |
| |<!-- [x3o3o3x3o3o3o4x] -->{{CDD|node_1|4|node|3|node|3|node|3|node_1|3|node|3|node|3|node_1}}||t<sub>0,3,7</sub>{3<sup>6</sup>,4}||[[Heptiruncinated 8-orthoplex]]<BR>Exiprismated diacosipentacontahexazetton||||||||||||||680960||71680
| |
| |- align=center BGCOLOR="#e0e0f0"
| |
| !76
| |
| |<!-- [o3x3o3x3o3o3o4x] -->{{CDD|node_1|4|node|3|node|3|node|3|node_1|3|node|3|node_1|3|node}}||t<sub>0,4,6</sub>{4,3<sup>6</sup>}||[[Hexistericated 8-cube]]<BR>Peticellated octeract||||||||||||||860160||107520
| |
| |- align=center BGCOLOR="#e0e0f0"
| |
| !77
| |
| |<!-- [o3o3x3x3o3o3o4x] -->{{CDD|node_1|4|node|3|node|3|node|3|node_1|3|node_1|3|node|3|node}}||t<sub>0,4,5</sub>{4,3<sup>6</sup>}||[[Pentistericated 8-cube]]<BR>Tericellated octeract||||||||||||||394240||71680
| |
| |- align=center BGCOLOR="#e0e0f0"
| |
| !78
| |
| |<!-- [x3o3o3o3x3o3o4x] -->{{CDD|node_1|4|node|3|node|3|node_1|3|node|3|node|3|node|3|node_1}}||t<sub>0,3,7</sub>{4,3<sup>6</sup>}||[[Heptiruncinated 8-cube]]<BR>Exiprismated octeract||||||||||||||680960||71680
| |
| |- align=center BGCOLOR="#e0e0f0"
| |
| !79
| |
| |<!-- [o3x3o3o3x3o3o4x] -->{{CDD|node_1|4|node|3|node|3|node_1|3|node|3|node|3|node_1|3|node}}||t<sub>0,3,6</sub>{4,3<sup>6</sup>}||[[Hexiruncinated 8-cube]]<BR>Petiprismated octeract||||||||||||||1290240||143360
| |
| |- align=center BGCOLOR="#e0e0f0"
| |
| !80
| |
| |<!-- [o3o3x3o3x3o3o4x] -->{{CDD|node_1|4|node|3|node|3|node_1|3|node|3|node_1|3|node|3|node}}||t<sub>0,3,5</sub>{4,3<sup>6</sup>}||[[Pentiruncinated 8-cube]]<BR>Teriprismated octeract||||||||||||||1075200||143360
| |
| |- align=center BGCOLOR="#e0e0f0"
| |
| !81
| |
| |<!-- [o3o3o3x3x3o3o4x] -->{{CDD|node_1|4|node|3|node|3|node_1|3|node_1|3|node|3|node|3|node}}||t<sub>0,3,4</sub>{4,3<sup>6</sup>}||[[Steriruncinated 8-cube]]<BR>Celliprismated octeract||||||||||||||358400||71680
| |
| |- align=center BGCOLOR="#e0e0f0"
| |
| !82
| |
| |<!-- [x3o3o3o3o3x3o4x] -->{{CDD|node_1|4|node|3|node_1|3|node|3|node|3|node|3|node|3|node_1}}||t<sub>0,2,7</sub>{4,3<sup>6</sup>}||[[Hepticantellated 8-cube]]<BR>Exirhombated octeract||||||||||||||365568||43008
| |
| |- align=center BGCOLOR="#e0e0f0"
| |
| !83
| |
| |<!-- [o3x3o3o3o3x3o4x] -->{{CDD|node_1|4|node|3|node_1|3|node|3|node|3|node|3|node_1|3|node}}||t<sub>0,2,6</sub>{4,3<sup>6</sup>}||[[Hexicantellated 8-cube]]<BR>Petirhombated octeract||||||||||||||967680||107520
| |
| |- align=center BGCOLOR="#e0e0f0"
| |
| !84
| |
| |<!-- [o3o3x3o3o3x3o4x] -->{{CDD|node_1|4|node|3|node_1|3|node|3|node|3|node_1|3|node|3|node}}||t<sub>0,2,5</sub>{4,3<sup>6</sup>}||[[Penticantellated 8-cube]]<BR>Terirhombated octeract||||||||||||||1218560||143360
| |
| |- align=center BGCOLOR="#e0e0f0"
| |
| !85
| |
| |<!-- [o3o3o3x3o3x3o4x] -->{{CDD|node_1|4|node|3|node_1|3|node|3|node_1|3|node|3|node|3|node}}||t<sub>0,2,4</sub>{4,3<sup>6</sup>}||[[Stericantellated 8-cube]]<BR>Cellirhombated octeract||||||||||||||752640||107520
| |
| |- align=center BGCOLOR="#e0e0f0"
| |
| !86
| |
| |<!-- [o3o3o3o3x3x3o4x] -->{{CDD|node_1|4|node|3|node_1|3|node_1|3|node|3|node|3|node|3|node}}||t<sub>0,2,3</sub>{4,3<sup>6</sup>}||[[Runcicantellated 8-cube]]<BR>Prismatorhombated octeract||||||||||||||193536||43008
| |
| |- align=center BGCOLOR="#e0e0f0"
| |
| !87
| |
| |<!-- [x3o3o3o3o3o3x4x] -->{{CDD|node_1|4|node_1|3|node|3|node|3|node|3|node|3|node|3|node_1}}||t<sub>0,1,7</sub>{4,3<sup>6</sup>}||[[Heptitruncated 8-cube]]<BR>Exitruncated octeract||||||||||||||93184||14336
| |
| |- align=center BGCOLOR="#e0e0f0"
| |
| !88
| |
| |<!-- [o3x3o3o3o3o3x4x] -->{{CDD|node_1|4|node_1|3|node|3|node|3|node|3|node|3|node_1|3|node}}||t<sub>0,1,6</sub>{4,3<sup>6</sup>}||[[Hexitruncated 8-cube]]<BR>Petitruncated octeract||||||||||||||344064||43008
| |
| |- align=center BGCOLOR="#e0e0f0"
| |
| !89
| |
| |<!-- [o3o3x3o3o3o3x4x] -->{{CDD|node_1|4|node_1|3|node|3|node|3|node|3|node_1|3|node|3|node}}||t<sub>0,1,5</sub>{4,3<sup>6</sup>}||[[Pentitruncated 8-cube]]<BR>Teritruncated octeract||||||||||||||609280||71680
| |
| |- align=center BGCOLOR="#e0e0f0"
| |
| !90
| |
| |<!-- [o3o3o3x3o3o3x4x] -->{{CDD|node_1|4|node_1|3|node|3|node|3|node_1|3|node|3|node|3|node}}||t<sub>0,1,4</sub>{4,3<sup>6</sup>}||[[Steritruncated 8-cube]]<BR>Cellitruncated octeract||||||||||||||573440||71680
| |
| |- align=center BGCOLOR="#e0e0f0"
| |
| !91
| |
| |<!-- [o3o3o3o3x3o3x4x] -->{{CDD|node_1|4|node_1|3|node|3|node_1|3|node|3|node|3|node|3|node}}||t<sub>0,1,3</sub>{4,3<sup>6</sup>}||[[Runcitruncated 8-cube]]<BR>Prismatotruncated octeract||||||||||||||279552||43008
| |
| |- align=center BGCOLOR="#e0e0f0"
| |
| !92
| |
| |<!-- [o3o3o3o3o3x3x4x] -->{{CDD|node_1|4|node_1|3|node_1|3|node|3|node|3|node|3|node|3|node}}||t<sub>0,1,2</sub>{4,3<sup>6</sup>}||[[Cantitruncated 8-cube]]<BR>Great rhombated octeract||||||||||||||57344||14336
| |
| |- align=center BGCOLOR="#f0e0e0"
| |
| !93
| |
| |<!-- [x3x3x3x3o3o3o4o] -->{{CDD|node|4|node|3|node|3|node|3|node_1|3|node_1|3|node_1|3|node_1}}||t<sub>0,1,2,3</sub>{3<sup>6</sup>,4}||[[Runcicantitruncated 8-orthoplex]]<BR>Great prismated diacosipentacontahexazetton||||||||||||||147840||26880
| |
| |- align=center BGCOLOR="#f0e0e0"
| |
| !94
| |
| |<!-- [x3x3x3o3x3o3o4o] -->{{CDD|node|4|node|3|node|3|node_1|3|node|3|node_1|3|node_1|3|node_1}}||t<sub>0,1,2,4</sub>{3<sup>6</sup>,4}||[[Stericantitruncated 8-orthoplex]]<BR>Celligreatorhombated diacosipentacontahexazetton||||||||||||||860160||107520
| |
| |- align=center BGCOLOR="#f0e0e0"
| |
| !95
| |
| |<!-- [x3x3o3x3x3o3o4o] -->{{CDD|node|4|node|3|node|3|node_1|3|node_1|3|node|3|node_1|3|node_1}}||t<sub>0,1,3,4</sub>{3<sup>6</sup>,4}||[[Steriruncitruncated 8-orthoplex]]<BR>Celliprismatotruncated diacosipentacontahexazetton||||||||||||||591360||107520
| |
| |- align=center BGCOLOR="#f0e0e0"
| |
| !96
| |
| |<!-- [x3o3x3x3x3o3o4o] -->{{CDD|node|4|node|3|node|3|node_1|3|node_1|3|node_1|3|node|3|node_1}}||t<sub>0,2,3,4</sub>{3<sup>6</sup>,4}||[[Steriruncicantellated 8-orthoplex]]<BR>Celliprismatorhombated diacosipentacontahexazetton||||||||||||||591360||107520
| |
| |- align=center BGCOLOR="#f0e0e0"
| |
| !97
| |
| |<!-- [o3x3x3x3x3o3o4o] -->{{CDD|node|4|node|3|node|3|node_1|3|node_1|3|node_1|3|node_1|3|node}}||t<sub>1,2,3,4</sub>{3<sup>6</sup>,4}||[[Biruncicantitruncated 8-orthoplex]]<BR>Great biprismated diacosipentacontahexazetton||||||||||||||537600||107520
| |
| |- align=center BGCOLOR="#f0e0e0"
| |
| !98
| |
| |<!-- [x3x3x3o3o3x3o4o] -->{{CDD|node|4|node|3|node_1|3|node|3|node|3|node_1|3|node_1|3|node_1}}||t<sub>0,1,2,5</sub>{3<sup>6</sup>,4}||[[Penticantitruncated 8-orthoplex]]<BR>Terigreatorhombated diacosipentacontahexazetton||||||||||||||1827840||215040
| |
| |- align=center BGCOLOR="#f0e0e0"
| |
| !99
| |
| |<!-- [x3x3o3x3o3x3o4o] -->{{CDD|node|4|node|3|node_1|3|node|3|node_1|3|node|3|node_1|3|node_1}}||t<sub>0,1,3,5</sub>{3<sup>6</sup>,4}||[[Pentiruncitruncated 8-orthoplex]]<BR>Teriprismatotruncated diacosipentacontahexazetton||||||||||||||2419200||322560
| |
| |- align=center BGCOLOR="#f0e0e0"
| |
| !100
| |
| |<!-- [x3o3x3x3o3x3o4o] -->{{CDD|node|4|node|3|node_1|3|node|3|node_1|3|node_1|3|node|3|node_1}}||t<sub>0,2,3,5</sub>{3<sup>6</sup>,4}||[[Pentiruncicantellated 8-orthoplex]]<BR>Teriprismatorhombated diacosipentacontahexazetton||||||||||||||2257920||322560
| |
| |- align=center BGCOLOR="#f0e0e0"
| |
| !101
| |
| |<!-- [o3x3x3x3o3x3o4o] -->{{CDD|node|4|node|3|node_1|3|node|3|node_1|3|node_1|3|node_1|3|node}}||t<sub>1,2,3,5</sub>{3<sup>6</sup>,4}||[[Bistericantitruncated 8-orthoplex]]<BR>Bicelligreatorhombated diacosipentacontahexazetton||||||||||||||2096640||322560
| |
| |- align=center BGCOLOR="#f0e0e0"
| |
| !102
| |
| |<!-- [x3x3o3o3x3x3o4o] -->{{CDD|node|4|node|3|node_1|3|node_1|3|node|3|node|3|node_1|3|node_1}}||t<sub>0,1,4,5</sub>{3<sup>6</sup>,4}||[[Pentisteritruncated 8-orthoplex]]<BR>Tericellitruncated diacosipentacontahexazetton||||||||||||||1182720||215040
| |
| |- align=center BGCOLOR="#f0e0e0"
| |
| !103
| |
| |<!-- [x3o3x3o3x3x3o4o] -->{{CDD|node|4|node|3|node_1|3|node_1|3|node|3|node_1|3|node|3|node_1}}||t<sub>0,2,4,5</sub>{3<sup>6</sup>,4}||[[Pentistericantellated 8-orthoplex]]<BR>Tericellirhombated diacosipentacontahexazetton||||||||||||||1935360||322560
| |
| |- align=center BGCOLOR="#f0e0e0"
| |
| !104
| |
| |<!-- [o3x3x3o3x3x3o4o] -->{{CDD|node|4|node|3|node_1|3|node_1|3|node|3|node_1|3|node_1|3|node}}||t<sub>1,2,4,5</sub>{3<sup>6</sup>,4}||[[Bisteriruncitruncated 8-orthoplex]]<BR>Bicelliprismatotruncated diacosipentacontahexazetton||||||||||||||1612800||322560
| |
| |- align=center BGCOLOR="#f0e0e0"
| |
| !105
| |
| |<!-- [x3o3o3x3x3x3o4o] -->{{CDD|node|4|node|3|node_1|3|node_1|3|node_1|3|node|3|node|3|node_1}}||t<sub>0,3,4,5</sub>{3<sup>6</sup>,4}||[[Pentisteriruncinated 8-orthoplex]]<BR>Tericelliprismated diacosipentacontahexazetton||||||||||||||1182720||215040
| |
| |- align=center BGCOLOR="#f0e0e0"
| |
| !106
| |
| |<!-- [o3x3o3x3x3x3o4o] -->{{CDD|node|4|node|3|node_1|3|node_1|3|node_1|3|node|3|node_1|3|node}}||t<sub>1,3,4,5</sub>{3<sup>6</sup>,4}||[[Bisteriruncicantellated 8-orthoplex]]<BR>Bicelliprismatorhombated diacosipentacontahexazetton||||||||||||||1774080||322560
| |
| |- align=center BGCOLOR="#e0f0e0"
| |
| !107
| |
| |<!-- [o3o3x3x3x3x3o4o] -->{{CDD|node|4|node|3|node_1|3|node_1|3|node_1|3|node_1|3|node|3|node}}||t<sub>2,3,4,5</sub>{4,3<sup>6</sup>}||[[Triruncicantitruncated 8-cube]]<BR>Great triprismato-octeractidiacosipentacontahexazetton||||||||||||||967680||215040
| |
| |- align=center BGCOLOR="#f0e0e0"
| |
| !108
| |
| |<!-- [x3x3x3o3o3o3x4o] -->{{CDD|node|4|node_1|3|node|3|node|3|node|3|node_1|3|node_1|3|node_1}}||t<sub>0,1,2,6</sub>{3<sup>6</sup>,4}||[[Hexicantitruncated 8-orthoplex]]<BR>Petigreatorhombated diacosipentacontahexazetton||||||||||||||1505280||215040
| |
| |- align=center BGCOLOR="#f0e0e0"
| |
| !109
| |
| |<!-- [x3x3o3x3o3o3x4o] -->{{CDD|node|4|node_1|3|node|3|node|3|node_1|3|node|3|node_1|3|node_1}}||t<sub>0,1,3,6</sub>{3<sup>6</sup>,4}||[[Hexiruncitruncated 8-orthoplex]]<BR>Petiprismatotruncated diacosipentacontahexazetton||||||||||||||3225600||430080
| |
| |- align=center BGCOLOR="#f0e0e0"
| |
| !110
| |
| |<!-- [x3o3x3x3o3o3x4o] -->{{CDD|node|4|node_1|3|node|3|node|3|node_1|3|node_1|3|node|3|node_1}}||t<sub>0,2,3,6</sub>{3<sup>6</sup>,4}||[[Hexiruncicantellated 8-orthoplex]]<BR>Petiprismatorhombated diacosipentacontahexazetton||||||||||||||2795520||430080
| |
| |- align=center BGCOLOR="#f0e0e0"
| |
| !111
| |
| |<!-- [o3x3x3x3o3o3x4o] -->{{CDD|node|4|node_1|3|node|3|node|3|node_1|3|node_1|3|node_1|3|node}}||t<sub>1,2,3,6</sub>{3<sup>6</sup>,4}||[[Bipenticantitruncated 8-orthoplex]]<BR>Biterigreatorhombated diacosipentacontahexazetton||||||||||||||2580480||430080
| |
| |- align=center BGCOLOR="#f0e0e0"
| |
| !112
| |
| |<!-- [x3x3o3o3x3o3x4o] -->{{CDD|node|4|node_1|3|node|3|node_1|3|node|3|node|3|node_1|3|node_1}}||t<sub>0,1,4,6</sub>{3<sup>6</sup>,4}||[[Hexisteritruncated 8-orthoplex]]<BR>Peticellitruncated diacosipentacontahexazetton||||||||||||||3010560||430080
| |
| |- align=center BGCOLOR="#f0e0e0"
| |
| !113
| |
| |<!-- [x3o3x3o3x3o3x4o] -->{{CDD|node|4|node_1|3|node|3|node_1|3|node|3|node_1|3|node|3|node_1}}||t<sub>0,2,4,6</sub>{3<sup>6</sup>,4}||[[Hexistericantellated 8-orthoplex]]<BR>Peticellirhombated diacosipentacontahexazetton||||||||||||||4515840||645120
| |
| |- align=center BGCOLOR="#f0e0e0"
| |
| !114
| |
| |<!-- [o3x3x3o3x3o3x4o] -->{{CDD|node|4|node_1|3|node|3|node_1|3|node|3|node_1|3|node_1|3|node}}||t<sub>1,2,4,6</sub>{3<sup>6</sup>,4}||[[Bipentiruncitruncated 8-orthoplex]]<BR>Biteriprismatotruncated diacosipentacontahexazetton||||||||||||||3870720||645120
| |
| |- align=center BGCOLOR="#f0e0e0"
| |
| !115
| |
| |<!-- [x3o3o3x3x3o3x4o] -->{{CDD|node|4|node_1|3|node|3|node_1|3|node_1|3|node|3|node|3|node_1}}||t<sub>0,3,4,6</sub>{3<sup>6</sup>,4}||[[Hexisteriruncinated 8-orthoplex]]<BR>Peticelliprismated diacosipentacontahexazetton||||||||||||||2580480||430080
| |
| |- align=center BGCOLOR="#e0f0e0"
| |
| !116
| |
| |<!-- [o3x3o3x3x3o3x4o] -->{{CDD|node|4|node_1|3|node|3|node_1|3|node_1|3|node|3|node_1|3|node}}||t<sub>1,3,4,6</sub>{4,3<sup>6</sup>}||[[Bipentiruncicantellated 8-cube]]<BR>Biteriprismatorhombi-octeractidiacosipentacontahexazetton||||||||||||||3870720||645120
| |
| |- align=center BGCOLOR="#e0e0f0"
| |
| !117
| |
| |<!-- [o3o3x3x3x3o3x4o] -->{{CDD|node|4|node_1|3|node|3|node_1|3|node_1|3|node_1|3|node|3|node}}||t<sub>1,3,4,5</sub>{4,3<sup>6</sup>}||[[Bisteriruncicantellated 8-cube]]<BR>Bicelliprismatorhombated octeract||||||||||||||2150400||430080
| |
| |- align=center BGCOLOR="#f0e0e0"
| |
| !118
| |
| |<!-- [x3x3o3o3o3x3x4o] -->{{CDD|node|4|node_1|3|node_1|3|node|3|node|3|node|3|node_1|3|node_1}}||t<sub>0,1,5,6</sub>{3<sup>6</sup>,4}||[[Hexipentitruncated 8-orthoplex]]<BR>Petiteritruncated diacosipentacontahexazetton||||||||||||||1182720||215040
| |
| |- align=center BGCOLOR="#f0e0e0"
| |
| !119
| |
| |<!-- [x3o3x3o3o3x3x4o] -->{{CDD|node|4|node_1|3|node_1|3|node|3|node|3|node_1|3|node|3|node_1}}||t<sub>0,2,5,6</sub>{3<sup>6</sup>,4}||[[Hexipenticantellated 8-orthoplex]]<BR>Petiterirhombated diacosipentacontahexazetton||||||||||||||2795520||430080
| |
| |- align=center BGCOLOR="#e0f0e0"
| |
| !120
| |
| |<!-- [o3x3x3o3o3x3x4o] -->{{CDD|node|4|node_1|3|node_1|3|node|3|node|3|node_1|3|node_1|3|node}}||t<sub>1,2,5,6</sub>{4,3<sup>6</sup>}||[[Bipentisteritruncated 8-cube]]<BR>Bitericellitrunki-octeractidiacosipentacontahexazetton||||||||||||||2150400||430080
| |
| |- align=center BGCOLOR="#f0e0e0"
| |
| !121
| |
| |<!-- [x3o3o3x3o3x3x4o] -->{{CDD|node|4|node_1|3|node_1|3|node|3|node_1|3|node|3|node|3|node_1}}||t<sub>0,3,5,6</sub>{3<sup>6</sup>,4}||[[Hexipentiruncinated 8-orthoplex]]<BR>Petiteriprismated diacosipentacontahexazetton||||||||||||||2795520||430080
| |
| |- align=center BGCOLOR="#e0e0f0"
| |
| !122
| |
| |<!-- [o3x3o3x3o3x3x4o] -->{{CDD|node|4|node_1|3|node_1|3|node|3|node_1|3|node|3|node_1|3|node}}||t<sub>1,2,4,6</sub>{4,3<sup>6</sup>}||[[Bipentiruncitruncated 8-cube]]<BR>Biteriprismatotruncated octeract||||||||||||||3870720||645120
| |
| |- align=center BGCOLOR="#e0e0f0"
| |
| !123
| |
| |<!-- [o3o3x3x3o3x3x4o] -->{{CDD|node|4|node_1|3|node_1|3|node|3|node_1|3|node_1|3|node|3|node}}||t<sub>1,2,4,5</sub>{4,3<sup>6</sup>}||[[Bisteriruncitruncated 8-cube]]<BR>Bicelliprismatotruncated octeract||||||||||||||1935360||430080
| |
| |- align=center BGCOLOR="#f0e0e0"
| |
| !124
| |
| |<!-- [x3o3o3o3x3x3x4o] -->{{CDD|node|4|node_1|3|node_1|3|node_1|3|node|3|node|3|node|3|node_1}}||t<sub>0,4,5,6</sub>{3<sup>6</sup>,4}||[[Hexipentistericated 8-orthoplex]]<BR>Petitericellated diacosipentacontahexazetton||||||||||||||1182720||215040
| |
| |- align=center BGCOLOR="#e0e0f0"
| |
| !125
| |
| |<!-- [o3x3o3o3x3x3x4o] -->{{CDD|node|4|node_1|3|node_1|3|node_1|3|node|3|node|3|node_1|3|node}}||t<sub>1,2,3,6</sub>{4,3<sup>6</sup>}||[[Bipenticantitruncated 8-cube]]<BR>Biterigreatorhombated octeract||||||||||||||2580480||430080
| |
| |- align=center BGCOLOR="#e0e0f0"
| |
| !126
| |
| |<!-- [o3o3x3o3x3x3x4o] -->{{CDD|node|4|node_1|3|node_1|3|node_1|3|node|3|node_1|3|node|3|node}}||t<sub>1,2,3,5</sub>{4,3<sup>6</sup>}||[[Bistericantitruncated 8-cube]]<BR>Bicelligreatorhombated octeract||||||||||||||2365440||430080
| |
| |- align=center BGCOLOR="#e0e0f0"
| |
| !127
| |
| |<!-- [o3o3o3x3x3x3x4o] -->{{CDD|node|4|node_1|3|node_1|3|node_1|3|node_1|3|node|3|node|3|node}}||t<sub>1,2,3,4</sub>{4,3<sup>6</sup>}||[[Biruncicantitruncated 8-cube]]<BR>Great biprismated octeract||||||||||||||860160||215040
| |
| |- align=center BGCOLOR="#f0e0e0"
| |
| !128
| |
| |<!-- [x3x3x3o3o3o3o4x] -->{{CDD|node_1|4|node|3|node|3|node|3|node|3|node_1|3|node_1|3|node_1}}||t<sub>0,1,2,7</sub>{3<sup>6</sup>,4}||[[Hepticantitruncated 8-orthoplex]]<BR>Exigreatorhombated diacosipentacontahexazetton||||||||||||||516096||86016
| |
| |- align=center BGCOLOR="#f0e0e0"
| |
| !129
| |
| |<!-- [x3x3o3x3o3o3o4x] -->{{CDD|node_1|4|node|3|node|3|node|3|node_1|3|node|3|node_1|3|node_1}}||t<sub>0,1,3,7</sub>{3<sup>6</sup>,4}||[[Heptiruncitruncated 8-orthoplex]]<BR>Exiprismatotruncated diacosipentacontahexazetton||||||||||||||1612800||215040
| |
| |- align=center BGCOLOR="#f0e0e0"
| |
| !130
| |
| |<!-- [x3o3x3x3o3o3o4x] -->{{CDD|node_1|4|node|3|node|3|node|3|node_1|3|node_1|3|node|3|node_1}}||t<sub>0,2,3,7</sub>{3<sup>6</sup>,4}||[[Heptiruncicantellated 8-orthoplex]]<BR>Exiprismatorhombated diacosipentacontahexazetton||||||||||||||1290240||215040
| |
| |- align=center BGCOLOR="#e0e0f0"
| |
| !131
| |
| |<!-- [o3x3x3x3o3o3o4x] -->{{CDD|node_1|4|node|3|node|3|node|3|node_1|3|node_1|3|node_1|3|node}}||t<sub>0,4,5,6</sub>{4,3<sup>6</sup>}||[[Hexipentistericated 8-cube]]<BR>Petitericellated octeract||||||||||||||1182720||215040
| |
| |- align=center BGCOLOR="#f0e0e0"
| |
| !132
| |
| |<!-- [x3x3o3o3x3o3o4x] -->{{CDD|node_1|4|node|3|node|3|node_1|3|node|3|node|3|node_1|3|node_1}}||t<sub>0,1,4,7</sub>{3<sup>6</sup>,4}||[[Heptisteritruncated 8-orthoplex]]<BR>Exicellitruncated diacosipentacontahexazetton||||||||||||||2293760||286720
| |
| |- align=center BGCOLOR="#f0e0e0"
| |
| !133
| |
| |<!-- [x3o3x3o3x3o3o4x] -->{{CDD|node_1|4|node|3|node|3|node_1|3|node|3|node_1|3|node|3|node_1}}||t<sub>0,2,4,7</sub>{3<sup>6</sup>,4}||[[Heptistericantellated 8-orthoplex]]<BR>Exicellirhombated diacosipentacontahexazetton||||||||||||||3225600||430080
| |
| |- align=center BGCOLOR="#e0e0f0"
| |
| !134
| |
| |<!-- [o3x3x3o3x3o3o4x] -->{{CDD|node_1|4|node|3|node|3|node_1|3|node|3|node_1|3|node_1|3|node}}||t<sub>0,3,5,6</sub>{4,3<sup>6</sup>}||[[Hexipentiruncinated 8-cube]]<BR>Petiteriprismated octeract||||||||||||||2795520||430080
| |
| |- align=center BGCOLOR="#e0f0e0"
| |
| !135
| |
| |<!-- [x3o3o3x3x3o3o4x] -->{{CDD|node_1|4|node|3|node|3|node_1|3|node_1|3|node|3|node|3|node_1}}||t<sub>0,3,4,7</sub>{4,3<sup>6</sup>}||[[Heptisteriruncinated 8-cube]]<BR>Exicelliprismato-octeractidiacosipentacontahexazetton||||||||||||||1720320||286720
| |
| |- align=center BGCOLOR="#e0e0f0"
| |
| !136
| |
| |<!-- [o3x3o3x3x3o3o4x] -->{{CDD|node_1|4|node|3|node|3|node_1|3|node_1|3|node|3|node_1|3|node}}||t<sub>0,3,4,6</sub>{4,3<sup>6</sup>}||[[Hexisteriruncinated 8-cube]]<BR>Peticelliprismated octeract||||||||||||||2580480||430080
| |
| |- align=center BGCOLOR="#e0e0f0"
| |
| !137
| |
| |<!-- [o3o3x3x3x3o3o4x] -->{{CDD|node_1|4|node|3|node|3|node_1|3|node_1|3|node_1|3|node|3|node}}||t<sub>0,3,4,5</sub>{4,3<sup>6</sup>}||[[Pentisteriruncinated 8-cube]]<BR>Tericelliprismated octeract||||||||||||||1433600||286720
| |
| |- align=center BGCOLOR="#f0e0e0"
| |
| !138
| |
| |<!-- [x3x3o3o3o3x3o4x] -->{{CDD|node_1|4|node|3|node_1|3|node|3|node|3|node|3|node_1|3|node_1}}||t<sub>0,1,5,7</sub>{3<sup>6</sup>,4}||[[Heptipentitruncated 8-orthoplex]]<BR>Exiteritruncated diacosipentacontahexazetton||||||||||||||1612800||215040
| |
| |- align=center BGCOLOR="#e0f0e0"
| |
| !139
| |
| |<!-- [x3o3x3o3o3x3o4x] -->{{CDD|node_1|4|node|3|node_1|3|node|3|node|3|node_1|3|node|3|node_1}}||t<sub>0,2,5,7</sub>{4,3<sup>6</sup>}||[[Heptipenticantellated 8-cube]]<BR>Exiterirhombi-octeractidiacosipentacontahexazetton||||||||||||||3440640||430080
| |
| |- align=center BGCOLOR="#e0e0f0"
| |
| !140
| |
| |<!-- [o3x3x3o3o3x3o4x] -->{{CDD|node_1|4|node|3|node_1|3|node|3|node|3|node_1|3|node_1|3|node}}||t<sub>0,2,5,6</sub>{4,3<sup>6</sup>}||[[Hexipenticantellated 8-cube]]<BR>Petiterirhombated octeract||||||||||||||2795520||430080
| |
| |- align=center BGCOLOR="#e0e0f0"
| |
| !141
| |
| |<!-- [x3o3o3x3o3x3o4x] -->{{CDD|node_1|4|node|3|node_1|3|node|3|node_1|3|node|3|node|3|node_1}}||t<sub>0,2,4,7</sub>{4,3<sup>6</sup>}||[[Heptistericantellated 8-cube]]<BR>Exicellirhombated octeract||||||||||||||3225600||430080
| |
| |- align=center BGCOLOR="#e0e0f0"
| |
| !142
| |
| |<!-- [o3x3o3x3o3x3o4x] -->{{CDD|node_1|4|node|3|node_1|3|node|3|node_1|3|node|3|node_1|3|node}}||t<sub>0,2,4,6</sub>{4,3<sup>6</sup>}||[[Hexistericantellated 8-cube]]<BR>Peticellirhombated octeract||||||||||||||4515840||645120
| |
| |- align=center BGCOLOR="#e0e0f0"
| |
| !143
| |
| |<!-- [o3o3x3x3o3x3o4x] -->{{CDD|node_1|4|node|3|node_1|3|node|3|node_1|3|node_1|3|node|3|node}}||t<sub>0,2,4,5</sub>{4,3<sup>6</sup>}||[[Pentistericantellated 8-cube]]<BR>Tericellirhombated octeract||||||||||||||2365440||430080
| |
| |- align=center BGCOLOR="#e0e0f0"
| |
| !144
| |
| |<!-- [x3o3o3o3x3x3o4x] -->{{CDD|node_1|4|node|3|node_1|3|node_1|3|node|3|node|3|node|3|node_1}}||t<sub>0,2,3,7</sub>{4,3<sup>6</sup>}||[[Heptiruncicantellated 8-cube]]<BR>Exiprismatorhombated octeract||||||||||||||1290240||215040
| |
| |- align=center BGCOLOR="#e0e0f0"
| |
| !145
| |
| |<!-- [o3x3o3o3x3x3o4x] -->{{CDD|node_1|4|node|3|node_1|3|node_1|3|node|3|node|3|node_1|3|node}}||t<sub>0,2,3,6</sub>{4,3<sup>6</sup>}||[[Hexiruncicantellated 8-cube]]<BR>Petiprismatorhombated octeract||||||||||||||2795520||430080
| |
| |- align=center BGCOLOR="#e0e0f0"
| |
| !146
| |
| |<!-- [o3o3x3o3x3x3o4x] -->{{CDD|node_1|4|node|3|node_1|3|node_1|3|node|3|node_1|3|node|3|node}}||t<sub>0,2,3,5</sub>{4,3<sup>6</sup>}||[[Pentiruncicantellated 8-cube]]<BR>Teriprismatorhombated octeract||||||||||||||2580480||430080
| |
| |- align=center BGCOLOR="#e0e0f0"
| |
| !147
| |
| |<!-- [o3o3o3x3x3x3o4x] -->{{CDD|node_1|4|node|3|node_1|3|node_1|3|node_1|3|node|3|node|3|node}}||t<sub>0,2,3,4</sub>{4,3<sup>6</sup>}||[[Steriruncicantellated 8-cube]]<BR>Celliprismatorhombated octeract||||||||||||||967680||215040
| |
| |- align=center BGCOLOR="#e0f0e0"
| |
| !148
| |
| |<!-- [x3x3o3o3o3o3x4x] -->{{CDD|node_1|4|node_1|3|node|3|node|3|node|3|node|3|node_1|3|node_1}}||t<sub>0,1,6,7</sub>{4,3<sup>6</sup>}||[[Heptihexitruncated 8-cube]]<BR>Exipetitrunki-octeractidiacosipentacontahexazetton||||||||||||||516096||86016
| |
| |- align=center BGCOLOR="#e0e0f0"
| |
| !149
| |
| |<!-- [x3o3x3o3o3o3x4x] -->{{CDD|node_1|4|node_1|3|node|3|node|3|node|3|node_1|3|node|3|node_1}}||t<sub>0,1,5,7</sub>{4,3<sup>6</sup>}||[[Heptipentitruncated 8-cube]]<BR>Exiteritruncated octeract||||||||||||||1612800||215040
| |
| |- align=center BGCOLOR="#e0e0f0"
| |
| !150
| |
| |<!-- [o3x3x3o3o3o3x4x] -->{{CDD|node_1|4|node_1|3|node|3|node|3|node|3|node_1|3|node_1|3|node}}||t<sub>0,1,5,6</sub>{4,3<sup>6</sup>}||[[Hexipentitruncated 8-cube]]<BR>Petiteritruncated octeract||||||||||||||1182720||215040
| |
| |- align=center BGCOLOR="#e0e0f0"
| |
| !151
| |
| |<!-- [x3o3o3x3o3o3x4x] -->{{CDD|node_1|4|node_1|3|node|3|node|3|node_1|3|node|3|node|3|node_1}}||t<sub>0,1,4,7</sub>{4,3<sup>6</sup>}||[[Heptisteritruncated 8-cube]]<BR>Exicellitruncated octeract||||||||||||||2293760||286720
| |
| |- align=center BGCOLOR="#e0e0f0"
| |
| !152
| |
| |<!-- [o3x3o3x3o3o3x4x] -->{{CDD|node_1|4|node_1|3|node|3|node|3|node_1|3|node|3|node_1|3|node}}||t<sub>0,1,4,6</sub>{4,3<sup>6</sup>}||[[Hexisteritruncated 8-cube]]<BR>Peticellitruncated octeract||||||||||||||3010560||430080
| |
| |- align=center BGCOLOR="#e0e0f0"
| |
| !153
| |
| |<!-- [o3o3x3x3o3o3x4x] -->{{CDD|node_1|4|node_1|3|node|3|node|3|node_1|3|node_1|3|node|3|node}}||t<sub>0,1,4,5</sub>{4,3<sup>6</sup>}||[[Pentisteritruncated 8-cube]]<BR>Tericellitruncated octeract||||||||||||||1433600||286720
| |
| |- align=center BGCOLOR="#e0e0f0"
| |
| !154
| |
| |<!-- [x3o3o3o3x3o3x4x] -->{{CDD|node_1|4|node_1|3|node|3|node_1|3|node|3|node|3|node|3|node_1}}||t<sub>0,1,3,7</sub>{4,3<sup>6</sup>}||[[Heptiruncitruncated 8-cube]]<BR>Exiprismatotruncated octeract||||||||||||||1612800||215040
| |
| |- align=center BGCOLOR="#e0e0f0"
| |
| !155
| |
| |<!-- [o3x3o3o3x3o3x4x] -->{{CDD|node_1|4|node_1|3|node|3|node_1|3|node|3|node|3|node_1|3|node}}||t<sub>0,1,3,6</sub>{4,3<sup>6</sup>}||[[Hexiruncitruncated 8-cube]]<BR>Petiprismatotruncated octeract||||||||||||||3225600||430080
| |
| |- align=center BGCOLOR="#e0e0f0"
| |
| !156
| |
| |<!-- [o3o3x3o3x3o3x4x] -->{{CDD|node_1|4|node_1|3|node|3|node_1|3|node|3|node_1|3|node|3|node}}||t<sub>0,1,3,5</sub>{4,3<sup>6</sup>}||[[Pentiruncitruncated 8-cube]]<BR>Teriprismatotruncated octeract||||||||||||||2795520||430080
| |
| |- align=center BGCOLOR="#e0e0f0"
| |
| !157
| |
| |<!-- [o3o3o3x3x3o3x4x] -->{{CDD|node_1|4|node_1|3|node|3|node_1|3|node_1|3|node|3|node|3|node}}||t<sub>0,1,3,4</sub>{4,3<sup>6</sup>}||[[Steriruncitruncated 8-cube]]<BR>Celliprismatotruncated octeract||||||||||||||967680||215040
| |
| |- align=center BGCOLOR="#e0e0f0"
| |
| !158
| |
| |<!-- [x3o3o3o3o3x3x4x] -->{{CDD|node_1|4|node_1|3|node_1|3|node|3|node|3|node|3|node|3|node_1}}||t<sub>0,1,2,7</sub>{4,3<sup>6</sup>}||[[Hepticantitruncated 8-cube]]<BR>Exigreatorhombated octeract||||||||||||||516096||86016
| |
| |- align=center BGCOLOR="#e0e0f0"
| |
| !159
| |
| |<!-- [o3x3o3o3o3x3x4x] -->{{CDD|node_1|4|node_1|3|node_1|3|node|3|node|3|node|3|node_1|3|node}}||t<sub>0,1,2,6</sub>{4,3<sup>6</sup>}||[[Hexicantitruncated 8-cube]]<BR>Petigreatorhombated octeract||||||||||||||1505280||215040
| |
| |- align=center BGCOLOR="#e0e0f0"
| |
| !160
| |
| |<!-- [o3o3x3o3o3x3x4x] -->{{CDD|node_1|4|node_1|3|node_1|3|node|3|node|3|node_1|3|node|3|node}}||t<sub>0,1,2,5</sub>{4,3<sup>6</sup>}||[[Penticantitruncated 8-cube]]<BR>Terigreatorhombated octeract||||||||||||||2007040||286720
| |
| |- align=center BGCOLOR="#e0e0f0"
| |
| !161
| |
| |<!-- [o3o3o3x3o3x3x4x] -->{{CDD|node_1|4|node_1|3|node_1|3|node|3|node_1|3|node|3|node|3|node}}||t<sub>0,1,2,4</sub>{4,3<sup>6</sup>}||[[Stericantitruncated 8-cube]]<BR>Celligreatorhombated octeract||||||||||||||1290240||215040
| |
| |- align=center BGCOLOR="#e0e0f0"
| |
| !162
| |
| |<!-- [o3o3o3o3x3x3x4x] -->{{CDD|node_1|4|node_1|3|node_1|3|node_1|3|node|3|node|3|node|3|node}}||t<sub>0,1,2,3</sub>{4,3<sup>6</sup>}||[[Runcicantitruncated 8-cube]]<BR>Great prismated octeract||||||||||||||344064||86016
| |
| |- align=center BGCOLOR="#f0e0e0"
| |
| !163
| |
| |<!-- [x3x3x3x3x3o3o4o] -->{{CDD|node|4|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>{3<sup>6</sup>,4}||[[Steriruncicantitruncated 8-orthoplex]]<BR>Great cellated diacosipentacontahexazetton||||||||||||||1075200||215040
| |
| |- align=center BGCOLOR="#f0e0e0"
| |
| !164
| |
| |<!-- [x3x3x3x3o3x3o4o] -->{{CDD|node|4|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>{3<sup>6</sup>,4}||[[Pentiruncicantitruncated 8-orthoplex]]<BR>Terigreatoprismated diacosipentacontahexazetton||||||||||||||4193280||645120
| |
| |- align=center BGCOLOR="#f0e0e0"
| |
| !165
| |
| |<!-- [x3x3x3o3x3x3o4o] -->{{CDD|node|4|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>{3<sup>6</sup>,4}||[[Pentistericantitruncated 8-orthoplex]]<BR>Tericelligreatorhombated diacosipentacontahexazetton||||||||||||||3225600||645120
| |
| |- align=center BGCOLOR="#f0e0e0"
| |
| !166
| |
| |<!-- [x3x3o3x3x3x3o4o] -->{{CDD|node|4|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>{3<sup>6</sup>,4}||[[Pentisteriruncitruncated 8-orthoplex]]<BR>Tericelliprismatotruncated diacosipentacontahexazetton||||||||||||||3225600||645120
| |
| |- align=center BGCOLOR="#f0e0e0"
| |
| !167
| |
| |<!-- [x3o3x3x3x3x3o4o] -->{{CDD|node|4|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>{3<sup>6</sup>,4}||[[Pentisteriruncicantellated 8-orthoplex]]<BR>Tericelliprismatorhombated diacosipentacontahexazetton||||||||||||||3225600||645120
| |
| |- align=center BGCOLOR="#f0e0e0"
| |
| !168
| |
| |<!-- [o3x3x3x3x3x3o4o] -->{{CDD|node|4|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>{3<sup>6</sup>,4}||[[Bisteriruncicantitruncated 8-orthoplex]]<BR>Great bicellated diacosipentacontahexazetton||||||||||||||2903040||645120
| |
| |- align=center BGCOLOR="#f0e0e0"
| |
| !169
| |
| |<!-- [x3x3x3x3o3o3x4o] -->{{CDD|node|4|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>{3<sup>6</sup>,4}||[[Hexiruncicantitruncated 8-orthoplex]]<BR>Petigreatoprismated diacosipentacontahexazetton||||||||||||||5160960||860160
| |
| |- align=center BGCOLOR="#f0e0e0"
| |
| !170
| |
| |<!-- [x3x3x3o3x3o3x4o] -->{{CDD|node|4|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>{3<sup>6</sup>,4}||[[Hexistericantitruncated 8-orthoplex]]<BR>Peticelligreatorhombated diacosipentacontahexazetton||||||||||||||7741440||1290240
| |
| |- align=center BGCOLOR="#f0e0e0"
| |
| !171
| |
| |<!-- [x3x3o3x3x3o3x4o] -->{{CDD|node|4|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>{3<sup>6</sup>,4}||[[Hexisteriruncitruncated 8-orthoplex]]<BR>Peticelliprismatotruncated diacosipentacontahexazetton||||||||||||||7096320||1290240
| |
| |- align=center BGCOLOR="#f0e0e0"
| |
| !172
| |
| |<!-- [x3o3x3x3x3o3x4o] -->{{CDD|node|4|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>{3<sup>6</sup>,4}||[[Hexisteriruncicantellated 8-orthoplex]]<BR>Peticelliprismatorhombated diacosipentacontahexazetton||||||||||||||7096320||1290240
| |
| |- align=center BGCOLOR="#f0e0e0"
| |
| !173
| |
| |<!-- [o3x3x3x3x3o3x4o] -->{{CDD|node|4|node_1|3|node|3|node_1|3|node_1|3|node_1|3|node_1|3|node}}||t<sub>1,2,3,4,6</sub>{3<sup>6</sup>,4}||[[Bipentiruncicantitruncated 8-orthoplex]]<BR>Biterigreatoprismated diacosipentacontahexazetton||||||||||||||6451200||1290240
| |
| |- align=center BGCOLOR="#f0e0e0"
| |
| !174
| |
| |<!-- [x3x3x3o3o3x3x4o] -->{{CDD|node|4|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>{3<sup>6</sup>,4}||[[Hexipenticantitruncated 8-orthoplex]]<BR>Petiterigreatorhombated diacosipentacontahexazetton||||||||||||||4300800||860160
| |
| |- align=center BGCOLOR="#f0e0e0"
| |
| !175
| |
| |<!-- [x3x3o3x3o3x3x4o] -->{{CDD|node|4|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>{3<sup>6</sup>,4}||[[Hexipentiruncitruncated 8-orthoplex]]<BR>Petiteriprismatotruncated diacosipentacontahexazetton||||||||||||||7096320||1290240
| |
| |- align=center BGCOLOR="#f0e0e0"
| |
| !176
| |
| |<!-- [x3o3x3x3o3x3x4o] -->{{CDD|node|4|node_1|3|node_1|3|node|3|node_1|3|node_1|3|node|3|node_1}}||t<sub>0,2,3,5,6</sub>{3<sup>6</sup>,4}||[[Hexipentiruncicantellated 8-orthoplex]]<BR>Petiteriprismatorhombated diacosipentacontahexazetton||||||||||||||6451200||1290240
| |
| |- align=center BGCOLOR="#f0e0e0"
| |
| !177
| |
| |<!-- [o3x3x3x3o3x3x4o] -->{{CDD|node|4|node_1|3|node_1|3|node|3|node_1|3|node_1|3|node_1|3|node}}||t<sub>1,2,3,5,6</sub>{3<sup>6</sup>,4}||[[Bipentistericantitruncated 8-orthoplex]]<BR>Bitericelligreatorhombated diacosipentacontahexazetton||||||||||||||5806080||1290240
| |
| |- align=center BGCOLOR="#f0e0e0"
| |
| !178
| |
| |<!-- [x3x3o3o3x3x3x4o] -->{{CDD|node|4|node_1|3|node_1|3|node_1|3|node|3|node|3|node_1|3|node_1}}||t<sub>0,1,4,5,6</sub>{3<sup>6</sup>,4}||[[Hexipentisteritruncated 8-orthoplex]]<BR>Petitericellitruncated diacosipentacontahexazetton||||||||||||||4300800||860160
| |
| |- align=center BGCOLOR="#f0e0e0"
| |
| !179
| |
| |<!-- [x3o3x3o3x3x3x4o] -->{{CDD|node|4|node_1|3|node_1|3|node_1|3|node|3|node_1|3|node|3|node_1}}||t<sub>0,2,4,5,6</sub>{3<sup>6</sup>,4}||[[Hexipentistericantellated 8-orthoplex]]<BR>Petitericellirhombated diacosipentacontahexazetton||||||||||||||7096320||1290240
| |
| |- align=center BGCOLOR="#e0e0f0"
| |
| !180
| |
| |<!-- [o3x3x3o3x3x3x4o] -->{{CDD|node|4|node_1|3|node_1|3|node_1|3|node|3|node_1|3|node_1|3|node}}||t<sub>1,2,3,5,6</sub>{4,3<sup>6</sup>}||[[Bipentistericantitruncated 8-cube]]<BR>Bitericelligreatorhombated octeract||||||||||||||5806080||1290240
| |
| |- align=center BGCOLOR="#f0e0e0"
| |
| !181
| |
| |<!-- [x3o3o3x3x3x3x4o] -->{{CDD|node|4|node_1|3|node_1|3|node_1|3|node_1|3|node|3|node|3|node_1}}||t<sub>0,3,4,5,6</sub>{3<sup>6</sup>,4}||[[Hexipentisteriruncinated 8-orthoplex]]<BR>Petitericelliprismated diacosipentacontahexazetton||||||||||||||4300800||860160
| |
| |- align=center BGCOLOR="#e0e0f0"
| |
| !182
| |
| |<!-- [o3x3o3x3x3x3x4o] -->{{CDD|node|4|node_1|3|node_1|3|node_1|3|node_1|3|node|3|node_1|3|node}}||t<sub>1,2,3,4,6</sub>{4,3<sup>6</sup>}||[[Bipentiruncicantitruncated 8-cube]]<BR>Biterigreatoprismated octeract||||||||||||||6451200||1290240
| |
| |- align=center BGCOLOR="#e0e0f0"
| |
| !183
| |
| |<!-- [o3o3x3x3x3x3x4o] -->{{CDD|node|4|node_1|3|node_1|3|node_1|3|node_1|3|node_1|3|node|3|node}}||t<sub>1,2,3,4,5</sub>{4,3<sup>6</sup>}||[[Bisteriruncicantitruncated 8-cube]]<BR>Great bicellated octeract||||||||||||||3440640||860160
| |
| |- align=center BGCOLOR="#f0e0e0"
| |
| !184
| |
| |<!-- [x3x3x3x3o3o3o4x] -->{{CDD|node_1|4|node|3|node|3|node|3|node_1|3|node_1|3|node_1|3|node_1}}||t<sub>0,1,2,3,7</sub>{3<sup>6</sup>,4}||[[Heptiruncicantitruncated 8-orthoplex]]<BR>Exigreatoprismated diacosipentacontahexazetton||||||||||||||2365440||430080
| |
| |- align=center BGCOLOR="#f0e0e0"
| |
| !185
| |
| |<!-- [x3x3x3o3x3o3o4x] -->{{CDD|node_1|4|node|3|node|3|node_1|3|node|3|node_1|3|node_1|3|node_1}}||t<sub>0,1,2,4,7</sub>{3<sup>6</sup>,4}||[[Heptistericantitruncated 8-orthoplex]]<BR>Exicelligreatorhombated diacosipentacontahexazetton||||||||||||||5591040||860160
| |
| |- align=center BGCOLOR="#f0e0e0"
| |
| !186
| |
| |<!-- [x3x3o3x3x3o3o4x] -->{{CDD|node_1|4|node|3|node|3|node_1|3|node_1|3|node|3|node_1|3|node_1}}||t<sub>0,1,3,4,7</sub>{3<sup>6</sup>,4}||[[Heptisteriruncitruncated 8-orthoplex]]<BR>Exicelliprismatotruncated diacosipentacontahexazetton||||||||||||||4730880||860160
| |
| |- align=center BGCOLOR="#f0e0e0"
| |
| !187
| |
| |<!-- [x3o3x3x3x3o3o4x] -->{{CDD|node_1|4|node|3|node|3|node_1|3|node_1|3|node_1|3|node|3|node_1}}||t<sub>0,2,3,4,7</sub>{3<sup>6</sup>,4}||[[Heptisteriruncicantellated 8-orthoplex]]<BR>Exicelliprismatorhombated diacosipentacontahexazetton||||||||||||||4730880||860160
| |
| |- align=center BGCOLOR="#e0e0f0"
| |
| !188
| |
| |<!-- [o3x3x3x3x3o3o4x] -->{{CDD|node_1|4|node|3|node|3|node_1|3|node_1|3|node_1|3|node_1|3|node}}||t<sub>0,3,4,5,6</sub>{4,3<sup>6</sup>}||[[Hexipentisteriruncinated 8-cube]]<BR>Petitericelliprismated octeract||||||||||||||4300800||860160
| |
| |- align=center BGCOLOR="#f0e0e0"
| |
| !189
| |
| |<!-- [x3x3x3o3o3x3o4x] -->{{CDD|node_1|4|node|3|node_1|3|node|3|node|3|node_1|3|node_1|3|node_1}}||t<sub>0,1,2,5,7</sub>{3<sup>6</sup>,4}||[[Heptipenticantitruncated 8-orthoplex]]<BR>Exiterigreatorhombated diacosipentacontahexazetton||||||||||||||5591040||860160
| |
| |- align=center BGCOLOR="#f0e0e0"
| |
| !190
| |
| |<!-- [x3x3o3x3o3x3o4x] -->{{CDD|node_1|4|node|3|node_1|3|node|3|node_1|3|node|3|node_1|3|node_1}}||t<sub>0,1,3,5,7</sub>{3<sup>6</sup>,4}||[[Heptipentiruncitruncated 8-orthoplex]]<BR>Exiteriprismatotruncated diacosipentacontahexazetton||||||||||||||8386560||1290240
| |
| |- align=center BGCOLOR="#f0e0e0"
| |
| !191
| |
| |<!-- [x3o3x3x3o3x3o4x] -->{{CDD|node_1|4|node|3|node_1|3|node|3|node_1|3|node_1|3|node|3|node_1}}||t<sub>0,2,3,5,7</sub>{3<sup>6</sup>,4}||[[Heptipentiruncicantellated 8-orthoplex]]<BR>Exiteriprismatorhombated diacosipentacontahexazetton||||||||||||||7741440||1290240
| |
| |- align=center BGCOLOR="#e0e0f0"
| |
| !192
| |
| |<!-- [o3x3x3x3o3x3o4x] -->{{CDD|node_1|4|node|3|node_1|3|node|3|node_1|3|node_1|3|node_1|3|node}}||t<sub>0,2,4,5,6</sub>{4,3<sup>6</sup>}||[[Hexipentistericantellated 8-cube]]<BR>Petitericellirhombated octeract||||||||||||||7096320||1290240
| |
| |- align=center BGCOLOR="#f0e0e0"
| |
| !193
| |
| |<!-- [x3x3o3o3x3x3o4x] -->{{CDD|node_1|4|node|3|node_1|3|node_1|3|node|3|node|3|node_1|3|node_1}}||t<sub>0,1,4,5,7</sub>{3<sup>6</sup>,4}||[[Heptipentisteritruncated 8-orthoplex]]<BR>Exitericellitruncated diacosipentacontahexazetton||||||||||||||4730880||860160
| |
| |- align=center BGCOLOR="#e0e0f0"
| |
| !194
| |
| |<!-- [x3o3x3o3x3x3o4x] -->{{CDD|node_1|4|node|3|node_1|3|node_1|3|node|3|node_1|3|node|3|node_1}}||t<sub>0,2,3,5,7</sub>{4,3<sup>6</sup>}||[[Heptipentiruncicantellated 8-cube]]<BR>Exiteriprismatorhombated octeract||||||||||||||7741440||1290240
| |
| |- align=center BGCOLOR="#e0e0f0"
| |
| !195
| |
| |<!-- [o3x3x3o3x3x3o4x] -->{{CDD|node_1|4|node|3|node_1|3|node_1|3|node|3|node_1|3|node_1|3|node}}||t<sub>0,2,3,5,6</sub>{4,3<sup>6</sup>}||[[Hexipentiruncicantellated 8-cube]]<BR>Petiteriprismatorhombated octeract||||||||||||||6451200||1290240
| |
| |- align=center BGCOLOR="#e0e0f0"
| |
| !196
| |
| |<!-- [x3o3o3x3x3x3o4x] -->{{CDD|node_1|4|node|3|node_1|3|node_1|3|node_1|3|node|3|node|3|node_1}}||t<sub>0,2,3,4,7</sub>{4,3<sup>6</sup>}||[[Heptisteriruncicantellated 8-cube]]<BR>Exicelliprismatorhombated octeract||||||||||||||4730880||860160
| |
| |- align=center BGCOLOR="#e0e0f0"
| |
| !197
| |
| |<!-- [o3x3o3x3x3x3o4x] -->{{CDD|node_1|4|node|3|node_1|3|node_1|3|node_1|3|node|3|node_1|3|node}}||t<sub>0,2,3,4,6</sub>{4,3<sup>6</sup>}||[[Hexisteriruncicantellated 8-cube]]<BR>Peticelliprismatorhombated octeract||||||||||||||7096320||1290240
| |
| |- align=center BGCOLOR="#e0e0f0"
| |
| !198
| |
| |<!-- [o3o3x3x3x3x3o4x] -->{{CDD|node_1|4|node|3|node_1|3|node_1|3|node_1|3|node_1|3|node|3|node}}||t<sub>0,2,3,4,5</sub>{4,3<sup>6</sup>}||[[Pentisteriruncicantellated 8-cube]]<BR>Tericelliprismatorhombated octeract||||||||||||||3870720||860160
| |
| |- align=center BGCOLOR="#f0e0e0"
| |
| !199
| |
| |<!-- [x3x3x3o3o3o3x4x] -->{{CDD|node_1|4|node_1|3|node|3|node|3|node|3|node_1|3|node_1|3|node_1}}||t<sub>0,1,2,6,7</sub>{3<sup>6</sup>,4}||[[Heptihexicantitruncated 8-orthoplex]]<BR>Exipetigreatorhombated diacosipentacontahexazetton||||||||||||||2365440||430080
| |
| |- align=center BGCOLOR="#f0e0e0"
| |
| !200
| |
| |<!-- [x3x3o3x3o3o3x4x] -->{{CDD|node_1|4|node_1|3|node|3|node|3|node_1|3|node|3|node_1|3|node_1}}||t<sub>0,1,3,6,7</sub>{3<sup>6</sup>,4}||[[Heptihexiruncitruncated 8-orthoplex]]<BR>Exipetiprismatotruncated diacosipentacontahexazetton||||||||||||||5591040||860160
| |
| |- align=center BGCOLOR="#e0e0f0"
| |
| !201
| |
| |<!-- [x3o3x3x3o3o3x4x] -->{{CDD|node_1|4|node_1|3|node|3|node|3|node_1|3|node_1|3|node|3|node_1}}||t<sub>0,1,4,5,7</sub>{4,3<sup>6</sup>}||[[Heptipentisteritruncated 8-cube]]<BR>Exitericellitruncated octeract||||||||||||||4730880||860160
| |
| |- align=center BGCOLOR="#e0e0f0"
| |
| !202
| |
| |<!-- [o3x3x3x3o3o3x4x] -->{{CDD|node_1|4|node_1|3|node|3|node|3|node_1|3|node_1|3|node_1|3|node}}||t<sub>0,1,4,5,6</sub>{4,3<sup>6</sup>}||[[Hexipentisteritruncated 8-cube]]<BR>Petitericellitruncated octeract||||||||||||||4300800||860160
| |
| |- align=center BGCOLOR="#e0e0f0"
| |
| !203
| |
| |<!-- [x3x3o3o3x3o3x4x] -->{{CDD|node_1|4|node_1|3|node|3|node_1|3|node|3|node|3|node_1|3|node_1}}||t<sub>0,1,3,6,7</sub>{4,3<sup>6</sup>}||[[Heptihexiruncitruncated 8-cube]]<BR>Exipetiprismatotruncated octeract||||||||||||||5591040||860160
| |
| |- align=center BGCOLOR="#e0e0f0"
| |
| !204
| |
| |<!-- [x3o3x3o3x3o3x4x] -->{{CDD|node_1|4|node_1|3|node|3|node_1|3|node|3|node_1|3|node|3|node_1}}||t<sub>0,1,3,5,7</sub>{4,3<sup>6</sup>}||[[Heptipentiruncitruncated 8-cube]]<BR>Exiteriprismatotruncated octeract||||||||||||||8386560||1290240
| |
| |- align=center BGCOLOR="#e0e0f0"
| |
| !205
| |
| |<!-- [o3x3x3o3x3o3x4x] -->{{CDD|node_1|4|node_1|3|node|3|node_1|3|node|3|node_1|3|node_1|3|node}}||t<sub>0,1,3,5,6</sub>{4,3<sup>6</sup>}||[[Hexipentiruncitruncated 8-cube]]<BR>Petiteriprismatotruncated octeract||||||||||||||7096320||1290240
| |
| |- align=center BGCOLOR="#e0e0f0"
| |
| !206
| |
| |<!-- [x3o3o3x3x3o3x4x] -->{{CDD|node_1|4|node_1|3|node|3|node_1|3|node_1|3|node|3|node|3|node_1}}||t<sub>0,1,3,4,7</sub>{4,3<sup>6</sup>}||[[Heptisteriruncitruncated 8-cube]]<BR>Exicelliprismatotruncated octeract||||||||||||||4730880||860160
| |
| |- align=center BGCOLOR="#e0e0f0"
| |
| !207
| |
| |<!-- [o3x3o3x3x3o3x4x] -->{{CDD|node_1|4|node_1|3|node|3|node_1|3|node_1|3|node|3|node_1|3|node}}||t<sub>0,1,3,4,6</sub>{4,3<sup>6</sup>}||[[Hexisteriruncitruncated 8-cube]]<BR>Peticelliprismatotruncated octeract||||||||||||||7096320||1290240
| |
| |- align=center BGCOLOR="#e0e0f0"
| |
| !208
| |
| |<!-- [o3o3x3x3x3o3x4x] -->{{CDD|node_1|4|node_1|3|node|3|node_1|3|node_1|3|node_1|3|node|3|node}}||t<sub>0,1,3,4,5</sub>{4,3<sup>6</sup>}||[[Pentisteriruncitruncated 8-cube]]<BR>Tericelliprismatotruncated octeract||||||||||||||3870720||860160
| |
| |- align=center BGCOLOR="#e0e0f0"
| |
| !209
| |
| |<!-- [x3x3o3o3o3x3x4x] -->{{CDD|node_1|4|node_1|3|node_1|3|node|3|node|3|node|3|node_1|3|node_1}}||t<sub>0,1,2,6,7</sub>{4,3<sup>6</sup>}||[[Heptihexicantitruncated 8-cube]]<BR>Exipetigreatorhombated octeract||||||||||||||2365440||430080
| |
| |- align=center BGCOLOR="#e0e0f0"
| |
| !210
| |
| |<!-- [x3o3x3o3o3x3x4x] -->{{CDD|node_1|4|node_1|3|node_1|3|node|3|node|3|node_1|3|node|3|node_1}}||t<sub>0,1,2,5,7</sub>{4,3<sup>6</sup>}||[[Heptipenticantitruncated 8-cube]]<BR>Exiterigreatorhombated octeract||||||||||||||5591040||860160
| |
| |- align=center BGCOLOR="#e0e0f0"
| |
| !211
| |
| |<!-- [o3x3x3o3o3x3x4x] -->{{CDD|node_1|4|node_1|3|node_1|3|node|3|node|3|node_1|3|node_1|3|node}}||t<sub>0,1,2,5,6</sub>{4,3<sup>6</sup>}||[[Hexipenticantitruncated 8-cube]]<BR>Petiterigreatorhombated octeract||||||||||||||4300800||860160
| |
| |- align=center BGCOLOR="#e0e0f0"
| |
| !212
| |
| |<!-- [x3o3o3x3o3x3x4x] -->{{CDD|node_1|4|node_1|3|node_1|3|node|3|node_1|3|node|3|node|3|node_1}}||t<sub>0,1,2,4,7</sub>{4,3<sup>6</sup>}||[[Heptistericantitruncated 8-cube]]<BR>Exicelligreatorhombated octeract||||||||||||||5591040||860160
| |
| |- align=center BGCOLOR="#e0e0f0"
| |
| !213
| |
| |<!-- [o3x3o3x3o3x3x4x] -->{{CDD|node_1|4|node_1|3|node_1|3|node|3|node_1|3|node|3|node_1|3|node}}||t<sub>0,1,2,4,6</sub>{4,3<sup>6</sup>}||[[Hexistericantitruncated 8-cube]]<BR>Peticelligreatorhombated octeract||||||||||||||7741440||1290240
| |
| |- align=center BGCOLOR="#e0e0f0"
| |
| !214
| |
| |<!-- [o3o3x3x3o3x3x4x] -->{{CDD|node_1|4|node_1|3|node_1|3|node|3|node_1|3|node_1|3|node|3|node}}||t<sub>0,1,2,4,5</sub>{4,3<sup>6</sup>}||[[Pentistericantitruncated 8-cube]]<BR>Tericelligreatorhombated octeract||||||||||||||3870720||860160
| |
| |- align=center BGCOLOR="#e0e0f0"
| |
| !215
| |
| |<!-- [x3o3o3o3x3x3x4x] -->{{CDD|node_1|4|node_1|3|node_1|3|node_1|3|node|3|node|3|node|3|node_1}}||t<sub>0,1,2,3,7</sub>{4,3<sup>6</sup>}||[[Heptiruncicantitruncated 8-cube]]<BR>Exigreatoprismated octeract||||||||||||||2365440||430080
| |
| |- align=center BGCOLOR="#e0e0f0"
| |
| !216
| |
| |<!-- [o3x3o3o3x3x3x4x] -->{{CDD|node_1|4|node_1|3|node_1|3|node_1|3|node|3|node|3|node_1|3|node}}||t<sub>0,1,2,3,6</sub>{4,3<sup>6</sup>}||[[Hexiruncicantitruncated 8-cube]]<BR>Petigreatoprismated octeract||||||||||||||5160960||860160
| |
| |- align=center BGCOLOR="#e0e0f0"
| |
| !217
| |
| |<!-- [o3o3x3o3x3x3x4x] -->{{CDD|node_1|4|node_1|3|node_1|3|node_1|3|node|3|node_1|3|node|3|node}}||t<sub>0,1,2,3,5</sub>{4,3<sup>6</sup>}||[[Pentiruncicantitruncated 8-cube]]<BR>Terigreatoprismated octeract||||||||||||||4730880||860160
| |
| |- align=center BGCOLOR="#e0e0f0"
| |
| !218
| |
| |<!-- [o3o3o3x3x3x3x4x] -->{{CDD|node_1|4|node_1|3|node_1|3|node_1|3|node_1|3|node|3|node|3|node}}||t<sub>0,1,2,3,4</sub>{4,3<sup>6</sup>}||[[Steriruncicantitruncated 8-cube]]<BR>Great cellated octeract||||||||||||||1720320||430080
| |
| |- align=center BGCOLOR="#f0e0e0"
| |
| !219
| |
| |<!-- [x3x3x3x3x3x3o4o] -->{{CDD|node|4|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>{3<sup>6</sup>,4}||[[Pentisteriruncicantitruncated 8-orthoplex]]<BR>Great terated diacosipentacontahexazetton||||||||||||||5806080||1290240
| |
| |- align=center BGCOLOR="#f0e0e0"
| |
| !220
| |
| |<!-- [x3x3x3x3x3o3x4o] -->{{CDD|node|4|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>{3<sup>6</sup>,4}||[[Hexisteriruncicantitruncated 8-orthoplex]]<BR>Petigreatocellated diacosipentacontahexazetton||||||||||||||12902400||2580480
| |
| |- align=center BGCOLOR="#f0e0e0"
| |
| !221
| |
| |<!-- [x3x3x3x3o3x3x4o] -->{{CDD|node|4|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>{3<sup>6</sup>,4}||[[Hexipentiruncicantitruncated 8-orthoplex]]<BR>Petiterigreatoprismated diacosipentacontahexazetton||||||||||||||11612160||2580480
| |
| |- align=center BGCOLOR="#f0e0e0"
| |
| !222
| |
| |<!-- [x3x3x3o3x3x3x4o] -->{{CDD|node|4|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>{3<sup>6</sup>,4}||[[Hexipentistericantitruncated 8-orthoplex]]<BR>Petitericelligreatorhombated diacosipentacontahexazetton||||||||||||||11612160||2580480
| |
| |- align=center BGCOLOR="#f0e0e0"
| |
| !223
| |
| |<!-- [x3x3o3x3x3x3x4o] -->{{CDD|node|4|node_1|3|node_1|3|node_1|3|node_1|3|node|3|node_1|3|node_1}}||t<sub>0,1,3,4,5,6</sub>{3<sup>6</sup>,4}||[[Hexipentisteriruncitruncated 8-orthoplex]]<BR>Petitericelliprismatotruncated diacosipentacontahexazetton||||||||||||||11612160||2580480
| |
| |- align=center BGCOLOR="#f0e0e0"
| |
| !224
| |
| |<!-- [x3o3x3x3x3x3x4o] -->{{CDD|node|4|node_1|3|node_1|3|node_1|3|node_1|3|node_1|3|node|3|node_1}}||t<sub>0,2,3,4,5,6</sub>{3<sup>6</sup>,4}||[[Hexipentisteriruncicantellated 8-orthoplex]]<BR>Petitericelliprismatorhombated diacosipentacontahexazetton||||||||||||||11612160||2580480
| |
| |- align=center BGCOLOR="#e0f0e0"
| |
| !225
| |
| |<!-- [o3x3x3x3x3x3x4o] -->{{CDD|node|4|node_1|3|node_1|3|node_1|3|node_1|3|node_1|3|node_1|3|node}}||t<sub>1,2,3,4,5,6</sub>{4,3<sup>6</sup>}||[[Bipentisteriruncicantitruncated 8-cube]]<BR>Great biteri-octeractidiacosipentacontahexazetton||||||||||||||10321920||2580480
| |
| |- align=center BGCOLOR="#f0e0e0"
| |
| !226
| |
| |<!-- [x3x3x3x3x3o3o4x] -->{{CDD|node_1|4|node|3|node|3|node_1|3|node_1|3|node_1|3|node_1|3|node_1}}||t<sub>0,1,2,3,4,7</sub>{3<sup>6</sup>,4}||[[Heptisteriruncicantitruncated 8-orthoplex]]<BR>Exigreatocellated diacosipentacontahexazetton||||||||||||||8601600||1720320
| |
| |- align=center BGCOLOR="#f0e0e0"
| |
| !227
| |
| |<!-- [x3x3x3x3o3x3o4x] -->{{CDD|node_1|4|node|3|node_1|3|node|3|node_1|3|node_1|3|node_1|3|node_1}}||t<sub>0,1,2,3,5,7</sub>{3<sup>6</sup>,4}||[[Heptipentiruncicantitruncated 8-orthoplex]]<BR>Exiterigreatoprismated diacosipentacontahexazetton||||||||||||||14192640||2580480
| |
| |- align=center BGCOLOR="#f0e0e0"
| |
| !228
| |
| |<!-- [x3x3x3o3x3x3o4x] -->{{CDD|node_1|4|node|3|node_1|3|node_1|3|node|3|node_1|3|node_1|3|node_1}}||t<sub>0,1,2,4,5,7</sub>{3<sup>6</sup>,4}||[[Heptipentistericantitruncated 8-orthoplex]]<BR>Exitericelligreatorhombated diacosipentacontahexazetton||||||||||||||12902400||2580480
| |
| |- align=center BGCOLOR="#f0e0e0"
| |
| !229
| |
| |<!-- [x3x3o3x3x3x3o4x] -->{{CDD|node_1|4|node|3|node_1|3|node_1|3|node_1|3|node|3|node_1|3|node_1}}||t<sub>0,1,3,4,5,7</sub>{3<sup>6</sup>,4}||[[Heptipentisteriruncitruncated 8-orthoplex]]<BR>Exitericelliprismatotruncated diacosipentacontahexazetton||||||||||||||12902400||2580480
| |
| |- align=center BGCOLOR="#e0f0e0"
| |
| !230
| |
| |<!-- [x3o3x3x3x3x3o4x] -->{{CDD|node_1|4|node|3|node_1|3|node_1|3|node_1|3|node_1|3|node|3|node_1}}||t<sub>0,2,3,4,5,7</sub>{4,3<sup>6</sup>}||[[Heptipentisteriruncicantellated 8-cube]]<BR>Exitericelliprismatorhombi-octeractidiacosipentacontahexazetton||||||||||||||12902400||2580480
| |
| |- align=center BGCOLOR="#e0e0f0"
| |
| !231
| |
| |<!-- [o3x3x3x3x3x3o4x] -->{{CDD|node_1|4|node|3|node_1|3|node_1|3|node_1|3|node_1|3|node_1|3|node}}||t<sub>0,2,3,4,5,6</sub>{4,3<sup>6</sup>}||[[Hexipentisteriruncicantellated 8-cube]]<BR>Petitericelliprismatorhombated octeract||||||||||||||11612160||2580480
| |
| |- align=center BGCOLOR="#f0e0e0"
| |
| !232
| |
| |<!-- [x3x3x3x3o3o3x4x] -->{{CDD|node_1|4|node_1|3|node|3|node|3|node_1|3|node_1|3|node_1|3|node_1}}||t<sub>0,1,2,3,6,7</sub>{3<sup>6</sup>,4}||[[Heptihexiruncicantitruncated 8-orthoplex]]<BR>Exipetigreatoprismated diacosipentacontahexazetton||||||||||||||8601600||1720320
| |
| |- align=center BGCOLOR="#f0e0e0"
| |
| !233
| |
| |<!-- [x3x3x3o3x3o3x4x] -->{{CDD|node_1|4|node_1|3|node|3|node_1|3|node|3|node_1|3|node_1|3|node_1}}||t<sub>0,1,2,4,6,7</sub>{3<sup>6</sup>,4}||[[Heptihexistericantitruncated 8-orthoplex]]<BR>Exipeticelligreatorhombated diacosipentacontahexazetton||||||||||||||14192640||2580480
| |
| |- align=center BGCOLOR="#e0f0e0"
| |
| !234
| |
| |<!-- [x3x3o3x3x3o3x4x] -->{{CDD|node_1|4|node_1|3|node|3|node_1|3|node_1|3|node|3|node_1|3|node_1}}||t<sub>0,1,3,4,6,7</sub>{4,3<sup>6</sup>}||[[Heptihexisteriruncitruncated 8-cube]]<BR>Exipeticelliprismatotrunki-octeractidiacosipentacontahexazetton||||||||||||||12902400||2580480
| |
| |- align=center BGCOLOR="#e0e0f0"
| |
| !235
| |
| |<!-- [x3o3x3x3x3o3x4x] -->{{CDD|node_1|4|node_1|3|node|3|node_1|3|node_1|3|node_1|3|node|3|node_1}}||t<sub>0,1,3,4,5,7</sub>{4,3<sup>6</sup>}||[[Heptipentisteriruncitruncated 8-cube]]<BR>Exitericelliprismatotruncated octeract||||||||||||||12902400||2580480
| |
| |- align=center BGCOLOR="#e0e0f0"
| |
| !236
| |
| |<!-- [o3x3x3x3x3o3x4x] -->{{CDD|node_1|4|node_1|3|node|3|node_1|3|node_1|3|node_1|3|node_1|3|node}}||t<sub>0,1,3,4,5,6</sub>{4,3<sup>6</sup>}||[[Hexipentisteriruncitruncated 8-cube]]<BR>Petitericelliprismatotruncated octeract||||||||||||||11612160||2580480
| |
| |- align=center BGCOLOR="#e0f0e0"
| |
| !237
| |
| |<!-- [x3x3x3o3o3x3x4x] -->{{CDD|node_1|4|node_1|3|node_1|3|node|3|node|3|node_1|3|node_1|3|node_1}}||t<sub>0,1,2,5,6,7</sub>{4,3<sup>6</sup>}||[[Heptihexipenticantitruncated 8-cube]]<BR>Exipetiterigreatorhombi-octeractidiacosipentacontahexazetton||||||||||||||8601600||1720320
| |
| |- align=center BGCOLOR="#e0e0f0"
| |
| !238
| |
| |<!-- [x3x3o3x3o3x3x4x] -->{{CDD|node_1|4|node_1|3|node_1|3|node|3|node_1|3|node|3|node_1|3|node_1}}||t<sub>0,1,2,4,6,7</sub>{4,3<sup>6</sup>}||[[Heptihexistericantitruncated 8-cube]]<BR>Exipeticelligreatorhombated octeract||||||||||||||14192640||2580480
| |
| |- align=center BGCOLOR="#e0e0f0"
| |
| !239
| |
| |<!-- [x3o3x3x3o3x3x4x] -->{{CDD|node_1|4|node_1|3|node_1|3|node|3|node_1|3|node_1|3|node|3|node_1}}||t<sub>0,1,2,4,5,7</sub>{4,3<sup>6</sup>}||[[Heptipentistericantitruncated 8-cube]]<BR>Exitericelligreatorhombated octeract||||||||||||||12902400||2580480
| |
| |- align=center BGCOLOR="#e0e0f0"
| |
| !240
| |
| |<!-- [o3x3x3x3o3x3x4x] -->{{CDD|node_1|4|node_1|3|node_1|3|node|3|node_1|3|node_1|3|node_1|3|node}}||t<sub>0,1,2,4,5,6</sub>{4,3<sup>6</sup>}||[[Hexipentistericantitruncated 8-cube]]<BR>Petitericelligreatorhombated octeract||||||||||||||11612160||2580480
| |
| |- align=center BGCOLOR="#e0e0f0"
| |
| !241
| |
| |<!-- [x3x3o3o3x3x3x4x] -->{{CDD|node_1|4|node_1|3|node_1|3|node_1|3|node|3|node|3|node_1|3|node_1}}||t<sub>0,1,2,3,6,7</sub>{4,3<sup>6</sup>}||[[Heptihexiruncicantitruncated 8-cube]]<BR>Exipetigreatoprismated octeract||||||||||||||8601600||1720320
| |
| |- align=center BGCOLOR="#e0e0f0"
| |
| !242
| |
| |<!-- [x3o3x3o3x3x3x4x] -->{{CDD|node_1|4|node_1|3|node_1|3|node_1|3|node|3|node_1|3|node|3|node_1}}||t<sub>0,1,2,3,5,7</sub>{4,3<sup>6</sup>}||[[Heptipentiruncicantitruncated 8-cube]]<BR>Exiterigreatoprismated octeract||||||||||||||14192640||2580480
| |
| |- align=center BGCOLOR="#e0e0f0"
| |
| !243
| |
| |<!-- [o3x3x3o3x3x3x4x] -->{{CDD|node_1|4|node_1|3|node_1|3|node_1|3|node|3|node_1|3|node_1|3|node}}||t<sub>0,1,2,3,5,6</sub>{4,3<sup>6</sup>}||[[Hexipentiruncicantitruncated 8-cube]]<BR>Petiterigreatoprismated octeract||||||||||||||11612160||2580480
| |
| |- align=center BGCOLOR="#e0e0f0"
| |
| !244
| |
| |<!-- [x3o3o3x3x3x3x4x] -->{{CDD|node_1|4|node_1|3|node_1|3|node_1|3|node_1|3|node|3|node|3|node_1}}||t<sub>0,1,2,3,4,7</sub>{4,3<sup>6</sup>}||[[Heptisteriruncicantitruncated 8-cube]]<BR>Exigreatocellated octeract||||||||||||||8601600||1720320
| |
| |- align=center BGCOLOR="#e0e0f0"
| |
| !245
| |
| |<!-- [o3x3o3x3x3x3x4x] -->{{CDD|node_1|4|node_1|3|node_1|3|node_1|3|node_1|3|node|3|node_1|3|node}}||t<sub>0,1,2,3,4,6</sub>{4,3<sup>6</sup>}||[[Hexisteriruncicantitruncated 8-cube]]<BR>Petigreatocellated octeract||||||||||||||12902400||2580480
| |
| |- align=center BGCOLOR="#e0e0f0"
| |
| !246
| |
| |<!-- [o3o3x3x3x3x3x4x] -->{{CDD|node_1|4|node_1|3|node_1|3|node_1|3|node_1|3|node_1|3|node|3|node}}||t<sub>0,1,2,3,4,5</sub>{4,3<sup>6</sup>}||[[Pentisteriruncicantitruncated 8-cube]]<BR>Great terated octeract||||||||||||||6881280||1720320
| |
| |- align=center BGCOLOR="#f0e0e0"
| |
| !247
| |
| |<!-- [x3x3x3x3x3x3x4o] -->{{CDD|node|4|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>{3<sup>6</sup>,4}||[[Hexipentisteriruncicantitruncated 8-orthoplex]]<BR>Great petated diacosipentacontahexazetton||||||||||||||20643840||5160960
| |
| |- align=center BGCOLOR="#f0e0e0"
| |
| !248
| |
| |<!-- [x3x3x3x3x3x3o4x] -->{{CDD|node_1|4|node|3|node_1|3|node_1|3|node_1|3|node_1|3|node_1|3|node_1}}||t<sub>0,1,2,3,4,5,7</sub>{3<sup>6</sup>,4}||[[Heptipentisteriruncicantitruncated 8-orthoplex]]<BR>Exigreatoterated diacosipentacontahexazetton||||||||||||||23224320||5160960
| |
| |- align=center BGCOLOR="#f0e0e0"
| |
| !249
| |
| |<!-- [x3x3x3x3x3o3x4x] -->{{CDD|node_1|4|node_1|3|node|3|node_1|3|node_1|3|node_1|3|node_1|3|node_1}}||t<sub>0,1,2,3,4,6,7</sub>{3<sup>6</sup>,4}||[[Heptihexisteriruncicantitruncated 8-orthoplex]]<BR>Exipetigreatocellated diacosipentacontahexazetton||||||||||||||23224320||5160960
| |
| |- align=center BGCOLOR="#f0e0e0"
| |
| !250
| |
| |<!-- [x3x3x3x3o3x3x4x] -->{{CDD|node_1|4|node_1|3|node_1|3|node|3|node_1|3|node_1|3|node_1|3|node_1}}||t<sub>0,1,2,3,5,6,7</sub>{3<sup>6</sup>,4}||[[Heptihexipentiruncicantitruncated 8-orthoplex]]<BR>Exipetiterigreatoprismated diacosipentacontahexazetton||||||||||||||23224320||5160960
| |
| |- align=center BGCOLOR="#e0e0f0"
| |
| !251
| |
| |<!-- [x3x3x3o3x3x3x4x] -->{{CDD|node_1|4|node_1|3|node_1|3|node_1|3|node|3|node_1|3|node_1|3|node_1}}||t<sub>0,1,2,3,5,6,7</sub>{4,3<sup>6</sup>}||[[Heptihexipentiruncicantitruncated 8-cube]]<BR>Exipetiterigreatoprismated octeract||||||||||||||23224320||5160960
| |
| |- align=center BGCOLOR="#e0e0f0"
| |
| !252
| |
| |<!-- [x3x3o3x3x3x3x4x] -->{{CDD|node_1|4|node_1|3|node_1|3|node_1|3|node_1|3|node|3|node_1|3|node_1}}||t<sub>0,1,2,3,4,6,7</sub>{4,3<sup>6</sup>}||[[Heptihexisteriruncicantitruncated 8-cube]]<BR>Exipetigreatocellated octeract||||||||||||||23224320||5160960
| |
| |- align=center BGCOLOR="#e0e0f0"
| |
| !253
| |
| |<!-- [x3o3x3x3x3x3x4x] -->{{CDD|node_1|4|node_1|3|node_1|3|node_1|3|node_1|3|node_1|3|node|3|node_1}}||t<sub>0,1,2,3,4,5,7</sub>{4,3<sup>6</sup>}||[[Heptipentisteriruncicantitruncated 8-cube]]<BR>Exigreatoterated octeract||||||||||||||23224320||5160960
| |
| |- align=center BGCOLOR="#e0e0f0"
| |
| !254
| |
| |<!-- [o3x3x3x3x3x3x4x] -->{{CDD|node_1|4|node_1|3|node_1|3|node_1|3|node_1|3|node_1|3|node_1|3|node}}||t<sub>0,1,2,3,4,5,6</sub>{4,3<sup>6</sup>}||[[Hexipentisteriruncicantitruncated 8-cube]]<BR>Great petated octeract||||||||||||||20643840||5160960
| |
| |- align=center BGCOLOR="#e0f0e0"
| |
| !255
| |
| |<!-- [x3x3x3x3x3x3x4x] -->{{CDD|node_1|4|node_1|3|node_1|3|node_1|3|node_1|3|node_1|3|node_1|3|node_1}}||t<sub>0,1,2,3,4,5,6,7</sub>{4,3<sup>6</sup>}||[[Omnitruncated 8-cube]]<BR>Great exi-octeractidiacosipentacontahexazetton||||||||||||||41287680||10321920
| |
| |}
| |
| | |
| === The D<sub>8</sub> family ===
| |
| | |
| The D<sub>8</sub> family has symmetry of order 5,160,960 (8 [[factorial]] x 2<sup>7</sup>).
| |
| | |
| This family has 191 Wythoffian uniform polytopes, from ''3x64-1'' permutations of the D<sub>8</sub> [[Coxeter-Dynkin diagram]] with one or more rings. 127 (2x64-1) are repeated from the B<sub>8</sub> family and 64 are unique to this family, all listed below.
| |
| | |
| See [[list of D8 polytopes]] for Coxeter plane graphs of these polytopes.
| |
| | |
| {| class="wikitable"
| |
| !rowspan=2|#
| |
| !rowspan=2|[[Coxeter-Dynkin diagram]]<BR>Name
| |
| !rowspan=2|Base point<BR>(Alternately signed)
| |
| !colspan=8|Element counts
| |
| !rowspan=2|Circumrad
| |
| |-
| |
| !7||6||5||4||3||2||1||0
| |
| |- align=center
| |
| !1
| |
| ||{{CDD|nodes_10ru|split2|node|3|node|3|node|3|node|3|node|3|node}}<BR>[[8-demicube]]||(1,1,1,1,1,1,1,1)||144||1136||4032||8288||10752||7168||1792||128||1.0000000
| |
| |- align=center
| |
| !2
| |
| ||{{CDD|nodes_10ru|split2|node_1|3|node|3|node|3|node|3|node|3|node}}<BR>[[Truncated 8-demicube]]||(1,1,3,3,3,3,3,3)|| || || || || || ||23296||3584||2.6457512
| |
| |- align=center
| |
| !3
| |
| ||{{CDD|nodes_10ru|split2|node|3|node_1|3|node|3|node|3|node|3|node}}||(1,1,1,3,3,3,3,3)|| || || || || || ||64512||7168||2.4494896
| |
| |- align=center
| |
| !4
| |
| ||{{CDD|nodes_10ru|split2|node|3|node|3|node_1|3|node|3|node|3|node}}||(1,1,1,1,3,3,3,3)|| || || || || || ||98560||8960||2.2360678
| |
| |- align=center
| |
| !5
| |
| ||{{CDD|nodes_10ru|split2|node|3|node|3|node|3|node_1|3|node|3|node}}||(1,1,1,1,1,3,3,3)|| || || || || || ||89600||7168||1.9999999
| |
| |- align=center
| |
| !6
| |
| ||{{CDD|nodes_10ru|split2|node|3|node|3|node|3|node|3|node_1|3|node}}||(1,1,1,1,1,1,3,3)|| || || || || || ||48384||3584||1.7320508
| |
| |- align=center
| |
| !7
| |
| ||{{CDD|nodes_10ru|split2|node|3|node|3|node|3|node|3|node|3|node_1}}||(1,1,1,1,1,1,1,3)|| || || || || || ||14336||1024||1.4142135
| |
| |- align=center
| |
| !8
| |
| ||{{CDD|nodes_10ru|split2|node_1|3|node_1|3|node|3|node|3|node|3|node}}||(1,1,3,5,5,5,5,5)|| || || || || || ||86016||21504||4.1231055
| |
| |- align=center
| |
| !9
| |
| ||{{CDD|nodes_10ru|split2|node_1|3|node|3|node_1|3|node|3|node|3|node}}||(1,1,3,3,5,5,5,5)|| || || || || || ||349440||53760||3.8729835
| |
| |- align=center
| |
| !10
| |
| ||{{CDD|nodes_10ru|split2|node|3|node_1|3|node_1|3|node|3|node|3|node}}||(1,1,1,3,5,5,5,5)|| || || || || || ||179200||35840||3.7416575
| |
| |- align=center
| |
| !11
| |
| ||{{CDD|nodes_10ru|split2|node_1|3|node|3|node|3|node_1|3|node|3|node}}||(1,1,3,3,3,5,5,5)|| || || || || || ||573440||71680||3.6055512
| |
| |- align=center
| |
| !12
| |
| ||{{CDD|nodes_10ru|split2|node|3|node_1|3|node|3|node_1|3|node|3|node}}||(1,1,1,3,3,5,5,5)|| || || || || || ||537600||71680||3.4641016
| |
| |- align=center
| |
| !13
| |
| ||{{CDD|nodes_10ru|split2|node|3|node|3|node_1|3|node_1|3|node|3|node}}||(1,1,1,1,3,5,5,5)|| || || || || || ||232960||35840||3.3166249
| |
| |- align=center
| |
| !14
| |
| ||{{CDD|nodes_10ru|split2|node_1|3|node|3|node|3|node|3|node_1|3|node}}||(1,1,3,3,3,3,5,5)|| || || || || || ||456960||53760||3.3166249
| |
| |- align=center
| |
| !15
| |
| ||{{CDD|nodes_10ru|split2|node|3|node_1|3|node|3|node|3|node_1|3|node}}||(1,1,1,3,3,3,5,5)|| || || || || || ||645120||71680||3.1622777
| |
| |- align=center
| |
| !16
| |
| ||{{CDD|nodes_10ru|split2|node|3|node|3|node_1|3|node|3|node_1|3|node}}||(1,1,1,1,3,3,5,5)|| || || || || || ||483840||53760||3
| |
| |- align=center
| |
| !17
| |
| ||{{CDD|nodes_10ru|split2|node|3|node|3|node|3|node_1|3|node_1|3|node}}||(1,1,1,1,1,3,5,5)|| || || || || || ||182784||21504||2.8284271
| |
| |- align=center
| |
| !18
| |
| ||{{CDD|nodes_10ru|split2|node_1|3|node|3|node|3|node|3|node|3|node_1}}||(1,1,3,3,3,3,3,5)|| || || || || || ||172032||21504||3
| |
| |- align=center
| |
| !19
| |
| ||{{CDD|nodes_10ru|split2|node|3|node_1|3|node|3|node|3|node|3|node_1}}||(1,1,1,3,3,3,3,5)|| || || || || || ||340480||35840||2.8284271
| |
| |- align=center
| |
| !20
| |
| ||{{CDD|nodes_10ru|split2|node|3|node|3|node_1|3|node|3|node|3|node_1}}||(1,1,1,1,3,3,3,5)|| || || || || || ||376320||35840||2.6457512
| |
| |- align=center
| |
| !21
| |
| ||{{CDD|nodes_10ru|split2|node|3|node|3|node|3|node_1|3|node|3|node_1}}||(1,1,1,1,1,3,3,5)|| || || || || || ||236544||21504||2.4494898
| |
| |- align=center
| |
| !22
| |
| ||{{CDD|nodes_10ru|split2|node|3|node|3|node|3|node|3|node_1|3|node_1}}||(1,1,1,1,1,1,3,5)|| || || || || || ||78848||7168||2.236068
| |
| |- align=center
| |
| !23
| |
| ||{{CDD|nodes_10ru|split2|node_1|3|node_1|3|node_1|3|node|3|node|3|node}}||(1,1,3,5,7,7,7,7)|| || || || || || ||430080||107520||5.3851647
| |
| |- align=center
| |
| !24
| |
| ||{{CDD|nodes_10ru|split2|node_1|3|node_1|3|node|3|node_1|3|node|3|node}}||(1,1,3,5,5,7,7,7)|| || || || || || ||1182720||215040||5.0990195
| |
| |- align=center
| |
| !25
| |
| ||{{CDD|nodes_10ru|split2|node_1|3|node|3|node_1|3|node_1|3|node|3|node}}||(1,1,3,3,5,7,7,7)|| || || || || || ||1075200||215040||4.8989797
| |
| |- align=center
| |
| !26
| |
| ||{{CDD|nodes_10ru|split2|node|3|node_1|3|node_1|3|node_1|3|node|3|node}}||(1,1,1,3,5,7,7,7)|| || || || || || ||716800||143360||4.7958317
| |
| |- align=center
| |
| !27
| |
| ||{{CDD|nodes_10ru|split2|node_1|3|node_1|3|node|3|node|3|node_1|3|node}}||(1,1,3,5,5,5,7,7)|| || || || || || ||1290240||215040||4.7958317
| |
| |- align=center
| |
| !28
| |
| ||{{CDD|nodes_10ru|split2|node_1|3|node|3|node_1|3|node|3|node_1|3|node}}||(1,1,3,3,5,5,7,7)|| || || || || || ||2096640||322560||4.5825758
| |
| |- align=center
| |
| !29
| |
| ||{{CDD|nodes_10ru|split2|node|3|node_1|3|node_1|3|node|3|node_1|3|node}}||(1,1,1,3,5,5,7,7)|| || || || || || ||1290240||215040||4.472136
| |
| |- align=center
| |
| !30
| |
| ||{{CDD|nodes_10ru|split2|node_1|3|node|3|node|3|node_1|3|node_1|3|node}}||(1,1,3,3,3,5,7,7)|| || || || || || ||1290240||215040||4.3588991
| |
| |- align=center
| |
| !31
| |
| ||{{CDD|nodes_10ru|split2|node|3|node_1|3|node|3|node_1|3|node_1|3|node}}||(1,1,1,3,3,5,7,7)|| || || || || || ||1397760||215040||4.2426405
| |
| |- align=center
| |
| !32
| |
| ||{{CDD|nodes_10ru|split2|node|3|node|3|node_1|3|node_1|3|node_1|3|node}}||(1,1,1,1,3,5,7,7)|| || || || || || ||698880||107520||4.1231055
| |
| |- align=center
| |
| !33
| |
| ||{{CDD|nodes_10ru|split2|node_1|3|node_1|3|node|3|node|3|node|3|node_1}}||(1,1,3,5,5,5,5,7)|| || || || || || ||591360||107520||4.472136
| |
| |- align=center
| |
| !34
| |
| ||{{CDD|nodes_10ru|split2|node_1|3|node|3|node_1|3|node|3|node|3|node_1}}||(1,1,3,3,5,5,5,7)|| || || || || || ||1505280||215040||4.2426405
| |
| |- align=center
| |
| !35
| |
| ||{{CDD|nodes_10ru|split2|node|3|node_1|3|node_1|3|node|3|node|3|node_1}}||(1,1,1,3,5,5,5,7)|| || || || || || ||860160||143360||4.1231055
| |
| |- align=center
| |
| !36
| |
| ||{{CDD|nodes_10ru|split2|node_1|3|node|3|node|3|node_1|3|node|3|node_1}}||(1,1,3,3,3,5,5,7)|| || || || || || ||1612800||215040||4
| |
| |- align=center
| |
| !37
| |
| ||{{CDD|nodes_10ru|split2|node|3|node_1|3|node|3|node_1|3|node|3|node_1}}||(1,1,1,3,3,5,5,7)|| || || || || || ||1612800||215040||3.8729835
| |
| |- align=center
| |
| !38
| |
| ||{{CDD|nodes_10ru|split2|node|3|node|3|node_1|3|node_1|3|node|3|node_1}}||(1,1,1,1,3,5,5,7)|| || || || || || ||752640||107520||3.7416575
| |
| |- align=center
| |
| !39
| |
| ||{{CDD|nodes_10ru|split2|node_1|3|node|3|node|3|node|3|node_1|3|node_1}}||(1,1,3,3,3,3,5,7)|| || || || || || ||752640||107520||3.7416575
| |
| |- align=center
| |
| !40
| |
| ||{{CDD|nodes_10ru|split2|node|3|node_1|3|node|3|node|3|node_1|3|node_1}}||(1,1,1,3,3,3,5,7)|| || || || || || ||1146880||143360||3.6055512
| |
| |- align=center
| |
| !41
| |
| ||{{CDD|nodes_10ru|split2|node|3|node|3|node_1|3|node|3|node_1|3|node_1}}||(1,1,1,1,3,3,5,7)|| || || || || || ||913920||107520||3.4641016
| |
| |- align=center
| |
| !42
| |
| ||{{CDD|nodes_10ru|split2|node|3|node|3|node|3|node_1|3|node_1|3|node_1}}||(1,1,1,1,1,3,5,7)|| || || || || || ||365568||43008||3.3166249
| |
| |- align=center
| |
| !43
| |
| ||{{CDD|nodes_10ru|split2|node_1|3|node_1|3|node_1|3|node_1|3|node|3|node}}||(1,1,3,5,7,9,9,9)|| || || || || || ||1720320||430080||6.4031243
| |
| |- align=center
| |
| !44
| |
| ||{{CDD|nodes_10ru|split2|node_1|3|node_1|3|node_1|3|node|3|node_1|3|node}}||(1,1,3,5,7,7,9,9)|| || || || || || ||3225600||645120||6.0827627
| |
| |- align=center
| |
| !45
| |
| ||{{CDD|nodes_10ru|split2|node_1|3|node_1|3|node|3|node_1|3|node_1|3|node}}||(1,1,3,5,5,7,9,9)|| || || || || || ||2903040||645120||5.8309517
| |
| |- align=center
| |
| !46
| |
| ||{{CDD|nodes_10ru|split2|node_1|3|node|3|node_1|3|node_1|3|node_1|3|node}}||(1,1,3,3,5,7,9,9)|| || || || || || ||3225600||645120||5.6568542
| |
| |- align=center
| |
| !47
| |
| ||{{CDD|nodes_10ru|split2|node|3|node_1|3|node_1|3|node_1|3|node_1|3|node}}||(1,1,1,3,5,7,9,9)|| || || || || || ||2150400||430080||5.5677648
| |
| |- align=center
| |
| !48
| |
| ||{{CDD|nodes_10ru|split2|node_1|3|node_1|3|node_1|3|node|3|node|3|node_1}}||(1,1,3,5,7,7,7,9)|| || || || || || ||2150400||430080||5.7445626
| |
| |- align=center
| |
| !49
| |
| ||{{CDD|nodes_10ru|split2|node_1|3|node_1|3|node|3|node_1|3|node|3|node_1}}||(1,1,3,5,5,7,7,9)|| || || || || || ||3548160||645120||5.4772258
| |
| |- align=center
| |
| !50
| |
| ||{{CDD|nodes_10ru|split2|node_1|3|node|3|node_1|3|node_1|3|node|3|node_1}}||(1,1,3,3,5,7,7,9)|| || || || || || ||3548160||645120||5.291503
| |
| |- align=center
| |
| !51
| |
| ||{{CDD|nodes_10ru|split2|node|3|node_1|3|node_1|3|node_1|3|node|3|node_1}}||(1,1,1,3,5,7,7,9)|| || || || || || ||2365440||430080||5.1961527
| |
| |- align=center
| |
| !52
| |
| ||{{CDD|nodes_10ru|split2|node_1|3|node_1|3|node|3|node|3|node_1|3|node_1}}||(1,1,3,5,5,5,7,9)|| || || || || || ||2150400||430080||5.1961527
| |
| |- align=center
| |
| !53
| |
| ||{{CDD|nodes_10ru|split2|node_1|3|node|3|node_1|3|node|3|node_1|3|node_1}}||(1,1,3,3,5,5,7,9)|| || || || || || ||3870720||645120||5
| |
| |- align=center
| |
| !54
| |
| ||{{CDD|nodes_10ru|split2|node|3|node_1|3|node_1|3|node|3|node_1|3|node_1}}||(1,1,1,3,5,5,7,9)|| || || || || || ||2365440||430080||4.8989797
| |
| |- align=center
| |
| !55
| |
| ||{{CDD|nodes_10ru|split2|node_1|3|node|3|node|3|node_1|3|node_1|3|node_1}}||(1,1,3,3,3,5,7,9)|| || || || || || ||2580480||430080||4.7958317
| |
| |- align=center
| |
| !56
| |
| ||{{CDD|nodes_10ru|split2|node|3|node_1|3|node|3|node_1|3|node_1|3|node_1}}||(1,1,1,3,3,5,7,9)|| || || || || || ||2795520||430080||4.6904159
| |
| |- align=center
| |
| !57
| |
| ||{{CDD|nodes_10ru|split2|node|3|node|3|node_1|3|node_1|3|node_1|3|node_1}}||(1,1,1,1,3,5,7,9)|| || || || || || ||1397760||215040||4.5825758
| |
| |- align=center
| |
| !58
| |
| ||{{CDD|nodes_10ru|split2|node_1|3|node_1|3|node_1|3|node_1|3|node_1|3|node}}||(1,1,3,5,7,9,11,11)|| || || || || || ||5160960||1290240||7.1414285
| |
| |- align=center
| |
| !59
| |
| ||{{CDD|nodes_10ru|split2|node_1|3|node_1|3|node_1|3|node_1|3|node|3|node_1}}||(1,1,3,5,7,9,9,11)|| || || || || || ||5806080||1290240||6.78233
| |
| |- align=center
| |
| !60
| |
| ||{{CDD|nodes_10ru|split2|node_1|3|node_1|3|node_1|3|node|3|node_1|3|node_1}}||(1,1,3,5,7,7,9,11)|| || || || || || ||5806080||1290240||6.480741
| |
| |- align=center
| |
| !61
| |
| ||{{CDD|nodes_10ru|split2|node_1|3|node_1|3|node|3|node_1|3|node_1|3|node_1}}||(1,1,3,5,5,7,9,11)|| || || || || || ||5806080||1290240||6.244998
| |
| |- align=center
| |
| !62
| |
| ||{{CDD|nodes_10ru|split2|node_1|3|node|3|node_1|3|node_1|3|node_1|3|node_1}}||(1,1,3,3,5,7,9,11)|| || || || || || ||6451200||1290240||6.0827627
| |
| |- align=center
| |
| !63
| |
| ||{{CDD|nodes_10ru|split2|node|3|node_1|3|node_1|3|node_1|3|node_1|3|node_1}}||(1,1,1,3,5,7,9,11)|| || || || || || ||4300800||860160||6.0000000
| |
| |- align=center
| |
| !64
| |
| ||{{CDD|nodes_10ru|split2|node_1|3|node_1|3|node_1|3|node_1|3|node_1|3|node_1}}||(1,1,3,5,7,9,11,13)|| || || || || || ||2580480||10321920||7.5498347
| |
| |}
| |
| | |
| === The E<sub>8</sub> family ===
| |
| | |
| The E<sub>8</sub> family has symmetry order 696,729,600.
| |
| | |
| There are 255 forms based on all permutations of the [[Coxeter-Dynkin diagram]]s with one or more rings. Eight forms are shown below, 4 single-ringed, 3 truncations (2 rings), and the final omnitruncation are given below. Bowers-style acronym names are given for cross-referencing.
| |
| | |
| See also [[list of E8 polytopes]] for Coxeter plane graphs of this family.
| |
| | |
| {| class="wikitable"
| |
| |-
| |
| !rowspan=2|#
| |
| !rowspan=2|[[Coxeter-Dynkin diagram]]<br/>
| |
| !rowspan=2|Names
| |
| !colspan=8|Element counts
| |
| |-
| |
| ! 7-faces
| |
| ! 6-faces
| |
| ! 5-faces
| |
| ! 4-faces
| |
| ! Cells
| |
| ! Faces
| |
| ! Edges
| |
| ! Vertices
| |
| |- align=center
| |
| |1||{{CDD|nodea_1|3a|nodea|3a|nodea|3a|nodea|3a|branch|3a|nodea|3a|nodea}}||[[Gosset 4 21 polytope|4<sub>21</sub>]] (fy)
| |
| |19440||207360||483840||483840||241920||60480||6720||240
| |
| |- align=center
| |
| |2||{{CDD|nodea_1|3a|nodea_1|3a|nodea|3a|nodea|3a|branch|3a|nodea|3a|nodea}}||[[Truncated 4 21 polytope|Truncated 4<sub>21</sub>]] (tiffy)
| |
| | || || || || || ||188160||13440
| |
| |- align=center
| |
| |3||{{CDD|nodea|3a|nodea_1|3a|nodea|3a|nodea|3a|branch|3a|nodea|3a|nodea}}||[[Rectified 4 21 polytope|Rectified 4<sub>21</sub>]] (riffy)
| |
| |19680||375840||1935360||3386880||2661120||1028160||181440||6720
| |
| |- align=center
| |
| |4||{{CDD|nodea|3a|nodea|3a|nodea_1|3a|nodea|3a|branch|3a|nodea|3a|nodea}}||[[Birectified 4 21 polytope|Birectified 4<sub>21</sub>]] (borfy)
| |
| |19680||382560||2600640||7741440||9918720||5806080||1451520||60480
| |
| |- align=center
| |
| |5||{{CDD|nodea|3a|nodea|3a|nodea|3a|nodea_1|3a|branch|3a|nodea|3a|nodea}}||[[Trirectified 4 21 polytope|Trirectified 4<sub>21</sub>]] (torfy)
| |
| |19680||382560||2661120||9313920||16934400||14515200||4838400||241920
| |
| |- align=center
| |
| |6||{{CDD|nodea|3a|nodea|3a|nodea|3a|nodea|3a|branch_10|3a|nodea|3a|nodea}}||[[Rectified 1 42 polytope|Rectified 1<sub>42</sub>]] (buffy)
| |
| |19680||382560||2661120||9072000||16934400||16934400||7257600||483840
| |
| |- align=center
| |
| |7||{{CDD|nodea|3a|nodea|3a|nodea|3a|nodea|3a|branch|3a|nodea_1|3a|nodea}}||[[Rectified 2 41 polytope|Rectified 2<sub>41</sub>]] (robay)
| |
| |19680||313440||1693440||4717440||7257600||5322240||1451520||69120
| |
| |- align=center
| |
| |8||{{CDD|nodea|3a|nodea|3a|nodea|3a|nodea|3a|branch|3a|nodea|3a|nodea_1}}||[[2 41 polytope|2<sub>41</sub>]] (bay)
| |
| |17520||144960||544320||1209600||1209600||483840||69120||2160
| |
| |- align=center
| |
| |9||{{CDD|nodea|3a|nodea|3a|nodea|3a|nodea|3a|branch|3a|nodea_1|3a|nodea_1}}||[[Truncated 2 41 polytope|Truncated 2<sub>41</sub>]]
| |
| | || || || || || || ||138240
| |
| |- align=center
| |
| |10||{{CDD|nodea|3a|nodea|3a|nodea|3a|nodea|3a|branch_01lr|3a|nodea|3a|nodea}}||[[1 42 polytope|1<sub>42</sub>]] (bif)
| |
| |2400||106080||725760||2298240||3628800||2419200||483840||17280
| |
| |- align=center
| |
| |11||{{CDD|nodea|3a|nodea|3a|nodea|3a|nodea|3a|branch_11|3a|nodea|3a|nodea}}||[[Truncated 1 42 polytope|Truncated 1<sub>42</sub>]]
| |
| | || || || || || || ||967680
| |
| |- align=center
| |
| |12||{{CDD|nodea_1|3a|nodea_1|3a|nodea_1|3a|nodea_1|3a|branch_11|3a|nodea_1|3a|nodea_1}}||[[Omnitruncated 4 21 polytope|Omnitruncated 4<sub>21</sub>]]
| |
| | || || || || || || ||696729600
| |
| |}
| |
| | |
| == Regular and uniform honeycombs ==
| |
| [[File:Coxeter diagram affine rank8 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.]]
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| There are five fundamental affine [[Coxeter groups]] that generate regular and uniform tessellations in 7-space:
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| {| class="wikitable"
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| |-
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| !#
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| !colspan=2|[[Coxeter group]]
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| ![[Coxeter diagram]]
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| !Forms
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| |- align=center
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| |1||<math>{\tilde{A}}_7</math>||[3<sup>[8]</sup>]||{{CDD|node|split1|nodes|3ab|nodes|3ab|nodes|split2|node}}||29
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| |- align=center
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| |2||<math>{\tilde{C}}_7</math>||[4,3<sup>5</sup>,4]||{{CDD|node|4|node|3|node|3|node|3|node|3|node|3|node|4|node}}||135
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| |- align=center
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| |3||<math>{\tilde{B}}_7</math>||[4,3<sup>4</sup>,3<sup>1,1</sup>]||{{CDD|nodes|split2|node|3|node|3|node|3|node|3|node|4|node}}||191 (64 new)
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| |- align=center
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| |4||<math>{\tilde{D}}_7</math>||[3<sup>1,1</sup>,3<sup>3</sup>,3<sup>1,1</sup>]||{{CDD|nodes|split2|node|3|node|3|node|3|node|split1|nodes}}||77 (10 new)
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| |- align=center
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| |5||<math>{\tilde{E}}_7</math>||[3<sup>3,3,1</sup>]||{{CDD|nodes|3ab|nodes|3ab|nodes|split2|node|3|node}}||143
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| |}
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| Regular and uniform tessellations include:
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| * <math>{\tilde{A}}_7</math> 29 uniquely ringed forms, including:
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| ** [[7-simplex honeycomb]]: {3<sup>[8]</sup>} {{CDD|node_1|split1|nodes|3ab|nodes|3ab|nodes|split2|node}}
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| * <math>{\tilde{C}}_7</math> 135 uniquely ringed forms, including:
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| ** Regular [[7-cube honeycomb]]: {4,3<sup>4</sup>,4} = {4,3<sup>4</sup>,3<sup>1,1</sup>}, {{CDD|node_1|4|node|3|node|3|node|3|node|3|node|4|node}} = {{CDD|node_1|4|node|3|node|3|node|3|node|3|node|3|node|split1|nodes}}
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| *<math>{\tilde{B}}_7</math> 191 uniquely ringed forms, 127 shared with <math>{\tilde{C}}_7</math>, and 64 new, including:
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| ** [[7-demicube honeycomb]]: h{4,3<sup>4</sup>,4} = {3<sup>1,1</sup>,3<sup>4</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|3|node|4|node}}
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| * <math>{\tilde{D}}_7</math>, [3<sup>1,1</sup>,3<sup>3</sup>,3<sup>1,1</sup>]: 77 unique ring permutations, and 10 are new, the first Coxeter called a [[quarter 7-cubic honeycomb]].
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| ** {{CDD|nodes_10ru|split2|node|3|node|3|node|3|node|split1|nodes_10lu}}, {{CDD|nodes_10ru|split2|node_1|3|node|3|node|3|node|split1|nodes_10lu}}, {{CDD|nodes_10ru|split2|node|3|node_1|3|node|3|node|split1|nodes_10lu}}, {{CDD|nodes_10ru|split2|node_1|3|node_1|3|node|3|node|split1|nodes_10lu}}, {{CDD|nodes_10ru|split2|node_1|3|node|3|node_1|3|node|split1|nodes_10lu}}, {{CDD|nodes_10ru|split2|node_1|3|node|3|node|3|node_1|split1|nodes_10lu}}, {{CDD|nodes_10ru|split2|node|3|node_1|3|node_1|3|node|split1|nodes_10lu}}, {{CDD|nodes_10ru|split2|node_1|3|node_1|3|node_1|3|node|split1|nodes_10lu}}, {{CDD|nodes_10ru|split2|node_1|3|node_1|3|node|3|node_1|split1|nodes_10lu}}, {{CDD|nodes_10ru|split2|node_1|3|node_1|3|node_1|3|node_1|split1|nodes_10lu}}
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| * <math>{\tilde{E}}_7</math> 143 uniquely ringed forms, including:
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| ** [[1 33 honeycomb|1<sub>33</sub> honeycomb]]: {3,3<sup>3,3</sup>}, {{CDD|nodes|3ab|nodes|3ab|nodes|split2|node|3|node_1}}
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| ** [[3 31 honeycomb|3<sub>31</sub> honeycomb]]: {3,3,3,3<sup>3,1</sup>}, {{CDD|nodes_10r|3ab|nodes|3ab|nodes|split2|node|3|node}}
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| === Regular and uniform hyperbolic honeycombs ===
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| There are no compact hyperbolic Coxeter groups of rank 8, groups that can generate honeycombs with all finite facets, and a finite [[vertex figure]]. However there are [[Coxeter-Dynkin_diagram#Rank_4_to_10|4 noncompact hyperbolic Coxeter groups]] of rank 8, each generating uniform honeycombs in 7-space as permutations of rings of the Coxeter diagrams.
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| {| class=wikitable
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| |align=right|<math>{\bar{P}}_7</math> = [3,3<sup>[7]</sup>]:<BR>{{CDD|branch|3ab|nodes|3ab|nodes|split2|node|3|node}}
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| |align=right|<math>{\bar{Q}}_7</math> = [3<sup>1,1</sup>,3<sup>2</sup>,3<sup>2,1</sup>]:<BR> {{CDD|nodea|3a|branch|3a|nodea|3a|branch|3a|nodea|3a|nodea}}
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| |align=right|<math>{\bar{S}}_7</math> = [4,3<sup>3</sup>,3<sup>2,1</sup>]:<BR> {{CDD|nodea|3a|nodea|3a|branch|3a|nodea|3a|nodea|3a|nodea|4a|nodea}}
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| |align=right|<math>{\bar{T}}_7</math> = [3<sup>3,2,2</sup>]:<BR>{{CDD|nodes|3ab|nodes|split2|node|3|node|3|node|3|node}}
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| |}
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| == References ==
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| * [[Thorold Gosset|T. Gosset]]: ''On the Regular and Semi-Regular Figures in Space of n Dimensions'', [[Messenger of Mathematics]], Macmillan, 1900
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| * [[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
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| * [[Harold Scott MacDonald Coxeter|H.S.M. Coxeter]]:
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| ** 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
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| ** H.S.M. Coxeter, ''Regular Polytopes'', 3rd Edition, Dover New York, 1973
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| * '''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 <ref>[http://www.wiley.com/WileyCDA/WileyTitle/productCd-0471010030.html Wiley::Kaleidoscopes: Selected Writings of H.S.M. Coxeter]</ref>
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| ** (Paper 22) H.S.M. Coxeter, ''Regular and Semi Regular Polytopes I'', [Math. Zeit. 46 (1940) 380-407, MR 2,10]
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| ** (Paper 23) H.S.M. Coxeter, ''Regular and Semi-Regular Polytopes II'', [Math. Zeit. 188 (1985) 559-591]
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| ** (Paper 24) H.S.M. Coxeter, ''Regular and Semi-Regular Polytopes III'', [Math. Zeit. 200 (1988) 3-45]
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| * [[Norman Johnson (mathematician)|N.W. Johnson]]: ''The Theory of Uniform Polytopes and Honeycombs'', Ph.D. Dissertation, University of Toronto, 1966
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| * {{KlitzingPolytopes|polyzetta.htm|8D|uniform polytopes (polyzetta)}}
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| == Notes ==
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| {{reflist}}
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| == External links ==
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| * [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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| {{DEFAULTSORT:8-Polytope}}
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| [[Category:8-polytopes]]
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