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Uniform 8-polytope#Regular and uniform honeycombs

{{short description|Polytope contained by 7-polytope facets}}

align=right class=wikitable width=300 style="margin-left:1em;"

|+ Graphs of three regular and related uniform polytopes.

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8-simplex

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Rectified 8-simplex

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Truncated 8-simplex

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Cantellated 8-simplex

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Runcinated 8-simplex

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Stericated 8-simplex

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Pentellated 8-simplex

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Hexicated 8-simplex

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Heptellated 8-simplex

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8-orthoplex

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Rectified 8-orthoplex

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Truncated 8-orthoplex

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Cantellated 8-orthoplex

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Runcinated 8-orthoplex

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Hexicated 8-orthoplex

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Cantellated 8-cube

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Runcinated 8-cube

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Stericated 8-cube

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Pentellated 8-cube

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Hexicated 8-cube

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Heptellated 8-cube

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8-cube

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Rectified 8-cube

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Truncated 8-cube

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8-demicube

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Truncated 8-demicube

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Cantellated 8-demicube

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Runcinated 8-demicube

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Stericated 8-demicube

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Pentellated 8-demicube

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Hexicated 8-demicube

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421

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142

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241

In eight-dimensional geometry, an eight-dimensional polytope or 8-polytope is a polytope contained by 7-polytope facets. Each 6-polytope ridge being shared by exactly two 7-polytope facets.

A uniform 8-polytope is one which is vertex-transitive, and constructed from uniform 7-polytope facets.

Regular 8-polytopes

Regular 8-polytopes can be represented by the Schläfli symbol {p,q,r,s,t,u,v}, with v {p,q,r,s,t,u} 7-polytope facets around each peak.

There are exactly three such convex regular 8-polytopes:

  1. {3,3,3,3,3,3,3} - 8-simplex
  2. {4,3,3,3,3,3,3} - 8-cube
  3. {3,3,3,3,3,3,4} - 8-orthoplex

There are no nonconvex regular 8-polytopes.

Characteristics

The topology of any given 8-polytope is defined by its Betti numbers and torsion coefficients.Richeson, D.; Euler's Gem: The Polyhedron Formula and the Birth of Topoplogy, Princeton, 2008.

The value of the Euler characteristic used to characterise polyhedra does not generalize usefully to higher dimensions, and is zero for all 8-polytopes, whatever their underlying topology. This inadequacy of the Euler characteristic to reliably distinguish between different topologies in higher dimensions led to the discovery of the more sophisticated Betti numbers.

Similarly, the notion of orientability of a polyhedron is insufficient to characterise the surface twistings of toroidal polytopes, and this led to the use of torsion coefficients.

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 diagrams:

class=wikitable
#

!colspan=3|Coxeter group

!Forms

1A8[37]{{CDD|node|3|node|3|node|3|node|3|node|3|node|3|node|3|node}}135
2BC8[4,36]{{CDD|node|4|node|3|node|3|node|3|node|3|node|3|node|3|node}}255
3D8[35,1,1]{{CDD|nodes|split2|node|3|node|3|node|3|node|3|node|3|node}}191 (64 unique)
4E8[34,2,1]{{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:

  1. Simplex family: A8 [37] - {{CDD|node|3|node|3|node|3|node|3|node|3|node|3|node|3|node}}
  2. * 135 uniform 8-polytopes as permutations of rings in the group diagram, including one regular:
  3. *# {37} - 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}}
  4. Hypercube/orthoplex family: B8 [4,36] - {{CDD|node|4|node|3|node|3|node|3|node|3|node|3|node|3|node}}
  5. * 255 uniform 8-polytopes as permutations of rings in the group diagram, including two regular ones:
  6. *# {4,36} - 8-cube or octeract- {{CDD|node_1|4|node|3|node|3|node|3|node|3|node|3|node|3|node}}
  7. *# {36,4} - 8-orthoplex or octacross - {{CDD|node_1|3|node|3|node|3|node|3|node|3|node|3|node|4|node}}
  8. Demihypercube D8 family: [35,1,1] - {{CDD|nodea|3a|branch|3a|nodea|3a|nodea|3a|nodea|3a|nodea|3a|nodea}}
  9. * 191 uniform 8-polytopes as permutations of rings in the group diagram, including:
  10. *# {3,35,1} - 8-demicube or demiocteract, 151 - {{CDD|nodea_1|3a|branch|3a|nodea|3a|nodea|3a|nodea|3a|nodea|3a|nodea}}; also as h{4,36} {{CDD|node_h|4|node|3|node|3|node|3|node|3|node|3|node|3|node}}.
  11. *# {3,3,3,3,3,31,1} - 8-orthoplex, 511 - {{CDD|nodea|3a|branch|3a|nodea|3a|nodea|3a|nodea|3a|nodea|3a|nodea_1}}
  12. E-polytope family E8 family: [34,1,1] - {{CDD|nodea|3a|nodea|3a|branch|3a|nodea|3a|nodea|3a|nodea|3a|nodea}}
  13. * 255 uniform 8-polytopes as permutations of rings in the group diagram, including:
  14. *# {3,3,3,3,32,1} - Thorold Gosset's semiregular 421, {{CDD|nodea|3a|nodea|3a|branch|3a|nodea|3a|nodea|3a|nodea|3a|nodea_1}}
  15. *# {3,34,2} - the uniform 142, {{CDD|nodea|3a|nodea|3a|branch_01lr|3a|nodea|3a|nodea|3a|nodea|3a|nodea}},
  16. *# {3,3,34,1} - the uniform 241, {{CDD|nodea_1|3a|nodea|3a|branch|3a|nodea|3a|nodea|3a|nodea|3a|nodea}}

= Uniform prismatic forms =

There are many uniform prismatic families, including:

class="wikitable collapsible collapsed"

!colspan=12|Uniform 8-polytope prism families

#

!colspan=2|Coxeter group

!Coxeter-Dynkin diagram

colspan=4|7+1
1A7A1[3,3,3,3,3,3]×[ ]{{CDD|node|3|node|3|node|3|node|3|node|3|node|3|node|2|node}}
2B7A1[4,3,3,3,3,3]×[ ]{{CDD|node|4|node|3|node|3|node|3|node|3|node|3|node|2|node}}
3D7A1[34,1,1]×[ ]{{CDD|nodes|split2|node|3|node|3|node|3|node|3|node|2|node}}
4E7A1[33,2,1]×[ ]{{CDD|nodea|3a|nodea|3a|branch|3a|nodea|3a|nodea|3a|nodea|2|nodea}}
colspan=4|6+2
1A6I2(p)[3,3,3,3,3]×[p]{{CDD|node|3|node|3|node|3|node|3|node|3|node|2|node|p|node}}
2B6I2(p)[4,3,3,3,3]×[p]{{CDD|node|4|node|3|node|3|node|3|node|3|node|2|node|p|node}}
3D6I2(p)[33,1,1]×[p]{{CDD|nodes|split2|node|3|node|3|node|3|node|2|node|p|node}}
4E6I2(p)[3,3,3,3,3]×[p]{{CDD|node|3|node|3|node|3|node|3|node|3|node|2|node|p|node}}
colspan=4|6+1+1
1A6A1A1[3,3,3,3,3]×[ ]x[ ]{{CDD|node|3|node|3|node|3|node|3|node|3|node|2|node|2|node}}
2B6A1A1[4,3,3,3,3]×[ ]x[ ]{{CDD|node|4|node|3|node|3|node|3|node|3|node|2|node|2|node}}
3D6A1A1[33,1,1]×[ ]x[ ]{{CDD|nodes|split2|node|3|node|3|node|3|node|2|node|2|node}}
4E6A1A1[3,3,3,3,3]×[ ]x[ ]{{CDD|node|3|node|3|node|3|node|3|node|3|node|2|node|2|node}}
colspan=4|5+3
1A5A3[34]×[3,3]{{CDD|node|3|node|3|node|3|node|3|node|2|node|3|node|3|node}}
2B5A3[4,33]×[3,3]{{CDD|node|4|node|3|node|3|node|3|node|2|node|3|node|3|node}}
3D5A3[32,1,1]×[3,3]{{CDD|nodes|split2|node|3|node|3|node|2|node|3|node|3|node}}
4A5B3[34]×[4,3]{{CDD|node|3|node|3|node|3|node|3|node|2|node|4|node|3|node}}
5B5B3[4,33]×[4,3]{{CDD|node|4|node|3|node|3|node|3|node|2|node|4|node|3|node}}
6D5B3[32,1,1]×[4,3]{{CDD|nodes|split2|node|3|node|3|node|2|node|4|node|3|node}}
7A5H3[34]×[5,3]{{CDD|node|3|node|3|node|3|node|3|node|2|node|5|node|3|node}}
8B5H3[4,33]×[5,3]{{CDD|node|4|node|3|node|3|node|3|node|2|node|5|node|3|node}}
9D5H3[32,1,1]×[5,3]{{CDD|nodes|split2|node|3|node|3|node|2|node|5|node|3|node}}
colspan=4|5+2+1
1A5I2(p)A1[3,3,3]×[p]×[ ]{{CDD|node|3|node|3|node|3|node|3|node|2|node|p|node|2|node}}
2B5I2(p)A1[4,3,3]×[p]×[ ]{{CDD|node|4|node|3|node|3|node|3|node|2|node|p|node|2|node}}
3D5I2(p)A1[32,1,1]×[p]×[ ]{{CDD|nodes|split2|node|3|node|3|node|2|node|p|node|2|node}}
colspan=4|5+1+1+1
1A5A1A1A1[3,3,3]×[ ]×[ ]×[ ]{{CDD|node|3|node|3|node|3|node|3|node|2|node|2|node|2|node}}
2B5A1A1A1[4,3,3]×[ ]×[ ]×[ ]{{CDD|node|4|node|3|node|3|node|3|node|2|node|2|node|2|node}}
3D5A1A1A1[32,1,1]×[ ]×[ ]×[ ]{{CDD|nodes|split2|node|3|node|3|node|2|node|2|node|2|node}}
colspan=4|4+4
1A4A4[3,3,3]×[3,3,3]{{CDD|node|3|node|3|node|3|node|2|node|3|node|3|node|3|node}}
2B4A4[4,3,3]×[3,3,3]{{CDD|node|4|node|3|node|3|node|2|node|3|node|3|node|3|node}}
3D4A4[31,1,1]×[3,3,3]{{CDD|nodes|split2|node|3|node|2|node|3|node|3|node|3|node}}
4F4A4[3,4,3]×[3,3,3]{{CDD|node|3|node|4|node|3|node|2|node|3|node|3|node|3|node}}
5H4A4[5,3,3]×[3,3,3]{{CDD|node|5|node|3|node|3|node|2|node|3|node|3|node|3|node}}
6B4B4[4,3,3]×[4,3,3]{{CDD|node|4|node|3|node|3|node|2|node|4|node|3|node|3|node}}
7D4B4[31,1,1]×[4,3,3]{{CDD|nodes|split2|node|3|node|2|node|4|node|3|node|3|node}}
8F4B4[3,4,3]×[4,3,3]{{CDD|node|3|node|4|node|3|node|2|node|4|node|3|node|3|node}}
9H4B4[5,3,3]×[4,3,3]{{CDD|node|5|node|3|node|3|node|2|node|4|node|3|node|3|node}}
10D4D4[31,1,1]×[31,1,1]{{CDD|nodes|split2|node|3|node|2|nodes|split2|node|3|node}}
11F4D4[3,4,3]×[31,1,1]{{CDD|node|3|node|4|node|3|node|2|nodes|split2|node|3|node}}
12H4D4[5,3,3]×[31,1,1]{{CDD|node|5|node|3|node|3|node|2|nodes|split2|node|3|node}}
13F4×F4[3,4,3]×[3,4,3]{{CDD|node|3|node|4|node|3|node|2|node|3|node|4|node|3|node}}
14H4×F4[5,3,3]×[3,4,3]{{CDD|node|5|node|3|node|3|node|2|node|3|node|4|node|3|node}}
15H4H4[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
1A4A3A1[3,3,3]×[3,3]×[ ]{{CDD|node|3|node|3|node|3|node|2|node|3|node|3|node|2|node}}
2A4B3A1[3,3,3]×[4,3]×[ ]{{CDD|node|3|node|3|node|3|node|2|node|4|node|3|node|2|node}}
3A4H3A1[3,3,3]×[5,3]×[ ]{{CDD|node|3|node|3|node|3|node|2|node|5|node|3|node|2|node}}
4B4A3A1[4,3,3]×[3,3]×[ ]{{CDD|node|4|node|3|node|3|node|2|node|3|node|3|node|2|node}}
5B4B3A1[4,3,3]×[4,3]×[ ]{{CDD|node|4|node|3|node|3|node|2|node|4|node|3|node|2|node}}
6B4H3A1[4,3,3]×[5,3]×[ ]{{CDD|node|4|node|3|node|3|node|2|node|5|node|3|node|2|node}}
7H4A3A1[5,3,3]×[3,3]×[ ]{{CDD|node|5|node|3|node|3|node|2|node|3|node|3|node|2|node}}
8H4B3A1[5,3,3]×[4,3]×[ ]{{CDD|node|5|node|3|node|3|node|2|node|4|node|3|node|2|node}}
9H4H3A1[5,3,3]×[5,3]×[ ]{{CDD|node|5|node|3|node|3|node|2|node|5|node|3|node|2|node}}
10F4A3A1[3,4,3]×[3,3]×[ ]{{CDD|node|3|node|4|node|3|node|2|node|3|node|3|node|2|node}}
11F4B3A1[3,4,3]×[4,3]×[ ]{{CDD|node|3|node|4|node|3|node|2|node|4|node|3|node|2|node}}
12F4H3A1[3,4,3]×[5,3]×[ ]{{CDD|node|3|node|4|node|3|node|2|node|5|node|3|node|2|node}}
13D4A3A1[31,1,1]×[3,3]×[ ]{{CDD|nodes|split2|node|3|node|2|node|3|node|3|node|2|node}}
14D4B3A1[31,1,1]×[4,3]×[ ]{{CDD|nodes|split2|node|3|node|2|node|4|node|3|node|2|node}}
15D4H3A1[31,1,1]×[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

|| A3A3I2(p)||[3,3]×[3,3]×[p]||{{CDD|node|3|node|3|node|2|node|3|node|3|node|2|node|p|node}}

2

|| B3A3I2(p)||[4,3]×[3,3]×[p]||{{CDD|node|4|node|3|node|2|node|3|node|3|node|2|node|p|node}}

3

||H3A3I2(p)||[5,3]×[3,3]×[p]||{{CDD|node|5|node|3|node|2|node|3|node|3|node|2|node|p|node}}

4

|| B3B3I2(p)||[4,3]×[4,3]×[p]||{{CDD|node|4|node|3|node|2|node|4|node|3|node|2|node|p|node}}

5

||H3B3I2(p)||[5,3]×[4,3]×[p]||{{CDD|node|5|node|3|node|2|node|4|node|3|node|2|node|p|node}}

6

||H3H3I2(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

|| A32A12||[3,3]×[3,3]×[ ]×[ ]||{{CDD|node|3|node|3|node|2|node|3|node|3|node|2|node|2|node}}

2

|| B3A3A12||[4,3]×[3,3]×[ ]×[ ]||{{CDD|node|4|node|3|node|2|node|3|node|3|node|2|node|2|node}}

3

||H3A3A12||[5,3]×[3,3]×[ ]×[ ]||{{CDD|node|5|node|3|node|2|node|3|node|3|node|2|node|2|node}}

4

|| B3B3A12||[4,3]×[4,3]×[ ]×[ ]||{{CDD|node|4|node|3|node|2|node|4|node|3|node|2|node|2|node}}

5

||H3B3A12||[5,3]×[4,3]×[ ]×[ ]||{{CDD|node|5|node|3|node|2|node|4|node|3|node|2|node|2|node}}

6

||H3H3A12||[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
1A3I2(p)I2(q)A1[3,3]×[p]×[q]×[ ]{{CDD|node|3|node|3|node|2|node|p|node|2|node|q|node|2|node}}
2B3I2(p)I2(q)A1[4,3]×[p]×[q]×[ ]{{CDD|node|4|node|3|node|2|node|p|node|2|node|q|node|2|node}}
3H3I2(p)I2(q)A1[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
1A3I2(p)A13[3,3]×[p]×[ ]x[ ]×[ ]{{CDD|node|3|node|3|node|2|node|p|node|2|node|2|node|2|node}}
2B3I2(p)A13[4,3]×[p]×[ ]x[ ]×[ ]{{CDD|node|4|node|3|node|2|node|p|node|2|node|2|node|2|node}}
3H3I2(p)A13[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
1A3A15[3,3]×[ ]x[ ]×[ ]x[ ]×[ ]{{CDD|node|3|node|3|node|2|node|2|node|2|node|2|node|2|node}}
2B3A15[4,3]×[ ]x[ ]×[ ]x[ ]×[ ]{{CDD|node|4|node|3|node|2|node|2|node|2|node|2|node|2|node}}
3H3A15[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
1I2(p)I2(q)I2(r)I2(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
1I2(p)I2(q)I2(r)A12[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
2I2(p)I2(q)A14[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
1I2(p)A16[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
1A18[ ]×[ ]×[ ]×[ ]×[ ]×[ ]×[ ]×[ ]{{CDD|node|2|node|2|node|2|node|2|node|2|node|2|node|2|node}}

= The A<sub>8</sub> family =

The A8 family has symmetry of order 362880 (9 factorial).

There are 135 forms based on all permutations of the Coxeter-Dynkin diagrams 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 collapsible collapsed"

!colspan=13|A8 uniform polytopes

rowspan=2|#

!rowspan=2|Coxeter-Dynkin diagram

!rowspan=2|Truncation
indices

!rowspan=2|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}}

|t0

|8-simplex (ene)

|(0,0,0,0,0,0,0,0,1)

9368412612684369
align=center

!2

|

{{CDD|node|3|node|3|node|3|node|3|node|3|node|3|node_1|3|node}}

|t1

|Rectified 8-simplex (rene)

|(0,0,0,0,0,0,0,1,1)

1810833663057658825236
align=center

!3

|

{{CDD|node|3|node|3|node|3|node|3|node|3|node_1|3|node|3|node}}

|t2

|Birectified 8-simplex (bene)

|(0,0,0,0,0,0,1,1,1)

1814458813862016176475684
align=center

!4

|

{{CDD|node|3|node|3|node|3|node|3|node_1|3|node|3|node|3|node}}

|t3

|Trirectified 8-simplex (trene)

|(0,0,0,0,0,1,1,1,1)

1260126
align=center

!5

|

{{CDD|node|3|node|3|node|3|node|3|node|3|node|3|node_1|3|node_1}}

|t0,1

|Truncated 8-simplex (tene)

|(0,0,0,0,0,0,0,1,2)

28872
align=center

!6

|

{{CDD|node|3|node|3|node|3|node|3|node|3|node_1|3|node|3|node_1}}

|t0,2

|Cantellated 8-simplex

|(0,0,0,0,0,0,1,1,2)

1764252
align=center

!7

|

{{CDD|node|3|node|3|node|3|node|3|node|3|node_1|3|node_1|3|node}}

|t1,2

|Bitruncated 8-simplex

|(0,0,0,0,0,0,1,2,2)

1008252
align=center

!8

|

{{CDD|node|3|node|3|node|3|node|3|node_1|3|node|3|node|3|node_1}}

|t0,3

|Runcinated 8-simplex

|(0,0,0,0,0,1,1,1,2)

4536504
align=center

!9

|

{{CDD|node|3|node|3|node|3|node|3|node_1|3|node|3|node_1|3|node}}

|t1,3

|Bicantellated 8-simplex

|(0,0,0,0,0,1,1,2,2)

5292756
align=center

!10

|

{{CDD|node|3|node|3|node|3|node|3|node_1|3|node_1|3|node|3|node}}

|t2,3

|Tritruncated 8-simplex

|(0,0,0,0,0,1,2,2,2)

2016504
align=center

!11

|

{{CDD|node|3|node|3|node|3|node_1|3|node|3|node|3|node|3|node_1}}

|t0,4

|Stericated 8-simplex

|(0,0,0,0,1,1,1,1,2)

6300630
align=center

!12

|

{{CDD|node|3|node|3|node|3|node_1|3|node|3|node|3|node_1|3|node}}

|t1,4

|Biruncinated 8-simplex

|(0,0,0,0,1,1,1,2,2)

113401260
align=center

!13

|

{{CDD|node|3|node|3|node|3|node_1|3|node|3|node_1|3|node|3|node}}

|t2,4

|Tricantellated 8-simplex

|(0,0,0,0,1,1,2,2,2)

88201260
align=center BGCOLOR="#e0f0e0"

!14

|

{{CDD|node|3|node|3|node|3|node_1|3|node_1|3|node|3|node|3|node}}

|t3,4

|Quadritruncated 8-simplex

|(0,0,0,0,1,2,2,2,2)

2520630
align=center

!15

|

{{CDD|node|3|node|3|node_1|3|node|3|node|3|node|3|node|3|node_1}}

|t0,5

|Pentellated 8-simplex

|(0,0,0,1,1,1,1,1,2)

5040504
align=center

!16

|

{{CDD|node|3|node|3|node_1|3|node|3|node|3|node|3|node_1|3|node}}

|t1,5

|Bistericated 8-simplex

|(0,0,0,1,1,1,1,2,2)

126001260
align=center BGCOLOR="#e0f0e0"

!17

|

{{CDD|node|3|node|3|node_1|3|node|3|node|3|node_1|3|node|3|node}}

|t2,5

|Triruncinated 8-simplex

|(0,0,0,1,1,1,2,2,2)

151201680
align=center

!18

|

{{CDD|node|3|node_1|3|node|3|node|3|node|3|node|3|node|3|node_1}}

|t0,6

|Hexicated 8-simplex

|(0,0,1,1,1,1,1,1,2)

2268252
align=center BGCOLOR="#e0f0e0"

!19

|

{{CDD|node|3|node_1|3|node|3|node|3|node|3|node|3|node_1|3|node}}

|t1,6

|Bipentellated 8-simplex

|(0,0,1,1,1,1,1,2,2)

7560756
align=center BGCOLOR="#e0f0e0"

!20

|

{{CDD|node_1|3|node|3|node|3|node|3|node|3|node|3|node|3|node_1}}

|t0,7

|Heptellated 8-simplex

|(0,1,1,1,1,1,1,1,2)

50472
align=center

!21

|

{{CDD|node|3|node|3|node|3|node|3|node|3|node_1|3|node_1|3|node_1}}

|t0,1,2

|Cantitruncated 8-simplex

|(0,0,0,0,0,0,1,2,3)

2016504
align=center

!22

|

{{CDD|node|3|node|3|node|3|node|3|node_1|3|node|3|node_1|3|node_1}}

|t0,1,3

|Runcitruncated 8-simplex

|(0,0,0,0,0,1,1,2,3)

98281512
align=center

!23

|

{{CDD|node|3|node|3|node|3|node|3|node_1|3|node_1|3|node|3|node_1}}

|t0,2,3

|Runcicantellated 8-simplex

|(0,0,0,0,0,1,2,2,3)

68041512
align=center

!24

|

{{CDD|node|3|node|3|node|3|node|3|node_1|3|node_1|3|node_1|3|node}}

|t1,2,3

|Bicantitruncated 8-simplex

|(0,0,0,0,0,1,2,3,3)

60481512
align=center

!25

|

{{CDD|node|3|node|3|node|3|node_1|3|node|3|node|3|node_1|3|node_1}}

|t0,1,4

|Steritruncated 8-simplex

|(0,0,0,0,1,1,1,2,3)

201602520
align=center

!26

|

{{CDD|node|3|node|3|node|3|node_1|3|node|3|node_1|3|node|3|node_1}}

|t0,2,4

|Stericantellated 8-simplex

|(0,0,0,0,1,1,2,2,3)

264603780
align=center

!27

|

{{CDD|node|3|node|3|node|3|node_1|3|node|3|node_1|3|node_1|3|node}}

|t1,2,4

|Biruncitruncated 8-simplex

|(0,0,0,0,1,1,2,3,3)

226803780
align=center

!28

|

{{CDD|node|3|node|3|node|3|node_1|3|node_1|3|node|3|node|3|node_1}}

|t0,3,4

|Steriruncinated 8-simplex

|(0,0,0,0,1,2,2,2,3)

126002520
align=center

!29

|

{{CDD|node|3|node|3|node|3|node_1|3|node_1|3|node|3|node_1|3|node}}

|t1,3,4

|Biruncicantellated 8-simplex

|(0,0,0,0,1,2,2,3,3)

189003780
align=center

!30

|

{{CDD|node|3|node|3|node|3|node_1|3|node_1|3|node_1|3|node|3|node}}

|t2,3,4

|Tricantitruncated 8-simplex

|(0,0,0,0,1,2,3,3,3)

100802520
align=center

!31

|

{{CDD|node|3|node|3|node_1|3|node|3|node|3|node|3|node_1|3|node_1}}

|t0,1,5

|Pentitruncated 8-simplex

|(0,0,0,1,1,1,1,2,3)

214202520
align=center

!32

|

{{CDD|node|3|node|3|node_1|3|node|3|node|3|node_1|3|node|3|node_1}}

|t0,2,5

|Penticantellated 8-simplex

|(0,0,0,1,1,1,2,2,3)

428405040
align=center

!33

|

{{CDD|node|3|node|3|node_1|3|node|3|node|3|node_1|3|node_1|3|node}}

|t1,2,5

|Bisteritruncated 8-simplex

|(0,0,0,1,1,1,2,3,3)

352805040
align=center

!34

|

{{CDD|node|3|node|3|node_1|3|node|3|node_1|3|node|3|node|3|node_1}}

|t0,3,5

|Pentiruncinated 8-simplex

|(0,0,0,1,1,2,2,2,3)

378005040
align=center

!35

|

{{CDD|node|3|node|3|node_1|3|node|3|node_1|3|node|3|node_1|3|node}}

|t1,3,5

|Bistericantellated 8-simplex

|(0,0,0,1,1,2,2,3,3)

529207560
align=center

!36

|

{{CDD|node|3|node|3|node_1|3|node|3|node_1|3|node_1|3|node|3|node}}

|t2,3,5

|Triruncitruncated 8-simplex

|(0,0,0,1,1,2,3,3,3)

277205040
align=center

!37

|

{{CDD|node|3|node|3|node_1|3|node_1|3|node|3|node|3|node|3|node_1}}

|t0,4,5

|Pentistericated 8-simplex

|(0,0,0,1,2,2,2,2,3)

138602520
align=center

!38

|

{{CDD|node|3|node|3|node_1|3|node_1|3|node|3|node|3|node_1|3|node}}

|t1,4,5

|Bisteriruncinated 8-simplex

|(0,0,0,1,2,2,2,3,3)

302405040
align=center

!39

|

{{CDD|node|3|node_1|3|node|3|node|3|node|3|node|3|node_1|3|node_1}}

|t0,1,6

|Hexitruncated 8-simplex

|(0,0,1,1,1,1,1,2,3)

120961512
align=center

!40

|

{{CDD|node|3|node_1|3|node|3|node|3|node|3|node_1|3|node|3|node_1}}

|t0,2,6

|Hexicantellated 8-simplex

|(0,0,1,1,1,1,2,2,3)

340203780
align=center

!41

|

{{CDD|node|3|node_1|3|node|3|node|3|node|3|node_1|3|node_1|3|node}}

|t1,2,6

|Bipentitruncated 8-simplex

|(0,0,1,1,1,1,2,3,3)

264603780
align=center

!42

|

{{CDD|node|3|node_1|3|node|3|node|3|node_1|3|node|3|node|3|node_1}}

|t0,3,6

|Hexiruncinated 8-simplex

|(0,0,1,1,1,2,2,2,3)

453605040
align=center

!43

|

{{CDD|node|3|node_1|3|node|3|node|3|node_1|3|node|3|node_1|3|node}}

|t1,3,6

|Bipenticantellated 8-simplex

|(0,0,1,1,1,2,2,3,3)

604807560
align=center

!44

|

{{CDD|node|3|node_1|3|node|3|node_1|3|node|3|node|3|node|3|node_1}}

|t0,4,6

|Hexistericated 8-simplex

|(0,0,1,1,2,2,2,2,3)

302403780
align=center

!45

|

{{CDD|node|3|node_1|3|node_1|3|node|3|node|3|node|3|node|3|node_1}}

|t0,5,6

|Hexipentellated 8-simplex

|(0,0,1,2,2,2,2,2,3)

90721512
align=center

!46

|

{{CDD|node_1|3|node|3|node|3|node|3|node|3|node|3|node_1|3|node_1}}

|t0,1,7

|Heptitruncated 8-simplex

|(0,1,1,1,1,1,1,2,3)

3276504
align=center

!47

|

{{CDD|node_1|3|node|3|node|3|node|3|node|3|node_1|3|node|3|node_1}}

|t0,2,7

|Hepticantellated 8-simplex

|(0,1,1,1,1,1,2,2,3)

128521512
align=center

!48

|

{{CDD|node_1|3|node|3|node|3|node|3|node_1|3|node|3|node|3|node_1}}

|t0,3,7

|Heptiruncinated 8-simplex

|(0,1,1,1,1,2,2,2,3)

239402520
align=center

!49

|

{{CDD|node|3|node|3|node|3|node|3|node_1|3|node_1|3|node_1|3|node_1}}

|t0,1,2,3

|Runcicantitruncated 8-simplex

|(0,0,0,0,0,1,2,3,4)

120963024
align=center

!50

|

{{CDD|node|3|node|3|node|3|node_1|3|node|3|node_1|3|node_1|3|node_1}}

|t0,1,2,4

|Stericantitruncated 8-simplex

|(0,0,0,0,1,1,2,3,4)

453607560
align=center

!51

|

{{CDD|node|3|node|3|node|3|node_1|3|node_1|3|node|3|node_1|3|node_1}}

|t0,1,3,4

|Steriruncitruncated 8-simplex

|(0,0,0,0,1,2,2,3,4)

340207560
align=center

!52

|

{{CDD|node|3|node|3|node|3|node_1|3|node_1|3|node_1|3|node|3|node_1}}

|t0,2,3,4

|Steriruncicantellated 8-simplex

|(0,0,0,0,1,2,3,3,4)

340207560
align=center

!53

|

{{CDD|node|3|node|3|node|3|node_1|3|node_1|3|node_1|3|node_1|3|node}}

|t1,2,3,4

|Biruncicantitruncated 8-simplex

|(0,0,0,0,1,2,3,4,4)

302407560
align=center

!54

|

{{CDD|node|3|node|3|node_1|3|node|3|node|3|node_1|3|node_1|3|node_1}}

|t0,1,2,5

|Penticantitruncated 8-simplex

|(0,0,0,1,1,1,2,3,4)

7056010080
align=center

!55

|

{{CDD|node|3|node|3|node_1|3|node|3|node_1|3|node|3|node_1|3|node_1}}

|t0,1,3,5

|Pentiruncitruncated 8-simplex

|(0,0,0,1,1,2,2,3,4)

9828015120
align=center

!56

|

{{CDD|node|3|node|3|node_1|3|node|3|node_1|3|node_1|3|node|3|node_1}}

|t0,2,3,5

|Pentiruncicantellated 8-simplex

|(0,0,0,1,1,2,3,3,4)

9072015120
align=center

!57

|

{{CDD|node|3|node|3|node_1|3|node|3|node_1|3|node_1|3|node_1|3|node}}

|t1,2,3,5

|Bistericantitruncated 8-simplex

|(0,0,0,1,1,2,3,4,4)

8316015120
align=center

!58

|

{{CDD|node|3|node|3|node_1|3|node_1|3|node|3|node|3|node_1|3|node_1}}

|t0,1,4,5

|Pentisteritruncated 8-simplex

|(0,0,0,1,2,2,2,3,4)

5040010080
align=center

!59

|

{{CDD|node|3|node|3|node_1|3|node_1|3|node|3|node_1|3|node|3|node_1}}

|t0,2,4,5

|Pentistericantellated 8-simplex

|(0,0,0,1,2,2,3,3,4)

8316015120
align=center

!60

|

{{CDD|node|3|node|3|node_1|3|node_1|3|node|3|node_1|3|node_1|3|node}}

|t1,2,4,5

|Bisteriruncitruncated 8-simplex

|(0,0,0,1,2,2,3,4,4)

6804015120
align=center

!61

|

{{CDD|node|3|node|3|node_1|3|node_1|3|node_1|3|node|3|node|3|node_1}}

|t0,3,4,5

|Pentisteriruncinated 8-simplex

|(0,0,0,1,2,3,3,3,4)

5040010080
align=center

!62

|

{{CDD|node|3|node|3|node_1|3|node_1|3|node_1|3|node|3|node_1|3|node}}

|t1,3,4,5

|Bisteriruncicantellated 8-simplex

|(0,0,0,1,2,3,3,4,4)

7560015120
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}}

|t2,3,4,5

|Triruncicantitruncated 8-simplex

|(0,0,0,1,2,3,4,4,4)

4032010080
align=center

!64

|

{{CDD|node|3|node_1|3|node|3|node|3|node|3|node_1|3|node_1|3|node_1}}

|t0,1,2,6

|Hexicantitruncated 8-simplex

|(0,0,1,1,1,1,2,3,4)

529207560
align=center

!65

|

{{CDD|node|3|node_1|3|node|3|node|3|node_1|3|node|3|node_1|3|node_1}}

|t0,1,3,6

|Hexiruncitruncated 8-simplex

|(0,0,1,1,1,2,2,3,4)

11340015120
align=center

!66

|

{{CDD|node|3|node_1|3|node|3|node|3|node_1|3|node_1|3|node|3|node_1}}

|t0,2,3,6

|Hexiruncicantellated 8-simplex

|(0,0,1,1,1,2,3,3,4)

9828015120
align=center

!67

|

{{CDD|node|3|node_1|3|node|3|node|3|node_1|3|node_1|3|node_1|3|node}}

|t1,2,3,6

|Bipenticantitruncated 8-simplex

|(0,0,1,1,1,2,3,4,4)

9072015120
align=center

!68

|

{{CDD|node|3|node_1|3|node|3|node_1|3|node|3|node|3|node_1|3|node_1}}

|t0,1,4,6

|Hexisteritruncated 8-simplex

|(0,0,1,1,2,2,2,3,4)

10584015120
align=center

!69

|

{{CDD|node|3|node_1|3|node|3|node_1|3|node|3|node_1|3|node|3|node_1}}

|t0,2,4,6

|Hexistericantellated 8-simplex

|(0,0,1,1,2,2,3,3,4)

15876022680
align=center

!70

|

{{CDD|node|3|node_1|3|node|3|node_1|3|node|3|node_1|3|node_1|3|node}}

|t1,2,4,6

|Bipentiruncitruncated 8-simplex

|(0,0,1,1,2,2,3,4,4)

13608022680
align=center

!71

|

{{CDD|node|3|node_1|3|node|3|node_1|3|node_1|3|node|3|node|3|node_1}}

|t0,3,4,6

|Hexisteriruncinated 8-simplex

|(0,0,1,1,2,3,3,3,4)

9072015120
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}}

|t1,3,4,6

|Bipentiruncicantellated 8-simplex

|(0,0,1,1,2,3,3,4,4)

13608022680
align=center

!73

|

{{CDD|node|3|node_1|3|node_1|3|node|3|node|3|node|3|node_1|3|node_1}}

|t0,1,5,6

|Hexipentitruncated 8-simplex

|(0,0,1,2,2,2,2,3,4)

415807560
align=center

!74

|

{{CDD|node|3|node_1|3|node_1|3|node|3|node|3|node_1|3|node|3|node_1}}

|t0,2,5,6

|Hexipenticantellated 8-simplex

|(0,0,1,2,2,2,3,3,4)

9828015120
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}}

|t1,2,5,6

|Bipentisteritruncated 8-simplex

|(0,0,1,2,2,2,3,4,4)

7560015120
align=center

!76

|

{{CDD|node|3|node_1|3|node_1|3|node|3|node_1|3|node|3|node|3|node_1}}

|t0,3,5,6

|Hexipentiruncinated 8-simplex

|(0,0,1,2,2,3,3,3,4)

9828015120
align=center

!77

|

{{CDD|node|3|node_1|3|node_1|3|node_1|3|node|3|node|3|node|3|node_1}}

|t0,4,5,6

|Hexipentistericated 8-simplex

|(0,0,1,2,3,3,3,3,4)

415807560
align=center

!78

|

{{CDD|node_1|3|node|3|node|3|node|3|node|3|node_1|3|node_1|3|node_1}}

|t0,1,2,7

|Hepticantitruncated 8-simplex

|(0,1,1,1,1,1,2,3,4)

181443024
align=center

!79

|

{{CDD|node_1|3|node|3|node|3|node|3|node_1|3|node|3|node_1|3|node_1}}

|t0,1,3,7

|Heptiruncitruncated 8-simplex

|(0,1,1,1,1,2,2,3,4)

567007560
align=center

!80

|

{{CDD|node_1|3|node|3|node|3|node|3|node_1|3|node_1|3|node|3|node_1}}

|t0,2,3,7

|Heptiruncicantellated 8-simplex

|(0,1,1,1,1,2,3,3,4)

453607560
align=center

!81

|

{{CDD|node_1|3|node|3|node|3|node_1|3|node|3|node|3|node_1|3|node_1}}

|t0,1,4,7

|Heptisteritruncated 8-simplex

|(0,1,1,1,2,2,2,3,4)

8064010080
align=center

!82

|

{{CDD|node_1|3|node|3|node|3|node_1|3|node|3|node_1|3|node|3|node_1}}

|t0,2,4,7

|Heptistericantellated 8-simplex

|(0,1,1,1,2,2,3,3,4)

11340015120
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}}

|t0,3,4,7

|Heptisteriruncinated 8-simplex

|(0,1,1,1,2,3,3,3,4)

6048010080
align=center

!84

|

{{CDD|node_1|3|node|3|node_1|3|node|3|node|3|node|3|node_1|3|node_1}}

|t0,1,5,7

|Heptipentitruncated 8-simplex

|(0,1,1,2,2,2,2,3,4)

567007560
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}}

|t0,2,5,7

|Heptipenticantellated 8-simplex

|(0,1,1,2,2,2,3,3,4)

12096015120
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}}

|t0,1,6,7

|Heptihexitruncated 8-simplex

|(0,1,2,2,2,2,2,3,4)

181443024
align=center

!87

|

{{CDD|node|3|node|3|node|3|node_1|3|node_1|3|node_1|3|node_1|3|node_1}}

|t0,1,2,3,4

|Steriruncicantitruncated 8-simplex

|(0,0,0,0,1,2,3,4,5)

6048015120
align=center

!88

|

{{CDD|node|3|node|3|node_1|3|node|3|node_1|3|node_1|3|node_1|3|node_1}}

|t0,1,2,3,5

|Pentiruncicantitruncated 8-simplex

|(0,0,0,1,1,2,3,4,5)

16632030240
align=center

!89

|

{{CDD|node|3|node|3|node_1|3|node_1|3|node|3|node_1|3|node_1|3|node_1}}

|t0,1,2,4,5

|Pentistericantitruncated 8-simplex

|(0,0,0,1,2,2,3,4,5)

13608030240
align=center

!90

|

{{CDD|node|3|node|3|node_1|3|node_1|3|node_1|3|node|3|node_1|3|node_1}}

|t0,1,3,4,5

|Pentisteriruncitruncated 8-simplex

|(0,0,0,1,2,3,3,4,5)

13608030240
align=center

!91

|

{{CDD|node|3|node|3|node_1|3|node_1|3|node_1|3|node_1|3|node|3|node_1}}

|t0,2,3,4,5

|Pentisteriruncicantellated 8-simplex

|(0,0,0,1,2,3,4,4,5)

13608030240
align=center

!92

|

{{CDD|node|3|node|3|node_1|3|node_1|3|node_1|3|node_1|3|node_1|3|node}}

|t1,2,3,4,5

|Bisteriruncicantitruncated 8-simplex

|(0,0,0,1,2,3,4,5,5)

12096030240
align=center

!93

|

{{CDD|node|3|node_1|3|node|3|node|3|node_1|3|node_1|3|node_1|3|node_1}}

|t0,1,2,3,6

|Hexiruncicantitruncated 8-simplex

|(0,0,1,1,1,2,3,4,5)

18144030240
align=center

!94

|

{{CDD|node|3|node_1|3|node|3|node_1|3|node|3|node_1|3|node_1|3|node_1}}

|t0,1,2,4,6

|Hexistericantitruncated 8-simplex

|(0,0,1,1,2,2,3,4,5)

27216045360
align=center

!95

|

{{CDD|node|3|node_1|3|node|3|node_1|3|node_1|3|node|3|node_1|3|node_1}}

|t0,1,3,4,6

|Hexisteriruncitruncated 8-simplex

|(0,0,1,1,2,3,3,4,5)

24948045360
align=center

!96

|

{{CDD|node|3|node_1|3|node|3|node_1|3|node_1|3|node_1|3|node|3|node_1}}

|t0,2,3,4,6

|Hexisteriruncicantellated 8-simplex

|(0,0,1,1,2,3,4,4,5)

24948045360
align=center

!97

|

{{CDD|node|3|node_1|3|node|3|node_1|3|node_1|3|node_1|3|node_1|3|node}}

|t1,2,3,4,6

|Bipentiruncicantitruncated 8-simplex

|(0,0,1,1,2,3,4,5,5)

22680045360
align=center

!98

|

{{CDD|node|3|node_1|3|node_1|3|node|3|node|3|node_1|3|node_1|3|node_1}}

|t0,1,2,5,6

|Hexipenticantitruncated 8-simplex

|(0,0,1,2,2,2,3,4,5)

15120030240
align=center

!99

|

{{CDD|node|3|node_1|3|node_1|3|node|3|node_1|3|node|3|node_1|3|node_1}}

|t0,1,3,5,6

|Hexipentiruncitruncated 8-simplex

|(0,0,1,2,2,3,3,4,5)

24948045360
align=center

!100

|

{{CDD|node|3|node_1|3|node_1|3|node|3|node_1|3|node_1|3|node|3|node_1}}

|t0,2,3,5,6

|Hexipentiruncicantellated 8-simplex

|(0,0,1,2,2,3,4,4,5)

22680045360
align=center

!101

|

{{CDD|node|3|node_1|3|node_1|3|node|3|node_1|3|node_1|3|node_1|3|node}}

|t1,2,3,5,6

|Bipentistericantitruncated 8-simplex

|(0,0,1,2,2,3,4,5,5)

20412045360
align=center

!102

|

{{CDD|node|3|node_1|3|node_1|3|node_1|3|node|3|node|3|node_1|3|node_1}}

|t0,1,4,5,6

|Hexipentisteritruncated 8-simplex

|(0,0,1,2,3,3,3,4,5)

15120030240
align=center

!103

|

{{CDD|node|3|node_1|3|node_1|3|node_1|3|node|3|node_1|3|node|3|node_1}}

|t0,2,4,5,6

|Hexipentistericantellated 8-simplex

|(0,0,1,2,3,3,4,4,5)

24948045360
align=center

!104

|

{{CDD|node|3|node_1|3|node_1|3|node_1|3|node_1|3|node|3|node|3|node_1}}

|t0,3,4,5,6

|Hexipentisteriruncinated 8-simplex

|(0,0,1,2,3,4,4,4,5)

15120030240
align=center

!105

|

{{CDD|node_1|3|node|3|node|3|node|3|node_1|3|node_1|3|node_1|3|node_1}}

|t0,1,2,3,7

|Heptiruncicantitruncated 8-simplex

|(0,1,1,1,1,2,3,4,5)

8316015120
align=center

!106

|

{{CDD|node_1|3|node|3|node|3|node_1|3|node|3|node_1|3|node_1|3|node_1}}

|t0,1,2,4,7

|Heptistericantitruncated 8-simplex

|(0,1,1,1,2,2,3,4,5)

19656030240
align=center

!107

|

{{CDD|node_1|3|node|3|node|3|node_1|3|node_1|3|node|3|node_1|3|node_1}}

|t0,1,3,4,7

|Heptisteriruncitruncated 8-simplex

|(0,1,1,1,2,3,3,4,5)

16632030240
align=center

!108

|

{{CDD|node_1|3|node|3|node|3|node_1|3|node_1|3|node_1|3|node|3|node_1}}

|t0,2,3,4,7

|Heptisteriruncicantellated 8-simplex

|(0,1,1,1,2,3,4,4,5)

16632030240
align=center

!109

|

{{CDD|node_1|3|node|3|node_1|3|node|3|node|3|node_1|3|node_1|3|node_1}}

|t0,1,2,5,7

|Heptipenticantitruncated 8-simplex

|(0,1,1,2,2,2,3,4,5)

19656030240
align=center

!110

|

{{CDD|node_1|3|node|3|node_1|3|node|3|node_1|3|node|3|node_1|3|node_1}}

|t0,1,3,5,7

|Heptipentiruncitruncated 8-simplex

|(0,1,1,2,2,3,3,4,5)

29484045360
align=center

!111

|

{{CDD|node_1|3|node|3|node_1|3|node|3|node_1|3|node_1|3|node|3|node_1}}

|t0,2,3,5,7

|Heptipentiruncicantellated 8-simplex

|(0,1,1,2,2,3,4,4,5)

27216045360
align=center

!112

|

{{CDD|node_1|3|node|3|node_1|3|node_1|3|node|3|node|3|node_1|3|node_1}}

|t0,1,4,5,7

|Heptipentisteritruncated 8-simplex

|(0,1,1,2,3,3,3,4,5)

16632030240
align=center

!113

|

{{CDD|node_1|3|node_1|3|node|3|node|3|node|3|node_1|3|node_1|3|node_1}}

|t0,1,2,6,7

|Heptihexicantitruncated 8-simplex

|(0,1,2,2,2,2,3,4,5)

8316015120
align=center

!114

|

{{CDD|node_1|3|node_1|3|node|3|node|3|node_1|3|node|3|node_1|3|node_1}}

|t0,1,3,6,7

|Heptihexiruncitruncated 8-simplex

|(0,1,2,2,2,3,3,4,5)

19656030240
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}}

|t0,1,2,3,4,5

|Pentisteriruncicantitruncated 8-simplex

|(0,0,0,1,2,3,4,5,6)

24192060480
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}}

|t0,1,2,3,4,6

|Hexisteriruncicantitruncated 8-simplex

|(0,0,1,1,2,3,4,5,6)

45360090720
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}}

|t0,1,2,3,5,6

|Hexipentiruncicantitruncated 8-simplex

|(0,0,1,2,2,3,4,5,6)

40824090720
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}}

|t0,1,2,4,5,6

|Hexipentistericantitruncated 8-simplex

|(0,0,1,2,3,3,4,5,6)

40824090720
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}}

|t0,1,3,4,5,6

|Hexipentisteriruncitruncated 8-simplex

|(0,0,1,2,3,4,4,5,6)

40824090720
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}}

|t0,2,3,4,5,6

|Hexipentisteriruncicantellated 8-simplex

|(0,0,1,2,3,4,5,5,6)

40824090720
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}}

|t1,2,3,4,5,6

|Bipentisteriruncicantitruncated 8-simplex

|(0,0,1,2,3,4,5,6,6)

36288090720
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}}

|t0,1,2,3,4,7

|Heptisteriruncicantitruncated 8-simplex

|(0,1,1,1,2,3,4,5,6)

30240060480
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}}

|t0,1,2,3,5,7

|Heptipentiruncicantitruncated 8-simplex

|(0,1,1,2,2,3,4,5,6)

49896090720
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}}

|t0,1,2,4,5,7

|Heptipentistericantitruncated 8-simplex

|(0,1,1,2,3,3,4,5,6)

45360090720
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}}

|t0,1,3,4,5,7

|Heptipentisteriruncitruncated 8-simplex

|(0,1,1,2,3,4,4,5,6)

45360090720
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}}

|t0,2,3,4,5,7

|Heptipentisteriruncicantellated 8-simplex

|(0,1,1,2,3,4,5,5,6)

45360090720
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}}

|t0,1,2,3,6,7

|Heptihexiruncicantitruncated 8-simplex

|(0,1,2,2,2,3,4,5,6)

30240060480
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}}

|t0,1,2,4,6,7

|Heptihexistericantitruncated 8-simplex

|(0,1,2,2,3,3,4,5,6)

49896090720
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}}

|t0,1,3,4,6,7

|Heptihexisteriruncitruncated 8-simplex

|(0,1,2,2,3,4,4,5,6)

45360090720
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}}

|t0,1,2,5,6,7

|Heptihexipenticantitruncated 8-simplex

|(0,1,2,3,3,3,4,5,6)

30240060480
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}}

|t0,1,2,3,4,5,6

|Hexipentisteriruncicantitruncated 8-simplex

|(0,0,1,2,3,4,5,6,7)

725760181440
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}}

|t0,1,2,3,4,5,7

|Heptipentisteriruncicantitruncated 8-simplex

|(0,1,1,2,3,4,5,6,7)

816480181440
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}}

|t0,1,2,3,4,6,7

|Heptihexisteriruncicantitruncated 8-simplex

|(0,1,2,2,3,4,5,6,7)

816480181440
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}}

|t0,1,2,3,5,6,7

|Heptihexipentiruncicantitruncated 8-simplex

|(0,1,2,3,3,4,5,6,7)

816480181440
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}}

|t0,1,2,3,4,5,6,7

|Omnitruncated 8-simplex

|(0,1,2,3,4,5,6,7,8)

1451520362880

= The B<sub>8</sub> family =

The B8 family has symmetry of order 10321920 (8 factorial x 28). There are 255 forms based on all permutations of the Coxeter-Dynkin diagrams with one or more rings.

See also a list of B8 polytopes for symmetric Coxeter plane graphs of these polytopes.

class="wikitable collapsible collapsed"

!colspan=13|B8 uniform polytopes

rowspan=2|#

!rowspan=2|Coxeter-Dynkin diagram

!rowspan=2|Schläfli
symbol

!rowspan=2|Name

!colspan=8|Element counts

7|| 6|| 5|| 4|| 3|| 2|| 1|| 0
align=center BGCOLOR="#f0e0e0"

!1

|{{CDD|node|4|node|3|node|3|node|3|node|3|node|3|node|3|node_1}}

t0{36,4}8-orthoplex
Diacosipentacontahexazetton (ek)		256102417921792112044811216
align=center BGCOLOR="#f0e0e0"

!2

|{{CDD|node|4|node|3|node|3|node|3|node|3|node|3|node_1|3|node}}

t1{36,4}Rectified 8-orthoplex
Rectified diacosipentacontahexazetton (rek)		27230728960125441008049281344112
align=center BGCOLOR="#f0e0e0"

!3

|{{CDD|node|4|node|3|node|3|node|3|node|3|node_1|3|node|3|node}}

t2{36,4}Birectified 8-orthoplex
Birectified diacosipentacontahexazetton (bark)		2723184161283404836960224006720448
align=center BGCOLOR="#f0e0e0"

!4

|{{CDD|node|4|node|3|node|3|node|3|node_1|3|node|3|node|3|node}}

t3{36,4}Trirectified 8-orthoplex
Trirectified diacosipentacontahexazetton (tark)		272318416576483847168053760179201120
align=center BGCOLOR="#e0e0f0"

!5

|{{CDD|node|4|node|3|node|3|node_1|3|node|3|node|3|node|3|node}}

t3{4,36}Trirectified 8-cube
Trirectified octeract (tro)		272318416576477128064071680268801792
align=center BGCOLOR="#e0e0f0"

!6

|{{CDD|node|4|node|3|node_1|3|node|3|node|3|node|3|node|3|node}}

t2{4,36}Birectified 8-cube
Birectified octeract (bro)		272318414784369605555250176215041792
align=center BGCOLOR="#e0e0f0"

!7

|{{CDD|node|4|node_1|3|node|3|node|3|node|3|node|3|node|3|node}}

t1{4,36}Rectified 8-cube
Rectified octeract (recto)		2722160761615456197121612871681024
align=center BGCOLOR="#e0e0f0"

!8

|{{CDD|node_1|4|node|3|node|3|node|3|node|3|node|3|node|3|node}}

t0{4,36}8-cube
Octeract (octo)		161124481120179217921024256
align=center BGCOLOR="#f0e0e0"

!9

|{{CDD|node|4|node|3|node|3|node|3|node|3|node|3|node_1|3|node_1}}

t0,1{36,4}Truncated 8-orthoplex
Truncated diacosipentacontahexazetton (tek)		1456224
align=center BGCOLOR="#f0e0e0"

!10

|{{CDD|node|4|node|3|node|3|node|3|node|3|node_1|3|node|3|node_1}}

t0,2{36,4}Cantellated 8-orthoplex
Small rhombated diacosipentacontahexazetton (srek)		147841344
align=center BGCOLOR="#f0e0e0"

!11

|{{CDD|node|4|node|3|node|3|node|3|node|3|node_1|3|node_1|3|node}}

t1,2{36,4}Bitruncated 8-orthoplex
Bitruncated diacosipentacontahexazetton (batek)		80641344
align=center BGCOLOR="#f0e0e0"

!12

|{{CDD|node|4|node|3|node|3|node|3|node_1|3|node|3|node|3|node_1}}

t0,3{36,4}Runcinated 8-orthoplex
Small prismated diacosipentacontahexazetton (spek)		604804480
align=center BGCOLOR="#f0e0e0"

!13

|{{CDD|node|4|node|3|node|3|node|3|node_1|3|node|3|node_1|3|node}}

t1,3{36,4}Bicantellated 8-orthoplex
Small birhombated diacosipentacontahexazetton (sabork)		672006720
align=center BGCOLOR="#f0e0e0"

!14

|{{CDD|node|4|node|3|node|3|node|3|node_1|3|node_1|3|node|3|node}}

t2,3{36,4}Tritruncated 8-orthoplex
Tritruncated diacosipentacontahexazetton (tatek)		246404480
align=center BGCOLOR="#f0e0e0"

!15

|{{CDD|node|4|node|3|node|3|node_1|3|node|3|node|3|node|3|node_1}}

t0,4{36,4}Stericated 8-orthoplex
Small cellated diacosipentacontahexazetton (scak)		1254408960
align=center BGCOLOR="#f0e0e0"

!16

|{{CDD|node|4|node|3|node|3|node_1|3|node|3|node|3|node_1|3|node}}

t1,4{36,4}Biruncinated 8-orthoplex
Small biprismated diacosipentacontahexazetton (sabpek)		21504017920
align=center BGCOLOR="#f0e0e0"

!17

|{{CDD|node|4|node|3|node|3|node_1|3|node|3|node_1|3|node|3|node}}

t2,4{36,4}Tricantellated 8-orthoplex
Small trirhombated diacosipentacontahexazetton (satrek)		16128017920
align=center BGCOLOR="#e0f0e0"

!18

|{{CDD|node|4|node|3|node|3|node_1|3|node_1|3|node|3|node|3|node}}

t3,4{4,36}Quadritruncated 8-cube
Octeractidiacosipentacontahexazetton (oke)		448008960
align=center BGCOLOR="#f0e0e0"

!19

|{{CDD|node|4|node|3|node_1|3|node|3|node|3|node|3|node|3|node_1}}

t0,5{36,4}Pentellated 8-orthoplex
Small terated diacosipentacontahexazetton (setek)		13440010752
align=center BGCOLOR="#f0e0e0"

!20

|{{CDD|node|4|node|3|node_1|3|node|3|node|3|node|3|node_1|3|node}}

t1,5{36,4}Bistericated 8-orthoplex
Small bicellated diacosipentacontahexazetton (sibcak)		32256026880
align=center BGCOLOR="#e0f0e0"

!21

|{{CDD|node|4|node|3|node_1|3|node|3|node|3|node_1|3|node|3|node}}

t2,5{4,36}Triruncinated 8-cube
Small triprismato-octeractidiacosipentacontahexazetton (sitpoke)		37632035840
align=center BGCOLOR="#e0e0f0"

!22

|{{CDD|node|4|node|3|node_1|3|node|3|node_1|3|node|3|node|3|node}}

t2,4{4,36}Tricantellated 8-cube
Small trirhombated octeract (satro)		21504026880
align=center BGCOLOR="#e0e0f0"

!23

|{{CDD|node|4|node|3|node_1|3|node_1|3|node|3|node|3|node|3|node}}

t2,3{4,36}Tritruncated 8-cube
Tritruncated octeract (tato)		4838410752
align=center BGCOLOR="#f0e0e0"

!24

|{{CDD|node|4|node_1|3|node|3|node|3|node|3|node|3|node|3|node_1}}

t0,6{36,4}Hexicated 8-orthoplex
Small petated diacosipentacontahexazetton (supek)		645127168
align=center BGCOLOR="#e0f0e0"

!25

|{{CDD|node|4|node_1|3|node|3|node|3|node|3|node|3|node_1|3|node}}

t1,6{4,36}Bipentellated 8-cube
Small biteri-octeractidiacosipentacontahexazetton (sabtoke)		21504021504
align=center BGCOLOR="#e0e0f0"

!26

|{{CDD|node|4|node_1|3|node|3|node|3|node|3|node_1|3|node|3|node}}

t1,5{4,36}Bistericated 8-cube
Small bicellated octeract (sobco)		35840035840
align=center BGCOLOR="#e0e0f0"

!27

|{{CDD|node|4|node_1|3|node|3|node|3|node_1|3|node|3|node|3|node}}

t1,4{4,36}Biruncinated 8-cube
Small biprismated octeract (sabepo)		32256035840
align=center BGCOLOR="#e0e0f0"

!28

|{{CDD|node|4|node_1|3|node|3|node_1|3|node|3|node|3|node|3|node}}

t1,3{4,36}Bicantellated 8-cube
Small birhombated octeract (subro)		15052821504
align=center BGCOLOR="#e0e0f0"

!29

|{{CDD|node|4|node_1|3|node_1|3|node|3|node|3|node|3|node|3|node}}

t1,2{4,36}Bitruncated 8-cube
Bitruncated octeract (bato)		286727168
align=center BGCOLOR="#e0f0e0"

!30

|{{CDD|node_1|4|node|3|node|3|node|3|node|3|node|3|node|3|node_1}}

t0,7{4,36}Heptellated 8-cube
Small exi-octeractidiacosipentacontahexazetton (saxoke)		143362048
align=center BGCOLOR="#e0e0f0"

!31

|{{CDD|node_1|4|node|3|node|3|node|3|node|3|node|3|node_1|3|node}}

t0,6{4,36}Hexicated 8-cube
Small petated octeract (supo)		645127168
align=center BGCOLOR="#e0e0f0"

!32

|{{CDD|node_1|4|node|3|node|3|node|3|node|3|node_1|3|node|3|node}}

t0,5{4,36}Pentellated 8-cube
Small terated octeract (soto)		14336014336
align=center BGCOLOR="#e0e0f0"

!33

|{{CDD|node_1|4|node|3|node|3|node|3|node_1|3|node|3|node|3|node}}

t0,4{4,36}Stericated 8-cube
Small cellated octeract (soco)		17920017920
align=center BGCOLOR="#e0e0f0"

!34

|{{CDD|node_1|4|node|3|node|3|node_1|3|node|3|node|3|node|3|node}}

t0,3{4,36}Runcinated 8-cube
Small prismated octeract (sopo)		12902414336
align=center BGCOLOR="#e0e0f0"

!35

|{{CDD|node_1|4|node|3|node_1|3|node|3|node|3|node|3|node|3|node}}

t0,2{4,36}Cantellated 8-cube
Small rhombated octeract (soro)		501767168
align=center BGCOLOR="#e0e0f0"

!36

|{{CDD|node_1|4|node_1|3|node|3|node|3|node|3|node|3|node|3|node}}

t0,1{4,36}Truncated 8-cube
Truncated octeract (tocto)		81922048
align=center BGCOLOR="#f0e0e0"

!37

|{{CDD|node|4|node|3|node|3|node|3|node|3|node_1|3|node_1|3|node_1}}

t0,1,2{36,4}Cantitruncated 8-orthoplex
Great rhombated diacosipentacontahexazetton		161282688
align=center BGCOLOR="#f0e0e0"

!38

|{{CDD|node|4|node|3|node|3|node|3|node_1|3|node|3|node_1|3|node_1}}

t0,1,3{36,4}Runcitruncated 8-orthoplex
Prismatotruncated diacosipentacontahexazetton		12768013440
align=center BGCOLOR="#f0e0e0"

!39

|{{CDD|node|4|node|3|node|3|node|3|node_1|3|node_1|3|node|3|node_1}}

t0,2,3{36,4}Runcicantellated 8-orthoplex
Prismatorhombated diacosipentacontahexazetton		8064013440
align=center BGCOLOR="#f0e0e0"

!40

|{{CDD|node|4|node|3|node|3|node|3|node_1|3|node_1|3|node_1|3|node}}

t1,2,3{36,4}Bicantitruncated 8-orthoplex
Great birhombated diacosipentacontahexazetton		7392013440
align=center BGCOLOR="#f0e0e0"

!41

|{{CDD|node|4|node|3|node|3|node_1|3|node|3|node|3|node_1|3|node_1}}

t0,1,4{36,4}Steritruncated 8-orthoplex
Cellitruncated diacosipentacontahexazetton		39424035840
align=center BGCOLOR="#f0e0e0"

!42

|{{CDD|node|4|node|3|node|3|node_1|3|node|3|node_1|3|node|3|node_1}}

t0,2,4{36,4}Stericantellated 8-orthoplex
Cellirhombated diacosipentacontahexazetton		48384053760
align=center BGCOLOR="#f0e0e0"

!43

|{{CDD|node|4|node|3|node|3|node_1|3|node|3|node_1|3|node_1|3|node}}

t1,2,4{36,4}Biruncitruncated 8-orthoplex
Biprismatotruncated diacosipentacontahexazetton		43008053760
align=center BGCOLOR="#f0e0e0"

!44

|{{CDD|node|4|node|3|node|3|node_1|3|node_1|3|node|3|node|3|node_1}}

t0,3,4{36,4}Steriruncinated 8-orthoplex
Celliprismated diacosipentacontahexazetton		21504035840
align=center BGCOLOR="#f0e0e0"

!45

|{{CDD|node|4|node|3|node|3|node_1|3|node_1|3|node|3|node_1|3|node}}

t1,3,4{36,4}Biruncicantellated 8-orthoplex
Biprismatorhombated diacosipentacontahexazetton		32256053760
align=center BGCOLOR="#f0e0e0"

!46

|{{CDD|node|4|node|3|node|3|node_1|3|node_1|3|node_1|3|node|3|node}}

t2,3,4{36,4}Tricantitruncated 8-orthoplex
Great trirhombated diacosipentacontahexazetton		17920035840
align=center BGCOLOR="#f0e0e0"

!47

|{{CDD|node|4|node|3|node_1|3|node|3|node|3|node|3|node_1|3|node_1}}

t0,1,5{36,4}Pentitruncated 8-orthoplex
Teritruncated diacosipentacontahexazetton		56448053760
align=center BGCOLOR="#f0e0e0"

!48

|{{CDD|node|4|node|3|node_1|3|node|3|node|3|node_1|3|node|3|node_1}}

t0,2,5{36,4}Penticantellated 8-orthoplex
Terirhombated diacosipentacontahexazetton		1075200107520
align=center BGCOLOR="#f0e0e0"

!49

|{{CDD|node|4|node|3|node_1|3|node|3|node|3|node_1|3|node_1|3|node}}

t1,2,5{36,4}Bisteritruncated 8-orthoplex
Bicellitruncated diacosipentacontahexazetton		913920107520
align=center BGCOLOR="#f0e0e0"

!50

|{{CDD|node|4|node|3|node_1|3|node|3|node_1|3|node|3|node|3|node_1}}

t0,3,5{36,4}Pentiruncinated 8-orthoplex
Teriprismated diacosipentacontahexazetton		913920107520
align=center BGCOLOR="#f0e0e0"

!51

|{{CDD|node|4|node|3|node_1|3|node|3|node_1|3|node|3|node_1|3|node}}

t1,3,5{36,4}Bistericantellated 8-orthoplex
Bicellirhombated diacosipentacontahexazetton		1290240161280
align=center BGCOLOR="#f0e0e0"

!52

|{{CDD|node|4|node|3|node_1|3|node|3|node_1|3|node_1|3|node|3|node}}

t2,3,5{36,4}Triruncitruncated 8-orthoplex
Triprismatotruncated diacosipentacontahexazetton		698880107520
align=center BGCOLOR="#f0e0e0"

!53

|{{CDD|node|4|node|3|node_1|3|node_1|3|node|3|node|3|node|3|node_1}}

t0,4,5{36,4}Pentistericated 8-orthoplex
Tericellated diacosipentacontahexazetton		32256053760
align=center BGCOLOR="#f0e0e0"

!54

|{{CDD|node|4|node|3|node_1|3|node_1|3|node|3|node|3|node_1|3|node}}

t1,4,5{36,4}Bisteriruncinated 8-orthoplex
Bicelliprismated diacosipentacontahexazetton		698880107520
align=center BGCOLOR="#e0e0f0"

!55

|{{CDD|node|4|node|3|node_1|3|node_1|3|node|3|node_1|3|node|3|node}}

t2,3,5{4,36}Triruncitruncated 8-cube
Triprismatotruncated octeract		645120107520
align=center BGCOLOR="#e0e0f0"

!56

|{{CDD|node|4|node|3|node_1|3|node_1|3|node_1|3|node|3|node|3|node}}

t2,3,4{4,36}Tricantitruncated 8-cube
Great trirhombated octeract		24192053760
align=center BGCOLOR="#f0e0e0"

!57

|{{CDD|node|4|node_1|3|node|3|node|3|node|3|node|3|node_1|3|node_1}}

t0,1,6{36,4}Hexitruncated 8-orthoplex
Petitruncated diacosipentacontahexazetton		34406443008
align=center BGCOLOR="#f0e0e0"

!58

|{{CDD|node|4|node_1|3|node|3|node|3|node|3|node_1|3|node|3|node_1}}

t0,2,6{36,4}Hexicantellated 8-orthoplex
Petirhombated diacosipentacontahexazetton		967680107520
align=center BGCOLOR="#f0e0e0"

!59

|{{CDD|node|4|node_1|3|node|3|node|3|node|3|node_1|3|node_1|3|node}}

t1,2,6{36,4}Bipentitruncated 8-orthoplex
Biteritruncated diacosipentacontahexazetton		752640107520
align=center BGCOLOR="#f0e0e0"

!60

|{{CDD|node|4|node_1|3|node|3|node|3|node_1|3|node|3|node|3|node_1}}

t0,3,6{36,4}Hexiruncinated 8-orthoplex
Petiprismated diacosipentacontahexazetton		1290240143360
align=center BGCOLOR="#f0e0e0"

!61

|{{CDD|node|4|node_1|3|node|3|node|3|node_1|3|node|3|node_1|3|node}}

t1,3,6{36,4}Bipenticantellated 8-orthoplex
Biterirhombated diacosipentacontahexazetton		1720320215040
align=center BGCOLOR="#e0e0f0"

!62

|{{CDD|node|4|node_1|3|node|3|node|3|node_1|3|node_1|3|node|3|node}}

t1,4,5{4,36}Bisteriruncinated 8-cube
Bicelliprismated octeract		860160143360
align=center BGCOLOR="#f0e0e0"

!63

|{{CDD|node|4|node_1|3|node|3|node_1|3|node|3|node|3|node|3|node_1}}

t0,4,6{36,4}Hexistericated 8-orthoplex
Peticellated diacosipentacontahexazetton		860160107520
align=center BGCOLOR="#e0e0f0"

!64

|{{CDD|node|4|node_1|3|node|3|node_1|3|node|3|node|3|node_1|3|node}}

t1,3,6{4,36}Bipenticantellated 8-cube
Biterirhombated octeract		1720320215040
align=center BGCOLOR="#e0e0f0"

!65

|{{CDD|node|4|node_1|3|node|3|node_1|3|node|3|node_1|3|node|3|node}}

t1,3,5{4,36}Bistericantellated 8-cube
Bicellirhombated octeract		1505280215040
align=center BGCOLOR="#e0e0f0"

!66

|{{CDD|node|4|node_1|3|node|3|node_1|3|node_1|3|node|3|node|3|node}}

t1,3,4{4,36}Biruncicantellated 8-cube
Biprismatorhombated octeract		537600107520
align=center BGCOLOR="#f0e0e0"

!67

|{{CDD|node|4|node_1|3|node_1|3|node|3|node|3|node|3|node|3|node_1}}

t0,5,6{36,4}Hexipentellated 8-orthoplex
Petiterated diacosipentacontahexazetton		25804843008
align=center BGCOLOR="#e0e0f0"

!68

|{{CDD|node|4|node_1|3|node_1|3|node|3|node|3|node|3|node_1|3|node}}

t1,2,6{4,36}Bipentitruncated 8-cube
Biteritruncated octeract		752640107520
align=center BGCOLOR="#e0e0f0"

!69

|{{CDD|node|4|node_1|3|node_1|3|node|3|node|3|node_1|3|node|3|node}}

t1,2,5{4,36}Bisteritruncated 8-cube
Bicellitruncated octeract		1003520143360
align=center BGCOLOR="#e0e0f0"

!70

|{{CDD|node|4|node_1|3|node_1|3|node|3|node_1|3|node|3|node|3|node}}

t1,2,4{4,36}Biruncitruncated 8-cube
Biprismatotruncated octeract		645120107520
align=center BGCOLOR="#e0e0f0"

!71

|{{CDD|node|4|node_1|3|node_1|3|node_1|3|node|3|node|3|node|3|node}}

t1,2,3{4,36}Bicantitruncated 8-cube
Great birhombated octeract		17203243008
align=center BGCOLOR="#f0e0e0"

!72

|{{CDD|node_1|4|node|3|node|3|node|3|node|3|node|3|node_1|3|node_1}}

t0,1,7{36,4}Heptitruncated 8-orthoplex
Exitruncated diacosipentacontahexazetton		9318414336
align=center BGCOLOR="#f0e0e0"

!73

|{{CDD|node_1|4|node|3|node|3|node|3|node|3|node_1|3|node|3|node_1}}

t0,2,7{36,4}Hepticantellated 8-orthoplex
Exirhombated diacosipentacontahexazetton		36556843008
align=center BGCOLOR="#e0e0f0"

!74

|{{CDD|node_1|4|node|3|node|3|node|3|node|3|node_1|3|node_1|3|node}}

t0,5,6{4,36}Hexipentellated 8-cube
Petiterated octeract		25804843008
align=center BGCOLOR="#f0e0e0"

!75

|{{CDD|node_1|4|node|3|node|3|node|3|node_1|3|node|3|node|3|node_1}}

t0,3,7{36,4}Heptiruncinated 8-orthoplex
Exiprismated diacosipentacontahexazetton		68096071680
align=center BGCOLOR="#e0e0f0"

!76

|{{CDD|node_1|4|node|3|node|3|node|3|node_1|3|node|3|node_1|3|node}}

t0,4,6{4,36}Hexistericated 8-cube
Peticellated octeract		860160107520
align=center BGCOLOR="#e0e0f0"

!77

|{{CDD|node_1|4|node|3|node|3|node|3|node_1|3|node_1|3|node|3|node}}

t0,4,5{4,36}Pentistericated 8-cube
Tericellated octeract		39424071680
align=center BGCOLOR="#e0e0f0"

!78

|{{CDD|node_1|4|node|3|node|3|node_1|3|node|3|node|3|node|3|node_1}}

t0,3,7{4,36}Heptiruncinated 8-cube
Exiprismated octeract		68096071680
align=center BGCOLOR="#e0e0f0"

!79

|{{CDD|node_1|4|node|3|node|3|node_1|3|node|3|node|3|node_1|3|node}}

t0,3,6{4,36}Hexiruncinated 8-cube
Petiprismated octeract		1290240143360
align=center BGCOLOR="#e0e0f0"

!80

|{{CDD|node_1|4|node|3|node|3|node_1|3|node|3|node_1|3|node|3|node}}

t0,3,5{4,36}Pentiruncinated 8-cube
Teriprismated octeract		1075200143360
align=center BGCOLOR="#e0e0f0"

!81

|{{CDD|node_1|4|node|3|node|3|node_1|3|node_1|3|node|3|node|3|node}}

t0,3,4{4,36}Steriruncinated 8-cube
Celliprismated octeract		35840071680
align=center BGCOLOR="#e0e0f0"

!82

|{{CDD|node_1|4|node|3|node_1|3|node|3|node|3|node|3|node|3|node_1}}

t0,2,7{4,36}Hepticantellated 8-cube
Exirhombated octeract		36556843008
align=center BGCOLOR="#e0e0f0"

!83

|{{CDD|node_1|4|node|3|node_1|3|node|3|node|3|node|3|node_1|3|node}}

t0,2,6{4,36}Hexicantellated 8-cube
Petirhombated octeract		967680107520
align=center BGCOLOR="#e0e0f0"

!84

|{{CDD|node_1|4|node|3|node_1|3|node|3|node|3|node_1|3|node|3|node}}

t0,2,5{4,36}Penticantellated 8-cube
Terirhombated octeract		1218560143360
align=center BGCOLOR="#e0e0f0"

!85

|{{CDD|node_1|4|node|3|node_1|3|node|3|node_1|3|node|3|node|3|node}}

t0,2,4{4,36}Stericantellated 8-cube
Cellirhombated octeract		752640107520
align=center BGCOLOR="#e0e0f0"

!86

|{{CDD|node_1|4|node|3|node_1|3|node_1|3|node|3|node|3|node|3|node}}

t0,2,3{4,36}Runcicantellated 8-cube
Prismatorhombated octeract		19353643008
align=center BGCOLOR="#e0e0f0"

!87

|{{CDD|node_1|4|node_1|3|node|3|node|3|node|3|node|3|node|3|node_1}}

t0,1,7{4,36}Heptitruncated 8-cube
Exitruncated octeract		9318414336
align=center BGCOLOR="#e0e0f0"

!88

|{{CDD|node_1|4|node_1|3|node|3|node|3|node|3|node|3|node_1|3|node}}

t0,1,6{4,36}Hexitruncated 8-cube
Petitruncated octeract		34406443008
align=center BGCOLOR="#e0e0f0"

!89

|{{CDD|node_1|4|node_1|3|node|3|node|3|node|3|node_1|3|node|3|node}}

t0,1,5{4,36}Pentitruncated 8-cube
Teritruncated octeract		60928071680
align=center BGCOLOR="#e0e0f0"

!90

|{{CDD|node_1|4|node_1|3|node|3|node|3|node_1|3|node|3|node|3|node}}

t0,1,4{4,36}Steritruncated 8-cube
Cellitruncated octeract		57344071680
align=center BGCOLOR="#e0e0f0"

!91

|{{CDD|node_1|4|node_1|3|node|3|node_1|3|node|3|node|3|node|3|node}}

t0,1,3{4,36}Runcitruncated 8-cube
Prismatotruncated octeract		27955243008
align=center BGCOLOR="#e0e0f0"

!92

|{{CDD|node_1|4|node_1|3|node_1|3|node|3|node|3|node|3|node|3|node}}

t0,1,2{4,36}Cantitruncated 8-cube
Great rhombated octeract		5734414336
align=center BGCOLOR="#f0e0e0"

!93

|{{CDD|node|4|node|3|node|3|node|3|node_1|3|node_1|3|node_1|3|node_1}}

t0,1,2,3{36,4}Runcicantitruncated 8-orthoplex
Great prismated diacosipentacontahexazetton		14784026880
align=center BGCOLOR="#f0e0e0"

!94

|{{CDD|node|4|node|3|node|3|node_1|3|node|3|node_1|3|node_1|3|node_1}}

t0,1,2,4{36,4}Stericantitruncated 8-orthoplex
Celligreatorhombated diacosipentacontahexazetton		860160107520
align=center BGCOLOR="#f0e0e0"

!95

|{{CDD|node|4|node|3|node|3|node_1|3|node_1|3|node|3|node_1|3|node_1}}

t0,1,3,4{36,4}Steriruncitruncated 8-orthoplex
Celliprismatotruncated diacosipentacontahexazetton		591360107520
align=center BGCOLOR="#f0e0e0"

!96

|{{CDD|node|4|node|3|node|3|node_1|3|node_1|3|node_1|3|node|3|node_1}}

t0,2,3,4{36,4}Steriruncicantellated 8-orthoplex
Celliprismatorhombated diacosipentacontahexazetton		591360107520
align=center BGCOLOR="#f0e0e0"

!97

|{{CDD|node|4|node|3|node|3|node_1|3|node_1|3|node_1|3|node_1|3|node}}

t1,2,3,4{36,4}Biruncicantitruncated 8-orthoplex
Great biprismated diacosipentacontahexazetton		537600107520
align=center BGCOLOR="#f0e0e0"

!98

|{{CDD|node|4|node|3|node_1|3|node|3|node|3|node_1|3|node_1|3|node_1}}

t0,1,2,5{36,4}Penticantitruncated 8-orthoplex
Terigreatorhombated diacosipentacontahexazetton		1827840215040
align=center BGCOLOR="#f0e0e0"

!99

|{{CDD|node|4|node|3|node_1|3|node|3|node_1|3|node|3|node_1|3|node_1}}

t0,1,3,5{36,4}Pentiruncitruncated 8-orthoplex
Teriprismatotruncated diacosipentacontahexazetton		2419200322560
align=center BGCOLOR="#f0e0e0"

!100

|{{CDD|node|4|node|3|node_1|3|node|3|node_1|3|node_1|3|node|3|node_1}}

t0,2,3,5{36,4}Pentiruncicantellated 8-orthoplex
Teriprismatorhombated diacosipentacontahexazetton		2257920322560
align=center BGCOLOR="#f0e0e0"

!101

|{{CDD|node|4|node|3|node_1|3|node|3|node_1|3|node_1|3|node_1|3|node}}

t1,2,3,5{36,4}Bistericantitruncated 8-orthoplex
Bicelligreatorhombated diacosipentacontahexazetton		2096640322560
align=center BGCOLOR="#f0e0e0"

!102

|{{CDD|node|4|node|3|node_1|3|node_1|3|node|3|node|3|node_1|3|node_1}}

t0,1,4,5{36,4}Pentisteritruncated 8-orthoplex
Tericellitruncated diacosipentacontahexazetton		1182720215040
align=center BGCOLOR="#f0e0e0"

!103

|{{CDD|node|4|node|3|node_1|3|node_1|3|node|3|node_1|3|node|3|node_1}}

t0,2,4,5{36,4}Pentistericantellated 8-orthoplex
Tericellirhombated diacosipentacontahexazetton		1935360322560
align=center BGCOLOR="#f0e0e0"

!104

|{{CDD|node|4|node|3|node_1|3|node_1|3|node|3|node_1|3|node_1|3|node}}

t1,2,4,5{36,4}Bisteriruncitruncated 8-orthoplex
Bicelliprismatotruncated diacosipentacontahexazetton		1612800322560
align=center BGCOLOR="#f0e0e0"

!105

|{{CDD|node|4|node|3|node_1|3|node_1|3|node_1|3|node|3|node|3|node_1}}

t0,3,4,5{36,4}Pentisteriruncinated 8-orthoplex
Tericelliprismated diacosipentacontahexazetton		1182720215040
align=center BGCOLOR="#f0e0e0"

!106

|{{CDD|node|4|node|3|node_1|3|node_1|3|node_1|3|node|3|node_1|3|node}}

t1,3,4,5{36,4}Bisteriruncicantellated 8-orthoplex
Bicelliprismatorhombated diacosipentacontahexazetton		1774080322560
align=center BGCOLOR="#e0f0e0"

!107

|{{CDD|node|4|node|3|node_1|3|node_1|3|node_1|3|node_1|3|node|3|node}}

t2,3,4,5{4,36}Triruncicantitruncated 8-cube
Great triprismato-octeractidiacosipentacontahexazetton		967680215040
align=center BGCOLOR="#f0e0e0"

!108

|{{CDD|node|4|node_1|3|node|3|node|3|node|3|node_1|3|node_1|3|node_1}}

t0,1,2,6{36,4}Hexicantitruncated 8-orthoplex
Petigreatorhombated diacosipentacontahexazetton		1505280215040
align=center BGCOLOR="#f0e0e0"

!109

|{{CDD|node|4|node_1|3|node|3|node|3|node_1|3|node|3|node_1|3|node_1}}

t0,1,3,6{36,4}Hexiruncitruncated 8-orthoplex
Petiprismatotruncated diacosipentacontahexazetton		3225600430080
align=center BGCOLOR="#f0e0e0"

!110

|{{CDD|node|4|node_1|3|node|3|node|3|node_1|3|node_1|3|node|3|node_1}}

t0,2,3,6{36,4}Hexiruncicantellated 8-orthoplex
Petiprismatorhombated diacosipentacontahexazetton		2795520430080
align=center BGCOLOR="#f0e0e0"

!111

|{{CDD|node|4|node_1|3|node|3|node|3|node_1|3|node_1|3|node_1|3|node}}

t1,2,3,6{36,4}Bipenticantitruncated 8-orthoplex
Biterigreatorhombated diacosipentacontahexazetton		2580480430080
align=center BGCOLOR="#f0e0e0"

!112

|{{CDD|node|4|node_1|3|node|3|node_1|3|node|3|node|3|node_1|3|node_1}}

t0,1,4,6{36,4}Hexisteritruncated 8-orthoplex
Peticellitruncated diacosipentacontahexazetton		3010560430080
align=center BGCOLOR="#f0e0e0"

!113

|{{CDD|node|4|node_1|3|node|3|node_1|3|node|3|node_1|3|node|3|node_1}}

t0,2,4,6{36,4}Hexistericantellated 8-orthoplex
Peticellirhombated diacosipentacontahexazetton		4515840645120
align=center BGCOLOR="#f0e0e0"

!114

|{{CDD|node|4|node_1|3|node|3|node_1|3|node|3|node_1|3|node_1|3|node}}

t1,2,4,6{36,4}Bipentiruncitruncated 8-orthoplex
Biteriprismatotruncated diacosipentacontahexazetton		3870720645120
align=center BGCOLOR="#f0e0e0"

!115

|{{CDD|node|4|node_1|3|node|3|node_1|3|node_1|3|node|3|node|3|node_1}}

t0,3,4,6{36,4}Hexisteriruncinated 8-orthoplex
Peticelliprismated diacosipentacontahexazetton		2580480430080
align=center BGCOLOR="#e0f0e0"

!116

|{{CDD|node|4|node_1|3|node|3|node_1|3|node_1|3|node|3|node_1|3|node}}

t1,3,4,6{4,36}Bipentiruncicantellated 8-cube
Biteriprismatorhombi-octeractidiacosipentacontahexazetton		3870720645120
align=center BGCOLOR="#e0e0f0"

!117

|{{CDD|node|4|node_1|3|node|3|node_1|3|node_1|3|node_1|3|node|3|node}}

t1,3,4,5{4,36}Bisteriruncicantellated 8-cube
Bicelliprismatorhombated octeract		2150400430080
align=center BGCOLOR="#f0e0e0"

!118

|{{CDD|node|4|node_1|3|node_1|3|node|3|node|3|node|3|node_1|3|node_1}}

t0,1,5,6{36,4}Hexipentitruncated 8-orthoplex
Petiteritruncated diacosipentacontahexazetton		1182720215040
align=center BGCOLOR="#f0e0e0"

!119

|{{CDD|node|4|node_1|3|node_1|3|node|3|node|3|node_1|3|node|3|node_1}}

t0,2,5,6{36,4}Hexipenticantellated 8-orthoplex
Petiterirhombated diacosipentacontahexazetton		2795520430080
align=center BGCOLOR="#e0f0e0"

!120

|{{CDD|node|4|node_1|3|node_1|3|node|3|node|3|node_1|3|node_1|3|node}}

t1,2,5,6{4,36}Bipentisteritruncated 8-cube
Bitericellitrunki-octeractidiacosipentacontahexazetton		2150400430080
align=center BGCOLOR="#f0e0e0"

!121

|{{CDD|node|4|node_1|3|node_1|3|node|3|node_1|3|node|3|node|3|node_1}}

t0,3,5,6{36,4}Hexipentiruncinated 8-orthoplex
Petiteriprismated diacosipentacontahexazetton		2795520430080
align=center BGCOLOR="#e0e0f0"

!122

|{{CDD|node|4|node_1|3|node_1|3|node|3|node_1|3|node|3|node_1|3|node}}

t1,2,4,6{4,36}Bipentiruncitruncated 8-cube
Biteriprismatotruncated octeract		3870720645120
align=center BGCOLOR="#e0e0f0"

!123

|{{CDD|node|4|node_1|3|node_1|3|node|3|node_1|3|node_1|3|node|3|node}}

t1,2,4,5{4,36}Bisteriruncitruncated 8-cube
Bicelliprismatotruncated octeract		1935360430080
align=center BGCOLOR="#f0e0e0"

!124

|{{CDD|node|4|node_1|3|node_1|3|node_1|3|node|3|node|3|node|3|node_1}}

t0,4,5,6{36,4}Hexipentistericated 8-orthoplex
Petitericellated diacosipentacontahexazetton		1182720215040
align=center BGCOLOR="#e0e0f0"

!125

|{{CDD|node|4|node_1|3|node_1|3|node_1|3|node|3|node|3|node_1|3|node}}

t1,2,3,6{4,36}Bipenticantitruncated 8-cube
Biterigreatorhombated octeract		2580480430080
align=center BGCOLOR="#e0e0f0"

!126

|{{CDD|node|4|node_1|3|node_1|3|node_1|3|node|3|node_1|3|node|3|node}}

t1,2,3,5{4,36}Bistericantitruncated 8-cube
Bicelligreatorhombated octeract		2365440430080
align=center BGCOLOR="#e0e0f0"

!127

|{{CDD|node|4|node_1|3|node_1|3|node_1|3|node_1|3|node|3|node|3|node}}

t1,2,3,4{4,36}Biruncicantitruncated 8-cube
Great biprismated octeract		860160215040
align=center BGCOLOR="#f0e0e0"

!128

|{{CDD|node_1|4|node|3|node|3|node|3|node|3|node_1|3|node_1|3|node_1}}

t0,1,2,7{36,4}Hepticantitruncated 8-orthoplex
Exigreatorhombated diacosipentacontahexazetton		51609686016
align=center BGCOLOR="#f0e0e0"

!129

|{{CDD|node_1|4|node|3|node|3|node|3|node_1|3|node|3|node_1|3|node_1}}

t0,1,3,7{36,4}Heptiruncitruncated 8-orthoplex
Exiprismatotruncated diacosipentacontahexazetton		1612800215040
align=center BGCOLOR="#f0e0e0"

!130

|{{CDD|node_1|4|node|3|node|3|node|3|node_1|3|node_1|3|node|3|node_1}}

t0,2,3,7{36,4}Heptiruncicantellated 8-orthoplex
Exiprismatorhombated diacosipentacontahexazetton		1290240215040
align=center BGCOLOR="#e0e0f0"

!131

|{{CDD|node_1|4|node|3|node|3|node|3|node_1|3|node_1|3|node_1|3|node}}

t0,4,5,6{4,36}Hexipentistericated 8-cube
Petitericellated octeract		1182720215040
align=center BGCOLOR="#f0e0e0"

!132

|{{CDD|node_1|4|node|3|node|3|node_1|3|node|3|node|3|node_1|3|node_1}}

t0,1,4,7{36,4}Heptisteritruncated 8-orthoplex
Exicellitruncated diacosipentacontahexazetton		2293760286720
align=center BGCOLOR="#f0e0e0"

!133

|{{CDD|node_1|4|node|3|node|3|node_1|3|node|3|node_1|3|node|3|node_1}}

t0,2,4,7{36,4}Heptistericantellated 8-orthoplex
Exicellirhombated diacosipentacontahexazetton		3225600430080
align=center BGCOLOR="#e0e0f0"

!134

|{{CDD|node_1|4|node|3|node|3|node_1|3|node|3|node_1|3|node_1|3|node}}

t0,3,5,6{4,36}Hexipentiruncinated 8-cube
Petiteriprismated octeract		2795520430080
align=center BGCOLOR="#e0f0e0"

!135

|{{CDD|node_1|4|node|3|node|3|node_1|3|node_1|3|node|3|node|3|node_1}}

t0,3,4,7{4,36}Heptisteriruncinated 8-cube
Exicelliprismato-octeractidiacosipentacontahexazetton		1720320286720
align=center BGCOLOR="#e0e0f0"

!136

|{{CDD|node_1|4|node|3|node|3|node_1|3|node_1|3|node|3|node_1|3|node}}

t0,3,4,6{4,36}Hexisteriruncinated 8-cube
Peticelliprismated octeract		2580480430080
align=center BGCOLOR="#e0e0f0"

!137

|{{CDD|node_1|4|node|3|node|3|node_1|3|node_1|3|node_1|3|node|3|node}}

t0,3,4,5{4,36}Pentisteriruncinated 8-cube
Tericelliprismated octeract		1433600286720
align=center BGCOLOR="#f0e0e0"

!138

|{{CDD|node_1|4|node|3|node_1|3|node|3|node|3|node|3|node_1|3|node_1}}

t0,1,5,7{36,4}Heptipentitruncated 8-orthoplex
Exiteritruncated diacosipentacontahexazetton		1612800215040
align=center BGCOLOR="#e0f0e0"

!139

|{{CDD|node_1|4|node|3|node_1|3|node|3|node|3|node_1|3|node|3|node_1}}

t0,2,5,7{4,36}Heptipenticantellated 8-cube
Exiterirhombi-octeractidiacosipentacontahexazetton		3440640430080
align=center BGCOLOR="#e0e0f0"

!140

|{{CDD|node_1|4|node|3|node_1|3|node|3|node|3|node_1|3|node_1|3|node}}

t0,2,5,6{4,36}Hexipenticantellated 8-cube
Petiterirhombated octeract		2795520430080
align=center BGCOLOR="#e0e0f0"

!141

|{{CDD|node_1|4|node|3|node_1|3|node|3|node_1|3|node|3|node|3|node_1}}

t0,2,4,7{4,36}Heptistericantellated 8-cube
Exicellirhombated octeract		3225600430080
align=center BGCOLOR="#e0e0f0"

!142

|{{CDD|node_1|4|node|3|node_1|3|node|3|node_1|3|node|3|node_1|3|node}}

t0,2,4,6{4,36}Hexistericantellated 8-cube
Peticellirhombated octeract		4515840645120
align=center BGCOLOR="#e0e0f0"

!143

|{{CDD|node_1|4|node|3|node_1|3|node|3|node_1|3|node_1|3|node|3|node}}

t0,2,4,5{4,36}Pentistericantellated 8-cube
Tericellirhombated octeract		2365440430080
align=center BGCOLOR="#e0e0f0"

!144

|{{CDD|node_1|4|node|3|node_1|3|node_1|3|node|3|node|3|node|3|node_1}}

t0,2,3,7{4,36}Heptiruncicantellated 8-cube
Exiprismatorhombated octeract		1290240215040
align=center BGCOLOR="#e0e0f0"

!145

|{{CDD|node_1|4|node|3|node_1|3|node_1|3|node|3|node|3|node_1|3|node}}

t0,2,3,6{4,36}Hexiruncicantellated 8-cube
Petiprismatorhombated octeract		2795520430080
align=center BGCOLOR="#e0e0f0"

!146

|{{CDD|node_1|4|node|3|node_1|3|node_1|3|node|3|node_1|3|node|3|node}}

t0,2,3,5{4,36}Pentiruncicantellated 8-cube
Teriprismatorhombated octeract		2580480430080
align=center BGCOLOR="#e0e0f0"

!147

|{{CDD|node_1|4|node|3|node_1|3|node_1|3|node_1|3|node|3|node|3|node}}

t0,2,3,4{4,36}Steriruncicantellated 8-cube
Celliprismatorhombated octeract		967680215040
align=center BGCOLOR="#e0f0e0"

!148

|{{CDD|node_1|4|node_1|3|node|3|node|3|node|3|node|3|node_1|3|node_1}}

t0,1,6,7{4,36}Heptihexitruncated 8-cube
Exipetitrunki-octeractidiacosipentacontahexazetton		51609686016
align=center BGCOLOR="#e0e0f0"

!149

|{{CDD|node_1|4|node_1|3|node|3|node|3|node|3|node_1|3|node|3|node_1}}

t0,1,5,7{4,36}Heptipentitruncated 8-cube
Exiteritruncated octeract		1612800215040
align=center BGCOLOR="#e0e0f0"

!150

|{{CDD|node_1|4|node_1|3|node|3|node|3|node|3|node_1|3|node_1|3|node}}

t0,1,5,6{4,36}Hexipentitruncated 8-cube
Petiteritruncated octeract		1182720215040
align=center BGCOLOR="#e0e0f0"

!151

|{{CDD|node_1|4|node_1|3|node|3|node|3|node_1|3|node|3|node|3|node_1}}

t0,1,4,7{4,36}Heptisteritruncated 8-cube
Exicellitruncated octeract		2293760286720
align=center BGCOLOR="#e0e0f0"

!152

|{{CDD|node_1|4|node_1|3|node|3|node|3|node_1|3|node|3|node_1|3|node}}

t0,1,4,6{4,36}Hexisteritruncated 8-cube
Peticellitruncated octeract		3010560430080
align=center BGCOLOR="#e0e0f0"

!153

|{{CDD|node_1|4|node_1|3|node|3|node|3|node_1|3|node_1|3|node|3|node}}

t0,1,4,5{4,36}Pentisteritruncated 8-cube
Tericellitruncated octeract		1433600286720
align=center BGCOLOR="#e0e0f0"

!154

|{{CDD|node_1|4|node_1|3|node|3|node_1|3|node|3|node|3|node|3|node_1}}

t0,1,3,7{4,36}Heptiruncitruncated 8-cube
Exiprismatotruncated octeract		1612800215040
align=center BGCOLOR="#e0e0f0"

!155

|{{CDD|node_1|4|node_1|3|node|3|node_1|3|node|3|node|3|node_1|3|node}}

t0,1,3,6{4,36}Hexiruncitruncated 8-cube
Petiprismatotruncated octeract		3225600430080
align=center BGCOLOR="#e0e0f0"

!156

|{{CDD|node_1|4|node_1|3|node|3|node_1|3|node|3|node_1|3|node|3|node}}

t0,1,3,5{4,36}Pentiruncitruncated 8-cube
Teriprismatotruncated octeract		2795520430080
align=center BGCOLOR="#e0e0f0"

!157

|{{CDD|node_1|4|node_1|3|node|3|node_1|3|node_1|3|node|3|node|3|node}}

t0,1,3,4{4,36}Steriruncitruncated 8-cube
Celliprismatotruncated octeract		967680215040
align=center BGCOLOR="#e0e0f0"

!158

|{{CDD|node_1|4|node_1|3|node_1|3|node|3|node|3|node|3|node|3|node_1}}

t0,1,2,7{4,36}Hepticantitruncated 8-cube
Exigreatorhombated octeract		51609686016
align=center BGCOLOR="#e0e0f0"

!159

|{{CDD|node_1|4|node_1|3|node_1|3|node|3|node|3|node|3|node_1|3|node}}

t0,1,2,6{4,36}Hexicantitruncated 8-cube
Petigreatorhombated octeract		1505280215040
align=center BGCOLOR="#e0e0f0"

!160

|{{CDD|node_1|4|node_1|3|node_1|3|node|3|node|3|node_1|3|node|3|node}}

t0,1,2,5{4,36}Penticantitruncated 8-cube
Terigreatorhombated octeract		2007040286720
align=center BGCOLOR="#e0e0f0"

!161

|{{CDD|node_1|4|node_1|3|node_1|3|node|3|node_1|3|node|3|node|3|node}}

t0,1,2,4{4,36}Stericantitruncated 8-cube
Celligreatorhombated octeract		1290240215040
align=center BGCOLOR="#e0e0f0"

!162

|{{CDD|node_1|4|node_1|3|node_1|3|node_1|3|node|3|node|3|node|3|node}}

t0,1,2,3{4,36}Runcicantitruncated 8-cube
Great prismated octeract		34406486016
align=center BGCOLOR="#f0e0e0"

!163

|{{CDD|node|4|node|3|node|3|node_1|3|node_1|3|node_1|3|node_1|3|node_1}}

t0,1,2,3,4{36,4}Steriruncicantitruncated 8-orthoplex
Great cellated diacosipentacontahexazetton		1075200215040
align=center BGCOLOR="#f0e0e0"

!164

|{{CDD|node|4|node|3|node_1|3|node|3|node_1|3|node_1|3|node_1|3|node_1}}

t0,1,2,3,5{36,4}Pentiruncicantitruncated 8-orthoplex
Terigreatoprismated diacosipentacontahexazetton		4193280645120
align=center BGCOLOR="#f0e0e0"

!165

|{{CDD|node|4|node|3|node_1|3|node_1|3|node|3|node_1|3|node_1|3|node_1}}

t0,1,2,4,5{36,4}Pentistericantitruncated 8-orthoplex
Tericelligreatorhombated diacosipentacontahexazetton		3225600645120
align=center BGCOLOR="#f0e0e0"

!166

|{{CDD|node|4|node|3|node_1|3|node_1|3|node_1|3|node|3|node_1|3|node_1}}

t0,1,3,4,5{36,4}Pentisteriruncitruncated 8-orthoplex
Tericelliprismatotruncated diacosipentacontahexazetton		3225600645120
align=center BGCOLOR="#f0e0e0"

!167

|{{CDD|node|4|node|3|node_1|3|node_1|3|node_1|3|node_1|3|node|3|node_1}}

t0,2,3,4,5{36,4}Pentisteriruncicantellated 8-orthoplex
Tericelliprismatorhombated diacosipentacontahexazetton		3225600645120
align=center BGCOLOR="#f0e0e0"

!168

|{{CDD|node|4|node|3|node_1|3|node_1|3|node_1|3|node_1|3|node_1|3|node}}

t1,2,3,4,5{36,4}Bisteriruncicantitruncated 8-orthoplex
Great bicellated diacosipentacontahexazetton		2903040645120
align=center BGCOLOR="#f0e0e0"

!169

|{{CDD|node|4|node_1|3|node|3|node|3|node_1|3|node_1|3|node_1|3|node_1}}

t0,1,2,3,6{36,4}Hexiruncicantitruncated 8-orthoplex
Petigreatoprismated diacosipentacontahexazetton		5160960860160
align=center BGCOLOR="#f0e0e0"

!170

|{{CDD|node|4|node_1|3|node|3|node_1|3|node|3|node_1|3|node_1|3|node_1}}

t0,1,2,4,6{36,4}Hexistericantitruncated 8-orthoplex
Peticelligreatorhombated diacosipentacontahexazetton		77414401290240
align=center BGCOLOR="#f0e0e0"

!171

|{{CDD|node|4|node_1|3|node|3|node_1|3|node_1|3|node|3|node_1|3|node_1}}

t0,1,3,4,6{36,4}Hexisteriruncitruncated 8-orthoplex
Peticelliprismatotruncated diacosipentacontahexazetton		70963201290240
align=center BGCOLOR="#f0e0e0"

!172

|{{CDD|node|4|node_1|3|node|3|node_1|3|node_1|3|node_1|3|node|3|node_1}}

t0,2,3,4,6{36,4}Hexisteriruncicantellated 8-orthoplex
Peticelliprismatorhombated diacosipentacontahexazetton		70963201290240
align=center BGCOLOR="#f0e0e0"

!173

|{{CDD|node|4|node_1|3|node|3|node_1|3|node_1|3|node_1|3|node_1|3|node}}

t1,2,3,4,6{36,4}Bipentiruncicantitruncated 8-orthoplex
Biterigreatoprismated diacosipentacontahexazetton		64512001290240
align=center BGCOLOR="#f0e0e0"

!174

|{{CDD|node|4|node_1|3|node_1|3|node|3|node|3|node_1|3|node_1|3|node_1}}

t0,1,2,5,6{36,4}Hexipenticantitruncated 8-orthoplex
Petiterigreatorhombated diacosipentacontahexazetton		4300800860160
align=center BGCOLOR="#f0e0e0"

!175

|{{CDD|node|4|node_1|3|node_1|3|node|3|node_1|3|node|3|node_1|3|node_1}}

t0,1,3,5,6{36,4}Hexipentiruncitruncated 8-orthoplex
Petiteriprismatotruncated diacosipentacontahexazetton		70963201290240
align=center BGCOLOR="#f0e0e0"

!176

|{{CDD|node|4|node_1|3|node_1|3|node|3|node_1|3|node_1|3|node|3|node_1}}

t0,2,3,5,6{36,4}Hexipentiruncicantellated 8-orthoplex
Petiteriprismatorhombated diacosipentacontahexazetton		64512001290240
align=center BGCOLOR="#f0e0e0"

!177

|{{CDD|node|4|node_1|3|node_1|3|node|3|node_1|3|node_1|3|node_1|3|node}}

t1,2,3,5,6{36,4}Bipentistericantitruncated 8-orthoplex
Bitericelligreatorhombated diacosipentacontahexazetton		58060801290240
align=center BGCOLOR="#f0e0e0"

!178

|{{CDD|node|4|node_1|3|node_1|3|node_1|3|node|3|node|3|node_1|3|node_1}}

t0,1,4,5,6{36,4}Hexipentisteritruncated 8-orthoplex
Petitericellitruncated diacosipentacontahexazetton		4300800860160
align=center BGCOLOR="#f0e0e0"

!179

|{{CDD|node|4|node_1|3|node_1|3|node_1|3|node|3|node_1|3|node|3|node_1}}

t0,2,4,5,6{36,4}Hexipentistericantellated 8-orthoplex
Petitericellirhombated diacosipentacontahexazetton		70963201290240
align=center BGCOLOR="#e0e0f0"

!180

|{{CDD|node|4|node_1|3|node_1|3|node_1|3|node|3|node_1|3|node_1|3|node}}

t1,2,3,5,6{4,36}Bipentistericantitruncated 8-cube
Bitericelligreatorhombated octeract		58060801290240
align=center BGCOLOR="#f0e0e0"

!181

|{{CDD|node|4|node_1|3|node_1|3|node_1|3|node_1|3|node|3|node|3|node_1}}

t0,3,4,5,6{36,4}Hexipentisteriruncinated 8-orthoplex
Petitericelliprismated diacosipentacontahexazetton		4300800860160
align=center BGCOLOR="#e0e0f0"

!182

|{{CDD|node|4|node_1|3|node_1|3|node_1|3|node_1|3|node|3|node_1|3|node}}

t1,2,3,4,6{4,36}Bipentiruncicantitruncated 8-cube
Biterigreatoprismated octeract		64512001290240
align=center BGCOLOR="#e0e0f0"

!183

|{{CDD|node|4|node_1|3|node_1|3|node_1|3|node_1|3|node_1|3|node|3|node}}

t1,2,3,4,5{4,36}Bisteriruncicantitruncated 8-cube
Great bicellated octeract		3440640860160
align=center BGCOLOR="#f0e0e0"

!184

|{{CDD|node_1|4|node|3|node|3|node|3|node_1|3|node_1|3|node_1|3|node_1}}

t0,1,2,3,7{36,4}Heptiruncicantitruncated 8-orthoplex
Exigreatoprismated diacosipentacontahexazetton		2365440430080
align=center BGCOLOR="#f0e0e0"

!185

|{{CDD|node_1|4|node|3|node|3|node_1|3|node|3|node_1|3|node_1|3|node_1}}

t0,1,2,4,7{36,4}Heptistericantitruncated 8-orthoplex
Exicelligreatorhombated diacosipentacontahexazetton		5591040860160
align=center BGCOLOR="#f0e0e0"

!186

|{{CDD|node_1|4|node|3|node|3|node_1|3|node_1|3|node|3|node_1|3|node_1}}

t0,1,3,4,7{36,4}Heptisteriruncitruncated 8-orthoplex
Exicelliprismatotruncated diacosipentacontahexazetton		4730880860160
align=center BGCOLOR="#f0e0e0"

!187

|{{CDD|node_1|4|node|3|node|3|node_1|3|node_1|3|node_1|3|node|3|node_1}}

t0,2,3,4,7{36,4}Heptisteriruncicantellated 8-orthoplex
Exicelliprismatorhombated diacosipentacontahexazetton		4730880860160
align=center BGCOLOR="#e0e0f0"

!188

|{{CDD|node_1|4|node|3|node|3|node_1|3|node_1|3|node_1|3|node_1|3|node}}

t0,3,4,5,6{4,36}Hexipentisteriruncinated 8-cube
Petitericelliprismated octeract		4300800860160
align=center BGCOLOR="#f0e0e0"

!189

|{{CDD|node_1|4|node|3|node_1|3|node|3|node|3|node_1|3|node_1|3|node_1}}

t0,1,2,5,7{36,4}Heptipenticantitruncated 8-orthoplex
Exiterigreatorhombated diacosipentacontahexazetton		5591040860160
align=center BGCOLOR="#f0e0e0"

!190

|{{CDD|node_1|4|node|3|node_1|3|node|3|node_1|3|node|3|node_1|3|node_1}}

t0,1,3,5,7{36,4}Heptipentiruncitruncated 8-orthoplex
Exiteriprismatotruncated diacosipentacontahexazetton		83865601290240
align=center BGCOLOR="#f0e0e0"

!191

|{{CDD|node_1|4|node|3|node_1|3|node|3|node_1|3|node_1|3|node|3|node_1}}

t0,2,3,5,7{36,4}Heptipentiruncicantellated 8-orthoplex
Exiteriprismatorhombated diacosipentacontahexazetton		77414401290240
align=center BGCOLOR="#e0e0f0"

!192

|{{CDD|node_1|4|node|3|node_1|3|node|3|node_1|3|node_1|3|node_1|3|node}}

t0,2,4,5,6{4,36}Hexipentistericantellated 8-cube
Petitericellirhombated octeract		70963201290240
align=center BGCOLOR="#f0e0e0"

!193

|{{CDD|node_1|4|node|3|node_1|3|node_1|3|node|3|node|3|node_1|3|node_1}}

t0,1,4,5,7{36,4}Heptipentisteritruncated 8-orthoplex
Exitericellitruncated diacosipentacontahexazetton		4730880860160
align=center BGCOLOR="#e0e0f0"

!194

|{{CDD|node_1|4|node|3|node_1|3|node_1|3|node|3|node_1|3|node|3|node_1}}

t0,2,3,5,7{4,36}Heptipentiruncicantellated 8-cube
Exiteriprismatorhombated octeract		77414401290240
align=center BGCOLOR="#e0e0f0"

!195

|{{CDD|node_1|4|node|3|node_1|3|node_1|3|node|3|node_1|3|node_1|3|node}}

t0,2,3,5,6{4,36}Hexipentiruncicantellated 8-cube
Petiteriprismatorhombated octeract		64512001290240
align=center BGCOLOR="#e0e0f0"

!196

|{{CDD|node_1|4|node|3|node_1|3|node_1|3|node_1|3|node|3|node|3|node_1}}

t0,2,3,4,7{4,36}Heptisteriruncicantellated 8-cube
Exicelliprismatorhombated octeract		4730880860160
align=center BGCOLOR="#e0e0f0"

!197

|{{CDD|node_1|4|node|3|node_1|3|node_1|3|node_1|3|node|3|node_1|3|node}}

t0,2,3,4,6{4,36}Hexisteriruncicantellated 8-cube
Peticelliprismatorhombated octeract		70963201290240
align=center BGCOLOR="#e0e0f0"

!198

|{{CDD|node_1|4|node|3|node_1|3|node_1|3|node_1|3|node_1|3|node|3|node}}

t0,2,3,4,5{4,36}Pentisteriruncicantellated 8-cube
Tericelliprismatorhombated octeract		3870720860160
align=center BGCOLOR="#f0e0e0"

!199

|{{CDD|node_1|4|node_1|3|node|3|node|3|node|3|node_1|3|node_1|3|node_1}}

t0,1,2,6,7{36,4}Heptihexicantitruncated 8-orthoplex
Exipetigreatorhombated diacosipentacontahexazetton		2365440430080
align=center BGCOLOR="#f0e0e0"

!200

|{{CDD|node_1|4|node_1|3|node|3|node|3|node_1|3|node|3|node_1|3|node_1}}

t0,1,3,6,7{36,4}Heptihexiruncitruncated 8-orthoplex
Exipetiprismatotruncated diacosipentacontahexazetton		5591040860160
align=center BGCOLOR="#e0e0f0"

!201

|{{CDD|node_1|4|node_1|3|node|3|node|3|node_1|3|node_1|3|node|3|node_1}}

t0,1,4,5,7{4,36}Heptipentisteritruncated 8-cube
Exitericellitruncated octeract		4730880860160
align=center BGCOLOR="#e0e0f0"

!202

|{{CDD|node_1|4|node_1|3|node|3|node|3|node_1|3|node_1|3|node_1|3|node}}

t0,1,4,5,6{4,36}Hexipentisteritruncated 8-cube
Petitericellitruncated octeract		4300800860160
align=center BGCOLOR="#e0e0f0"

!203

|{{CDD|node_1|4|node_1|3|node|3|node_1|3|node|3|node|3|node_1|3|node_1}}

t0,1,3,6,7{4,36}Heptihexiruncitruncated 8-cube
Exipetiprismatotruncated octeract		5591040860160
align=center BGCOLOR="#e0e0f0"

!204

|{{CDD|node_1|4|node_1|3|node|3|node_1|3|node|3|node_1|3|node|3|node_1}}

t0,1,3,5,7{4,36}Heptipentiruncitruncated 8-cube
Exiteriprismatotruncated octeract		83865601290240
align=center BGCOLOR="#e0e0f0"

!205

|{{CDD|node_1|4|node_1|3|node|3|node_1|3|node|3|node_1|3|node_1|3|node}}

t0,1,3,5,6{4,36}Hexipentiruncitruncated 8-cube
Petiteriprismatotruncated octeract		70963201290240
align=center BGCOLOR="#e0e0f0"

!206

|{{CDD|node_1|4|node_1|3|node|3|node_1|3|node_1|3|node|3|node|3|node_1}}

t0,1,3,4,7{4,36}Heptisteriruncitruncated 8-cube
Exicelliprismatotruncated octeract		4730880860160
align=center BGCOLOR="#e0e0f0"

!207

|{{CDD|node_1|4|node_1|3|node|3|node_1|3|node_1|3|node|3|node_1|3|node}}

t0,1,3,4,6{4,36}Hexisteriruncitruncated 8-cube
Peticelliprismatotruncated octeract		70963201290240
align=center BGCOLOR="#e0e0f0"

!208

|{{CDD|node_1|4|node_1|3|node|3|node_1|3|node_1|3|node_1|3|node|3|node}}

t0,1,3,4,5{4,36}Pentisteriruncitruncated 8-cube
Tericelliprismatotruncated octeract		3870720860160
align=center BGCOLOR="#e0e0f0"

!209

|{{CDD|node_1|4|node_1|3|node_1|3|node|3|node|3|node|3|node_1|3|node_1}}

t0,1,2,6,7{4,36}Heptihexicantitruncated 8-cube
Exipetigreatorhombated octeract		2365440430080
align=center BGCOLOR="#e0e0f0"

!210

|{{CDD|node_1|4|node_1|3|node_1|3|node|3|node|3|node_1|3|node|3|node_1}}

t0,1,2,5,7{4,36}Heptipenticantitruncated 8-cube
Exiterigreatorhombated octeract		5591040860160
align=center BGCOLOR="#e0e0f0"

!211

|{{CDD|node_1|4|node_1|3|node_1|3|node|3|node|3|node_1|3|node_1|3|node}}

t0,1,2,5,6{4,36}Hexipenticantitruncated 8-cube
Petiterigreatorhombated octeract		4300800860160
align=center BGCOLOR="#e0e0f0"

!212

|{{CDD|node_1|4|node_1|3|node_1|3|node|3|node_1|3|node|3|node|3|node_1}}

t0,1,2,4,7{4,36}Heptistericantitruncated 8-cube
Exicelligreatorhombated octeract		5591040860160
align=center BGCOLOR="#e0e0f0"

!213

|{{CDD|node_1|4|node_1|3|node_1|3|node|3|node_1|3|node|3|node_1|3|node}}

t0,1,2,4,6{4,36}Hexistericantitruncated 8-cube
Peticelligreatorhombated octeract		77414401290240
align=center BGCOLOR="#e0e0f0"

!214

|{{CDD|node_1|4|node_1|3|node_1|3|node|3|node_1|3|node_1|3|node|3|node}}

t0,1,2,4,5{4,36}Pentistericantitruncated 8-cube
Tericelligreatorhombated octeract		3870720860160
align=center BGCOLOR="#e0e0f0"

!215

|{{CDD|node_1|4|node_1|3|node_1|3|node_1|3|node|3|node|3|node|3|node_1}}

t0,1,2,3,7{4,36}Heptiruncicantitruncated 8-cube
Exigreatoprismated octeract		2365440430080
align=center BGCOLOR="#e0e0f0"

!216

|{{CDD|node_1|4|node_1|3|node_1|3|node_1|3|node|3|node|3|node_1|3|node}}

t0,1,2,3,6{4,36}Hexiruncicantitruncated 8-cube
Petigreatoprismated octeract		5160960860160
align=center BGCOLOR="#e0e0f0"

!217

|{{CDD|node_1|4|node_1|3|node_1|3|node_1|3|node|3|node_1|3|node|3|node}}

t0,1,2,3,5{4,36}Pentiruncicantitruncated 8-cube
Terigreatoprismated octeract		4730880860160
align=center BGCOLOR="#e0e0f0"

!218

|{{CDD|node_1|4|node_1|3|node_1|3|node_1|3|node_1|3|node|3|node|3|node}}

t0,1,2,3,4{4,36}Steriruncicantitruncated 8-cube
Great cellated octeract		1720320430080
align=center BGCOLOR="#f0e0e0"

!219

|{{CDD|node|4|node|3|node_1|3|node_1|3|node_1|3|node_1|3|node_1|3|node_1}}

t0,1,2,3,4,5{36,4}Pentisteriruncicantitruncated 8-orthoplex
Great terated diacosipentacontahexazetton		58060801290240
align=center BGCOLOR="#f0e0e0"

!220

|{{CDD|node|4|node_1|3|node|3|node_1|3|node_1|3|node_1|3|node_1|3|node_1}}

t0,1,2,3,4,6{36,4}Hexisteriruncicantitruncated 8-orthoplex
Petigreatocellated diacosipentacontahexazetton		129024002580480
align=center BGCOLOR="#f0e0e0"

!221

|{{CDD|node|4|node_1|3|node_1|3|node|3|node_1|3|node_1|3|node_1|3|node_1}}

t0,1,2,3,5,6{36,4}Hexipentiruncicantitruncated 8-orthoplex
Petiterigreatoprismated diacosipentacontahexazetton		116121602580480
align=center BGCOLOR="#f0e0e0"

!222

|{{CDD|node|4|node_1|3|node_1|3|node_1|3|node|3|node_1|3|node_1|3|node_1}}

t0,1,2,4,5,6{36,4}Hexipentistericantitruncated 8-orthoplex
Petitericelligreatorhombated diacosipentacontahexazetton		116121602580480
align=center BGCOLOR="#f0e0e0"

!223

|{{CDD|node|4|node_1|3|node_1|3|node_1|3|node_1|3|node|3|node_1|3|node_1}}

t0,1,3,4,5,6{36,4}Hexipentisteriruncitruncated 8-orthoplex
Petitericelliprismatotruncated diacosipentacontahexazetton		116121602580480
align=center BGCOLOR="#f0e0e0"

!224

|{{CDD|node|4|node_1|3|node_1|3|node_1|3|node_1|3|node_1|3|node|3|node_1}}

t0,2,3,4,5,6{36,4}Hexipentisteriruncicantellated 8-orthoplex
Petitericelliprismatorhombated diacosipentacontahexazetton		116121602580480
align=center BGCOLOR="#e0f0e0"

!225

|{{CDD|node|4|node_1|3|node_1|3|node_1|3|node_1|3|node_1|3|node_1|3|node}}

t1,2,3,4,5,6{4,36}Bipentisteriruncicantitruncated 8-cube
Great biteri-octeractidiacosipentacontahexazetton		103219202580480
align=center BGCOLOR="#f0e0e0"

!226

|{{CDD|node_1|4|node|3|node|3|node_1|3|node_1|3|node_1|3|node_1|3|node_1}}

t0,1,2,3,4,7{36,4}Heptisteriruncicantitruncated 8-orthoplex
Exigreatocellated diacosipentacontahexazetton		86016001720320
align=center BGCOLOR="#f0e0e0"

!227

|{{CDD|node_1|4|node|3|node_1|3|node|3|node_1|3|node_1|3|node_1|3|node_1}}

t0,1,2,3,5,7{36,4}Heptipentiruncicantitruncated 8-orthoplex
Exiterigreatoprismated diacosipentacontahexazetton		141926402580480
align=center BGCOLOR="#f0e0e0"

!228

|{{CDD|node_1|4|node|3|node_1|3|node_1|3|node|3|node_1|3|node_1|3|node_1}}

t0,1,2,4,5,7{36,4}Heptipentistericantitruncated 8-orthoplex
Exitericelligreatorhombated diacosipentacontahexazetton		129024002580480
align=center BGCOLOR="#f0e0e0"

!229

|{{CDD|node_1|4|node|3|node_1|3|node_1|3|node_1|3|node|3|node_1|3|node_1}}

t0,1,3,4,5,7{36,4}Heptipentisteriruncitruncated 8-orthoplex
Exitericelliprismatotruncated diacosipentacontahexazetton		129024002580480
align=center BGCOLOR="#e0f0e0"

!230

|{{CDD|node_1|4|node|3|node_1|3|node_1|3|node_1|3|node_1|3|node|3|node_1}}

t0,2,3,4,5,7{4,36}Heptipentisteriruncicantellated 8-cube
Exitericelliprismatorhombi-octeractidiacosipentacontahexazetton		129024002580480
align=center BGCOLOR="#e0e0f0"

!231

|{{CDD|node_1|4|node|3|node_1|3|node_1|3|node_1|3|node_1|3|node_1|3|node}}

t0,2,3,4,5,6{4,36}Hexipentisteriruncicantellated 8-cube
Petitericelliprismatorhombated octeract		116121602580480
align=center BGCOLOR="#f0e0e0"

!232

|{{CDD|node_1|4|node_1|3|node|3|node|3|node_1|3|node_1|3|node_1|3|node_1}}

t0,1,2,3,6,7{36,4}Heptihexiruncicantitruncated 8-orthoplex
Exipetigreatoprismated diacosipentacontahexazetton		86016001720320
align=center BGCOLOR="#f0e0e0"

!233

|{{CDD|node_1|4|node_1|3|node|3|node_1|3|node|3|node_1|3|node_1|3|node_1}}

t0,1,2,4,6,7{36,4}Heptihexistericantitruncated 8-orthoplex
Exipeticelligreatorhombated diacosipentacontahexazetton		141926402580480
align=center BGCOLOR="#e0f0e0"

!234

|{{CDD|node_1|4|node_1|3|node|3|node_1|3|node_1|3|node|3|node_1|3|node_1}}

t0,1,3,4,6,7{4,36}Heptihexisteriruncitruncated 8-cube
Exipeticelliprismatotrunki-octeractidiacosipentacontahexazetton		129024002580480
align=center BGCOLOR="#e0e0f0"

!235

|{{CDD|node_1|4|node_1|3|node|3|node_1|3|node_1|3|node_1|3|node|3|node_1}}

t0,1,3,4,5,7{4,36}Heptipentisteriruncitruncated 8-cube
Exitericelliprismatotruncated octeract		129024002580480
align=center BGCOLOR="#e0e0f0"

!236

|{{CDD|node_1|4|node_1|3|node|3|node_1|3|node_1|3|node_1|3|node_1|3|node}}

t0,1,3,4,5,6{4,36}Hexipentisteriruncitruncated 8-cube
Petitericelliprismatotruncated octeract		116121602580480
align=center BGCOLOR="#e0f0e0"

!237

|{{CDD|node_1|4|node_1|3|node_1|3|node|3|node|3|node_1|3|node_1|3|node_1}}

t0,1,2,5,6,7{4,36}Heptihexipenticantitruncated 8-cube
Exipetiterigreatorhombi-octeractidiacosipentacontahexazetton		86016001720320
align=center BGCOLOR="#e0e0f0"

!238

|{{CDD|node_1|4|node_1|3|node_1|3|node|3|node_1|3|node|3|node_1|3|node_1}}

t0,1,2,4,6,7{4,36}Heptihexistericantitruncated 8-cube
Exipeticelligreatorhombated octeract		141926402580480
align=center BGCOLOR="#e0e0f0"

!239

|{{CDD|node_1|4|node_1|3|node_1|3|node|3|node_1|3|node_1|3|node|3|node_1}}

t0,1,2,4,5,7{4,36}Heptipentistericantitruncated 8-cube
Exitericelligreatorhombated octeract		129024002580480
align=center BGCOLOR="#e0e0f0"

!240

|{{CDD|node_1|4|node_1|3|node_1|3|node|3|node_1|3|node_1|3|node_1|3|node}}

t0,1,2,4,5,6{4,36}Hexipentistericantitruncated 8-cube
Petitericelligreatorhombated octeract		116121602580480
align=center BGCOLOR="#e0e0f0"

!241

|{{CDD|node_1|4|node_1|3|node_1|3|node_1|3|node|3|node|3|node_1|3|node_1}}

t0,1,2,3,6,7{4,36}Heptihexiruncicantitruncated 8-cube
Exipetigreatoprismated octeract		86016001720320
align=center BGCOLOR="#e0e0f0"

!242

|{{CDD|node_1|4|node_1|3|node_1|3|node_1|3|node|3|node_1|3|node|3|node_1}}

t0,1,2,3,5,7{4,36}Heptipentiruncicantitruncated 8-cube
Exiterigreatoprismated octeract		141926402580480
align=center BGCOLOR="#e0e0f0"

!243

|{{CDD|node_1|4|node_1|3|node_1|3|node_1|3|node|3|node_1|3|node_1|3|node}}

t0,1,2,3,5,6{4,36}Hexipentiruncicantitruncated 8-cube
Petiterigreatoprismated octeract		116121602580480
align=center BGCOLOR="#e0e0f0"

!244

|{{CDD|node_1|4|node_1|3|node_1|3|node_1|3|node_1|3|node|3|node|3|node_1}}

t0,1,2,3,4,7{4,36}Heptisteriruncicantitruncated 8-cube
Exigreatocellated octeract		86016001720320
align=center BGCOLOR="#e0e0f0"

!245

|{{CDD|node_1|4|node_1|3|node_1|3|node_1|3|node_1|3|node|3|node_1|3|node}}

t0,1,2,3,4,6{4,36}Hexisteriruncicantitruncated 8-cube
Petigreatocellated octeract		129024002580480
align=center BGCOLOR="#e0e0f0"

!246

|{{CDD|node_1|4|node_1|3|node_1|3|node_1|3|node_1|3|node_1|3|node|3|node}}

t0,1,2,3,4,5{4,36}Pentisteriruncicantitruncated 8-cube
Great terated octeract		68812801720320
align=center BGCOLOR="#f0e0e0"

!247

|{{CDD|node|4|node_1|3|node_1|3|node_1|3|node_1|3|node_1|3|node_1|3|node_1}}

t0,1,2,3,4,5,6{36,4}Hexipentisteriruncicantitruncated 8-orthoplex
Great petated diacosipentacontahexazetton		206438405160960
align=center BGCOLOR="#f0e0e0"

!248

|{{CDD|node_1|4|node|3|node_1|3|node_1|3|node_1|3|node_1|3|node_1|3|node_1}}

t0,1,2,3,4,5,7{36,4}Heptipentisteriruncicantitruncated 8-orthoplex
Exigreatoterated diacosipentacontahexazetton		232243205160960
align=center BGCOLOR="#f0e0e0"

!249

|{{CDD|node_1|4|node_1|3|node|3|node_1|3|node_1|3|node_1|3|node_1|3|node_1}}

t0,1,2,3,4,6,7{36,4}Heptihexisteriruncicantitruncated 8-orthoplex
Exipetigreatocellated diacosipentacontahexazetton		232243205160960
align=center BGCOLOR="#f0e0e0"

!250

|{{CDD|node_1|4|node_1|3|node_1|3|node|3|node_1|3|node_1|3|node_1|3|node_1}}

t0,1,2,3,5,6,7{36,4}Heptihexipentiruncicantitruncated 8-orthoplex
Exipetiterigreatoprismated diacosipentacontahexazetton		232243205160960
align=center BGCOLOR="#e0e0f0"

!251

|{{CDD|node_1|4|node_1|3|node_1|3|node_1|3|node|3|node_1|3|node_1|3|node_1}}

t0,1,2,3,5,6,7{4,36}Heptihexipentiruncicantitruncated 8-cube
Exipetiterigreatoprismated octeract		232243205160960
align=center BGCOLOR="#e0e0f0"

!252

|{{CDD|node_1|4|node_1|3|node_1|3|node_1|3|node_1|3|node|3|node_1|3|node_1}}

t0,1,2,3,4,6,7{4,36}Heptihexisteriruncicantitruncated 8-cube
Exipetigreatocellated octeract		232243205160960
align=center BGCOLOR="#e0e0f0"

!253

|{{CDD|node_1|4|node_1|3|node_1|3|node_1|3|node_1|3|node_1|3|node|3|node_1}}

t0,1,2,3,4,5,7{4,36}Heptipentisteriruncicantitruncated 8-cube
Exigreatoterated octeract		232243205160960
align=center BGCOLOR="#e0e0f0"

!254

|{{CDD|node_1|4|node_1|3|node_1|3|node_1|3|node_1|3|node_1|3|node_1|3|node}}

t0,1,2,3,4,5,6{4,36}Hexipentisteriruncicantitruncated 8-cube
Great petated octeract		206438405160960
align=center BGCOLOR="#e0f0e0"

!255

|{{CDD|node_1|4|node_1|3|node_1|3|node_1|3|node_1|3|node_1|3|node_1|3|node_1}}

t0,1,2,3,4,5,6,7{4,36}Omnitruncated 8-cube
Great exi-octeractidiacosipentacontahexazetton		4128768010321920

= The D<sub>8</sub> family =

The D8 family has symmetry of order 5,160,960 (8 factorial x 27).

This family has 191 Wythoffian uniform polytopes, from 3x64-1 permutations of the D8 Coxeter-Dynkin diagram with one or more rings. 127 (2x64-1) are repeated from the B8 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 collapsible collapsed"

!colspan=15|D8 uniform polytopes

rowspan=2|#

!rowspan=2|Coxeter-Dynkin diagram

!rowspan=2|Name

!rowspan=2|Base point
(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}}
= {{CDD|node_h1|4|node|3|node|3|node|3|node|3|node|3|node|3|node}}		8-demicube
h{4,3,3,3,3,3,3}		(1,1,1,1,1,1,1,1)14411364032828810752716817921281.0000000
align=center

!2

{{CDD|nodes_10ru|split2|node_1|3|node|3|node|3|node|3|node|3|node}}
= {{CDD|node_h1|4|node|3|node_1|3|node|3|node|3|node|3|node|3|node}}		cantic 8-cube
h2{4,3,3,3,3,3,3}		(1,1,3,3,3,3,3,3)2329635842.6457512
align=center

!3

{{CDD|nodes_10ru|split2|node|3|node_1|3|node|3|node|3|node|3|node}}
= {{CDD|node_h1|4|node|3|node|3|node_1|3|node|3|node|3|node|3|node}}		runcic 8-cube
h3{4,3,3,3,3,3,3}		(1,1,1,3,3,3,3,3)6451271682.4494896
align=center

!4

{{CDD|nodes_10ru|split2|node|3|node|3|node_1|3|node|3|node|3|node}}
= {{CDD|node_h1|4|node|3|node|3|node|3|node_1|3|node|3|node|3|node}}		steric 8-cube
h4{4,3,3,3,3,3,3}		(1,1,1,1,3,3,3,3)9856089602.2360678
align=center

!5

{{CDD|nodes_10ru|split2|node|3|node|3|node|3|node_1|3|node|3|node}}
= {{CDD|node_h1|4|node|3|node|3|node|3|node|3|node_1|3|node|3|node}}		pentic 8-cube
h5{4,3,3,3,3,3,3}		(1,1,1,1,1,3,3,3)8960071681.9999999
align=center

!6

{{CDD|nodes_10ru|split2|node|3|node|3|node|3|node|3|node_1|3|node}}
= {{CDD|node_h1|4|node|3|node|3|node|3|node|3|node|3|node_1|3|node}}		hexic 8-cube
h6{4,3,3,3,3,3,3}		(1,1,1,1,1,1,3,3)4838435841.7320508
align=center

!7

{{CDD|nodes_10ru|split2|node|3|node|3|node|3|node|3|node|3|node_1}}
= {{CDD|node_h1|4|node|3|node|3|node|3|node|3|node|3|node|3|node_1}}		heptic 8-cube
h7{4,3,3,3,3,3,3}		(1,1,1,1,1,1,1,3)1433610241.4142135
align=center

!8

{{CDD|nodes_10ru|split2|node_1|3|node_1|3|node|3|node|3|node|3|node}}
= {{CDD|node_h1|4|node|3|node_1|3|node_1|3|node|3|node|3|node|3|node}}		runcicantic 8-cube
h2,3{4,3,3,3,3,3,3}		(1,1,3,5,5,5,5,5)86016215044.1231055
align=center

!9

{{CDD|nodes_10ru|split2|node_1|3|node|3|node_1|3|node|3|node|3|node}}
= {{CDD|node_h1|4|node|3|node_1|3|node|3|node_1|3|node|3|node|3|node}}		stericantic 8-cube
h2,4{4,3,3,3,3,3,3}		(1,1,3,3,5,5,5,5)349440537603.8729835
align=center

!10

{{CDD|nodes_10ru|split2|node|3|node_1|3|node_1|3|node|3|node|3|node}}
= {{CDD|node_h1|4|node|3|node|3|node_1|3|node_1|3|node|3|node|3|node}}		steriruncic 8-cube
h3,4{4,3,3,3,3,3,3}		(1,1,1,3,5,5,5,5)179200358403.7416575
align=center

!11

{{CDD|nodes_10ru|split2|node_1|3|node|3|node|3|node_1|3|node|3|node}}
= {{CDD|node_h1|4|node|3|node_1|3|node|3|node|3|node_1|3|node|3|node}}		penticantic 8-cube
h2,5{4,3,3,3,3,3,3}		(1,1,3,3,3,5,5,5)573440716803.6055512
align=center

!12

{{CDD|nodes_10ru|split2|node|3|node_1|3|node|3|node_1|3|node|3|node}}
= {{CDD|node_h1|4|node|3|node|3|node_1|3|node|3|node_1|3|node|3|node}}		pentiruncic 8-cube
h3,5{4,3,3,3,3,3,3}		(1,1,1,3,3,5,5,5)537600716803.4641016
align=center

!13

{{CDD|nodes_10ru|split2|node|3|node|3|node_1|3|node_1|3|node|3|node}}
= {{CDD|node_h1|4|node|3|node|3|node|3|node_1|3|node_1|3|node|3|node}}		pentisteric 8-cube
h4,5{4,3,3,3,3,3,3}		(1,1,1,1,3,5,5,5)232960358403.3166249
align=center

!14

{{CDD|nodes_10ru|split2|node_1|3|node|3|node|3|node|3|node_1|3|node}}
= {{CDD|node_h1|4|node|3|node_1|3|node|3|node|3|node|3|node_1|3|node}}		hexicantic 8-cube
h2,6{4,3,3,3,3,3,3}		(1,1,3,3,3,3,5,5)456960537603.3166249
align=center

!15

{{CDD|nodes_10ru|split2|node|3|node_1|3|node|3|node|3|node_1|3|node}}
= {{CDD|node_h1|4|node|3|node|3|node_1|3|node|3|node|3|node_1|3|node}}		hexicruncic 8-cube
h3,6{4,3,3,3,3,3,3}		(1,1,1,3,3,3,5,5)645120716803.1622777
align=center

!16

{{CDD|nodes_10ru|split2|node|3|node|3|node_1|3|node|3|node_1|3|node}}
= {{CDD|node_h1|4|node|3|node|3|node|3|node_1|3|node|3|node_1|3|node}}		hexisteric 8-cube
h4,6{4,3,3,3,3,3,3}		(1,1,1,1,3,3,5,5)483840537603
align=center

!17

{{CDD|nodes_10ru|split2|node|3|node|3|node|3|node_1|3|node_1|3|node}}
= {{CDD|node_h1|4|node|3|node|3|node|3|node|3|node_1|3|node_1|3|node}}		hexipentic 8-cube
h5,6{4,3,3,3,3,3,3}		(1,1,1,1,1,3,5,5)182784215042.8284271
align=center

!18

{{CDD|nodes_10ru|split2|node_1|3|node|3|node|3|node|3|node|3|node_1}}
= {{CDD|node_h1|4|node|3|node_1|3|node|3|node|3|node|3|node|3|node_1}}		hepticantic 8-cube
h2,7{4,3,3,3,3,3,3}		(1,1,3,3,3,3,3,5)172032215043
align=center

!19

{{CDD|nodes_10ru|split2|node|3|node_1|3|node|3|node|3|node|3|node_1}}
= {{CDD|node_h1|4|node|3|node|3|node_1|3|node|3|node|3|node|3|node_1}}		heptiruncic 8-cube
h3,7{4,3,3,3,3,3,3}		(1,1,1,3,3,3,3,5)340480358402.8284271
align=center

!20

{{CDD|nodes_10ru|split2|node|3|node|3|node_1|3|node|3|node|3|node_1}}
= {{CDD|node_h1|4|node|3|node|3|node|3|node_1|3|node|3|node|3|node_1}}		heptsteric 8-cube
h4,7{4,3,3,3,3,3,3}		(1,1,1,1,3,3,3,5)376320358402.6457512
align=center

!21

{{CDD|nodes_10ru|split2|node|3|node|3|node|3|node_1|3|node|3|node_1}}
= {{CDD|node_h1|4|node|3|node|3|node|3|node|3|node_1|3|node|3|node_1}}		heptipentic 8-cube
h5,7{4,3,3,3,3,3,3}		(1,1,1,1,1,3,3,5)236544215042.4494898
align=center

!22

{{CDD|nodes_10ru|split2|node|3|node|3|node|3|node|3|node_1|3|node_1}}
= {{CDD|node_h1|4|node|3|node|3|node|3|node|3|node|3|node_1|3|node_1}}		heptihexic 8-cube
h6,7{4,3,3,3,3,3,3}		(1,1,1,1,1,1,3,5)7884871682.236068
align=center

!23

{{CDD|nodes_10ru|split2|node_1|3|node_1|3|node_1|3|node|3|node|3|node}}
= {{CDD|node_h1|4|node|3|node_1|3|node_1|3|node_1|3|node|3|node|3|node}}		steriruncicantic 8-cube
h2,3,4{4,36}		(1,1,3,5,7,7,7,7)4300801075205.3851647
align=center

!24

{{CDD|nodes_10ru|split2|node_1|3|node_1|3|node|3|node_1|3|node|3|node}}
= {{CDD|node_h1|4|node|3|node_1|3|node_1|3|node|3|node_1|3|node|3|node}}		pentiruncicantic 8-cube
h2,3,5{4,36}		(1,1,3,5,5,7,7,7)11827202150405.0990195
align=center

!25

{{CDD|nodes_10ru|split2|node_1|3|node|3|node_1|3|node_1|3|node|3|node}}
= {{CDD|node_h1|4|node|3|node_1|3|node|3|node_1|3|node_1|3|node|3|node}}		pentistericantic 8-cube
h2,4,5{4,36}		(1,1,3,3,5,7,7,7)10752002150404.8989797
align=center

!26

{{CDD|nodes_10ru|split2|node|3|node_1|3|node_1|3|node_1|3|node|3|node}}
= {{CDD|node_h1|4|node|3|node|3|node_1|3|node_1|3|node_1|3|node|3|node}}		pentisterirunic 8-cube
h3,4,5{4,36}		(1,1,1,3,5,7,7,7)7168001433604.7958317
align=center

!27

{{CDD|nodes_10ru|split2|node_1|3|node_1|3|node|3|node|3|node_1|3|node}}
= {{CDD|node_h1|4|node|3|node_1|3|node_1|3|node|3|node|3|node_1|3|node}}		hexiruncicantic 8-cube
h2,3,6{4,36}		(1,1,3,5,5,5,7,7)12902402150404.7958317
align=center

!28

{{CDD|nodes_10ru|split2|node_1|3|node|3|node_1|3|node|3|node_1|3|node}}
= {{CDD|node_h1|4|node|3|node_1|3|node|3|node_1|3|node|3|node_1|3|node}}		hexistericantic 8-cube
h2,4,6{4,36}		(1,1,3,3,5,5,7,7)20966403225604.5825758
align=center

!29

{{CDD|nodes_10ru|split2|node|3|node_1|3|node_1|3|node|3|node_1|3|node}}
= {{CDD|node_h1|4|node|3|node|3|node_1|3|node_1|3|node|3|node_1|3|node}}		hexisterirunic 8-cube
h3,4,6{4,36}		(1,1,1,3,5,5,7,7)12902402150404.472136
align=center

!30

{{CDD|nodes_10ru|split2|node_1|3|node|3|node|3|node_1|3|node_1|3|node}}
= {{CDD|node_h1|4|node|3|node_1|3|node|3|node|3|node_1|3|node_1|3|node}}		hexipenticantic 8-cube
h2,5,6{4,36}		(1,1,3,3,3,5,7,7)12902402150404.3588991
align=center

!31

{{CDD|nodes_10ru|split2|node|3|node_1|3|node|3|node_1|3|node_1|3|node}}
= {{CDD|node_h1|4|node|3|node|3|node_1|3|node|3|node_1|3|node_1|3|node}}		hexipentirunic 8-cube
h3,5,6{4,36}		(1,1,1,3,3,5,7,7)13977602150404.2426405
align=center

!32

{{CDD|nodes_10ru|split2|node|3|node|3|node_1|3|node_1|3|node_1|3|node}}
= {{CDD|node_h1|4|node|3|node|3|node|3|node_1|3|node_1|3|node_1|3|node}}		hexipentisteric 8-cube
h4,5,6{4,36}		(1,1,1,1,3,5,7,7)6988801075204.1231055
align=center

!33

{{CDD|nodes_10ru|split2|node_1|3|node_1|3|node|3|node|3|node|3|node_1}}
= {{CDD|node_h1|4|node|3|node_1|3|node_1|3|node|3|node|3|node|3|node_1}}		heptiruncicantic 8-cube
h2,3,7{4,36}		(1,1,3,5,5,5,5,7)5913601075204.472136
align=center

!34

{{CDD|nodes_10ru|split2|node_1|3|node|3|node_1|3|node|3|node|3|node_1}}
= {{CDD|node_h1|4|node|3|node_1|3|node|3|node_1|3|node|3|node|3|node_1}}		heptistericantic 8-cube
h2,4,7{4,36}		(1,1,3,3,5,5,5,7)15052802150404.2426405
align=center

!35

{{CDD|nodes_10ru|split2|node|3|node_1|3|node_1|3|node|3|node|3|node_1}}
= {{CDD|node_h1|4|node|3|node|3|node_1|3|node_1|3|node|3|node|3|node_1}}		heptisterruncic 8-cube
h3,4,7{4,36}		(1,1,1,3,5,5,5,7)8601601433604.1231055
align=center

!36

{{CDD|nodes_10ru|split2|node_1|3|node|3|node|3|node_1|3|node|3|node_1}}
= {{CDD|node_h1|4|node|3|node_1|3|node|3|node|3|node_1|3|node|3|node_1}}		heptipenticantic 8-cube
h2,5,7{4,36}		(1,1,3,3,3,5,5,7)16128002150404
align=center

!37

{{CDD|nodes_10ru|split2|node|3|node_1|3|node|3|node_1|3|node|3|node_1}}
= {{CDD|node_h1|4|node|3|node|3|node_1|3|node|3|node_1|3|node|3|node_1}}		heptipentiruncic 8-cube
h3,5,7{4,36}		(1,1,1,3,3,5,5,7)16128002150403.8729835
align=center

!38

{{CDD|nodes_10ru|split2|node|3|node|3|node_1|3|node_1|3|node|3|node_1}}
= {{CDD|node_h1|4|node|3|node|3|node|3|node_1|3|node_1|3|node|3|node_1}}		heptipentisteric 8-cube
h4,5,7{4,36}		(1,1,1,1,3,5,5,7)7526401075203.7416575
align=center

!39

{{CDD|nodes_10ru|split2|node_1|3|node|3|node|3|node|3|node_1|3|node_1}}
= {{CDD|node_h1|4|node|3|node_1|3|node|3|node|3|node|3|node_1|3|node_1}}		heptihexicantic 8-cube
h2,6,7{4,36}		(1,1,3,3,3,3,5,7)7526401075203.7416575
align=center

!40

{{CDD|nodes_10ru|split2|node|3|node_1|3|node|3|node|3|node_1|3|node_1}}
= {{CDD|node_h1|4|node|3|node|3|node_1|3|node|3|node|3|node_1|3|node_1}}		heptihexiruncic 8-cube
h3,6,7{4,36}		(1,1,1,3,3,3,5,7)11468801433603.6055512
align=center

!41

{{CDD|nodes_10ru|split2|node|3|node|3|node_1|3|node|3|node_1|3|node_1}}
= {{CDD|node_h1|4|node|3|node|3|node|3|node_1|3|node|3|node_1|3|node_1}}		heptihexisteric 8-cube
h4,6,7{4,36}		(1,1,1,1,3,3,5,7)9139201075203.4641016
align=center

!42

{{CDD|nodes_10ru|split2|node|3|node|3|node|3|node_1|3|node_1|3|node_1}}
= {{CDD|node_h1|4|node|3|node|3|node|3|node|3|node_1|3|node_1|3|node_1}}		heptihexipentic 8-cube
h5,6,7{4,36}		(1,1,1,1,1,3,5,7)365568430083.3166249
align=center

!43

{{CDD|nodes_10ru|split2|node_1|3|node_1|3|node_1|3|node_1|3|node|3|node}}
= {{CDD|node_h1|4|node|3|node_1|3|node_1|3|node_1|3|node_1|3|node|3|node}}		pentisteriruncicantic 8-cube
h2,3,4,5{4,36}		(1,1,3,5,7,9,9,9)17203204300806.4031243
align=center

!44

{{CDD|nodes_10ru|split2|node_1|3|node_1|3|node_1|3|node|3|node_1|3|node}}
= {{CDD|node_h1|4|node|3|node_1|3|node_1|3|node_1|3|node|3|node_1|3|node}}		hexisteriruncicantic 8-cube
h2,3,4,6{4,36}		(1,1,3,5,7,7,9,9)32256006451206.0827627
align=center

!45

{{CDD|nodes_10ru|split2|node_1|3|node_1|3|node|3|node_1|3|node_1|3|node}}
= {{CDD|node_h1|4|node|3|node_1|3|node_1|3|node|3|node_1|3|node_1|3|node}}		hexipentiruncicantic 8-cube
h2,3,5,6{4,36}		(1,1,3,5,5,7,9,9)29030406451205.8309517
align=center

!46

{{CDD|nodes_10ru|split2|node_1|3|node|3|node_1|3|node_1|3|node_1|3|node}}
= {{CDD|node_h1|4|node|3|node_1|3|node|3|node_1|3|node_1|3|node_1|3|node}}		hexipentistericantic 8-cube
h2,4,5,6{4,36}		(1,1,3,3,5,7,9,9)32256006451205.6568542
align=center

!47

{{CDD|nodes_10ru|split2|node|3|node_1|3|node_1|3|node_1|3|node_1|3|node}}
= {{CDD|node_h1|4|node|3|node|3|node_1|3|node_1|3|node_1|3|node_1|3|node}}		hexipentisteriruncic 8-cube
h3,4,5,6{4,36}		(1,1,1,3,5,7,9,9)21504004300805.5677648
align=center

!48

{{CDD|nodes_10ru|split2|node_1|3|node_1|3|node_1|3|node|3|node|3|node_1}}
= {{CDD|node_h1|4|node|3|node_1|3|node_1|3|node_1|3|node|3|node|3|node_1}}		heptsteriruncicantic 8-cube
h2,3,4,7{4,36}		(1,1,3,5,7,7,7,9)21504004300805.7445626
align=center

!49

{{CDD|nodes_10ru|split2|node_1|3|node_1|3|node|3|node_1|3|node|3|node_1}}
= {{CDD|node_h1|4|node|3|node_1|3|node_1|3|node|3|node_1|3|node|3|node_1}}		heptipentiruncicantic 8-cube
h2,3,5,7{4,36}		(1,1,3,5,5,7,7,9)35481606451205.4772258
align=center

!50

{{CDD|nodes_10ru|split2|node_1|3|node|3|node_1|3|node_1|3|node|3|node_1}}
= {{CDD|node_h1|4|node|3|node_1|3|node|3|node_1|3|node_1|3|node|3|node_1}}		heptipentistericantic 8-cube
h2,4,5,7{4,36}		(1,1,3,3,5,7,7,9)35481606451205.291503
align=center

!51

{{CDD|nodes_10ru|split2|node|3|node_1|3|node_1|3|node_1|3|node|3|node_1}}
= {{CDD|node_h1|4|node|3|node|3|node_1|3|node_1|3|node_1|3|node|3|node_1}}		heptipentisteriruncic 8-cube
h3,4,5,7{4,36}		(1,1,1,3,5,7,7,9)23654404300805.1961527
align=center

!52

{{CDD|nodes_10ru|split2|node_1|3|node_1|3|node|3|node|3|node_1|3|node_1}}
= {{CDD|node_h1|4|node|3|node_1|3|node_1|3|node|3|node|3|node_1|3|node_1}}		heptihexiruncicantic 8-cube
h2,3,6,7{4,36}		(1,1,3,5,5,5,7,9)21504004300805.1961527
align=center

!53

{{CDD|nodes_10ru|split2|node_1|3|node|3|node_1|3|node|3|node_1|3|node_1}}
= {{CDD|node_h1|4|node|3|node_1|3|node|3|node_1|3|node|3|node_1|3|node_1}}		heptihexistericantic 8-cube
h2,4,6,7{4,36}		(1,1,3,3,5,5,7,9)38707206451205
align=center

!54

{{CDD|nodes_10ru|split2|node|3|node_1|3|node_1|3|node|3|node_1|3|node_1}}
= {{CDD|node_h1|4|node|3|node|3|node_1|3|node_1|3|node|3|node_1|3|node_1}}		heptihexisteriruncic 8-cube
h3,4,6,7{4,36}		(1,1,1,3,5,5,7,9)23654404300804.8989797
align=center

!55

{{CDD|nodes_10ru|split2|node_1|3|node|3|node|3|node_1|3|node_1|3|node_1}}
= {{CDD|node_h1|4|node|3|node_1|3|node|3|node|3|node_1|3|node_1|3|node_1}}		heptihexipenticantic 8-cube
h2,5,6,7{4,36}		(1,1,3,3,3,5,7,9)25804804300804.7958317
align=center

!56

{{CDD|nodes_10ru|split2|node|3|node_1|3|node|3|node_1|3|node_1|3|node_1}}
= {{CDD|node_h1|4|node|3|node|3|node_1|3|node|3|node_1|3|node_1|3|node_1}}		heptihexipentiruncic 8-cube
h3,5,6,7{4,36}		(1,1,1,3,3,5,7,9)27955204300804.6904159
align=center

!57

{{CDD|nodes_10ru|split2|node|3|node|3|node_1|3|node_1|3|node_1|3|node_1}}
= {{CDD|node_h1|4|node|3|node|3|node|3|node_1|3|node_1|3|node_1|3|node_1}}		heptihexipentisteric 8-cube
h4,5,6,7{4,36}		(1,1,1,1,3,5,7,9)13977602150404.5825758
align=center

!58

{{CDD|nodes_10ru|split2|node_1|3|node_1|3|node_1|3|node_1|3|node_1|3|node}}
= {{CDD|node_h1|4|node|3|node_1|3|node_1|3|node_1|3|node_1|3|node_1|3|node}}		hexipentisteriruncicantic 8-cube
h2,3,4,5,6{4,36}		(1,1,3,5,7,9,11,11)516096012902407.1414285
align=center

!59

{{CDD|nodes_10ru|split2|node_1|3|node_1|3|node_1|3|node_1|3|node|3|node_1}}
= {{CDD|node_h1|4|node|3|node_1|3|node_1|3|node_1|3|node_1|3|node|3|node_1}}		heptipentisteriruncicantic 8-cube
h2,3,4,5,7{4,36}		(1,1,3,5,7,9,9,11)580608012902406.78233
align=center

!60

{{CDD|nodes_10ru|split2|node_1|3|node_1|3|node_1|3|node|3|node_1|3|node_1}}
= {{CDD|node_h1|4|node|3|node_1|3|node_1|3|node_1|3|node|3|node_1|3|node_1}}		heptihexisteriruncicantic 8-cube
h2,3,4,6,7{4,36}		(1,1,3,5,7,7,9,11)580608012902406.480741
align=center

!61

{{CDD|nodes_10ru|split2|node_1|3|node_1|3|node|3|node_1|3|node_1|3|node_1}}
= {{CDD|node_h1|4|node|3|node_1|3|node_1|3|node|3|node_1|3|node_1|3|node_1}}		heptihexipentiruncicantic 8-cube
h2,3,5,6,7{4,36}		(1,1,3,5,5,7,9,11)580608012902406.244998
align=center

!62

{{CDD|nodes_10ru|split2|node_1|3|node|3|node_1|3|node_1|3|node_1|3|node_1}}
= {{CDD|node_h1|4|node|3|node_1|3|node|3|node_1|3|node_1|3|node_1|3|node_1}}		heptihexipentistericantic 8-cube
h2,4,5,6,7{4,36}		(1,1,3,3,5,7,9,11)645120012902406.0827627
align=center

!63

{{CDD|nodes_10ru|split2|node|3|node_1|3|node_1|3|node_1|3|node_1|3|node_1}}
= {{CDD|node_h1|4|node|3|node|3|node_1|3|node_1|3|node_1|3|node_1|3|node_1}}		heptihexipentisteriruncic 8-cube
h3,4,5,6,7{4,36}		(1,1,1,3,5,7,9,11)43008008601606.0000000
align=center

!64

{{CDD|nodes_10ru|split2|node_1|3|node_1|3|node_1|3|node_1|3|node_1|3|node_1}}
= {{CDD|node_h1|4|node|3|node_1|3|node_1|3|node_1|3|node_1|3|node_1|3|node_1}}		heptihexipentisteriruncicantic 8-cube
h2,3,4,5,6,7{4,36}		(1,1,3,5,7,9,11,13)2580480103219207.5498347

= The E<sub>8</sub> family =

The E8 family has symmetry order 696,729,600.

There are 255 forms based on all permutations of the Coxeter-Dynkin diagrams 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 collapsible collapsed"

!colspan=15|E8 uniform polytopes

rowspan=2|#

!rowspan=2|Coxeter-Dynkin diagram

!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}}421 (fy)

|19440

207360483840483840241920604806720240
align=center

|2

{{CDD|nodea_1|3a|nodea_1|3a|nodea|3a|nodea|3a|branch|3a|nodea|3a|nodea}}Truncated 421 (tiffy)

|

18816013440
align=center

|3

{{CDD|nodea|3a|nodea_1|3a|nodea|3a|nodea|3a|branch|3a|nodea|3a|nodea}}Rectified 421 (riffy)

|19680

37584019353603386880266112010281601814406720
align=center

|4

{{CDD|nodea|3a|nodea|3a|nodea_1|3a|nodea|3a|branch|3a|nodea|3a|nodea}}Birectified 421 (borfy)

|19680

3825602600640774144099187205806080145152060480
align=center

|5

{{CDD|nodea|3a|nodea|3a|nodea|3a|nodea_1|3a|branch|3a|nodea|3a|nodea}}Trirectified 421 (torfy)

|19680

3825602661120931392016934400145152004838400241920
align=center

|6

{{CDD|nodea|3a|nodea|3a|nodea|3a|nodea|3a|branch_10|3a|nodea|3a|nodea}}Rectified 142 (buffy)

|19680

3825602661120907200016934400169344007257600483840
align=center

|7

{{CDD|nodea|3a|nodea|3a|nodea|3a|nodea|3a|branch|3a|nodea_1|3a|nodea}}Rectified 241 (robay)

|19680

3134401693440471744072576005322240145152069120
align=center

|8

{{CDD|nodea|3a|nodea|3a|nodea|3a|nodea|3a|branch|3a|nodea|3a|nodea_1}}241 (bay)

|17520

14496054432012096001209600483840691202160
align=center

|9

{{CDD|nodea|3a|nodea|3a|nodea|3a|nodea|3a|branch|3a|nodea_1|3a|nodea_1}}Truncated 241

|

138240
align=center

|10

{{CDD|nodea|3a|nodea|3a|nodea|3a|nodea|3a|branch_01lr|3a|nodea|3a|nodea}}142 (bif)

|2400

10608072576022982403628800241920048384017280
align=center

|11

{{CDD|nodea|3a|nodea|3a|nodea|3a|nodea|3a|branch_11|3a|nodea|3a|nodea}}Truncated 142

|

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 421

|

696729600

Regular and uniform honeycombs

File:Coxeter diagram affine rank8 correspondence.png

There are five fundamental affine Coxeter groups that generate regular and uniform tessellations in 7-space:

class="wikitable"
#

!colspan=2|Coxeter group

!Coxeter diagram

!Forms

align=center

|1

{\tilde{A}}_7[3[8]]{{CDD|node|split1|nodes|3ab|nodes|3ab|nodes|split2|node}}29
align=center

|2

{\tilde{C}}_7[4,35,4]{{CDD|node|4|node|3|node|3|node|3|node|3|node|3|node|4|node}}135
align=center

|3

{\tilde{B}}_7[4,34,31,1]{{CDD|nodes|split2|node|3|node|3|node|3|node|3|node|4|node}}191 (64 new)
align=center

|4

{\tilde{D}}_7[31,1,33,31,1]{{CDD|nodes|split2|node|3|node|3|node|3|node|split1|nodes}}77 (10 new)
align=center

|5

{\tilde{E}}_7[33,3,1]{{CDD|nodes|3ab|nodes|3ab|nodes|split2|node|3|node}}143

Regular and uniform tessellations include:

  • {\tilde{A}}_7 29 uniquely ringed forms, including:
  • 7-simplex honeycomb: {3[8]} {{CDD|node_1|split1|nodes|3ab|nodes|3ab|nodes|split2|node}}
  • {\tilde{C}}_7 135 uniquely ringed forms, including:
  • Regular 7-cube honeycomb: {4,34,4} = {4,34,31,1}, {{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}}
  • {\tilde{B}}_7 191 uniquely ringed forms, 127 shared with {\tilde{C}}_7, and 64 new, including:
  • 7-demicube honeycomb: h{4,34,4} = {31,1,34,4}, {{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}}
  • {\tilde{D}}_7, [31,1,33,31,1]: 77 unique ring permutations, and 10 are new, the first Coxeter called a quarter 7-cubic honeycomb.
  • {{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}}
  • {\tilde{E}}_7 143 uniquely ringed forms, including:
  • 133 honeycomb: {3,33,3}, {{CDD|nodes|3ab|nodes|3ab|nodes|split2|node|3|node_1}}
  • 331 honeycomb: {3,3,3,33,1}, {{CDD|nodes_10r|3ab|nodes|3ab|nodes|split2|node|3|node}}

= Regular and uniform hyperbolic honeycombs =

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 4 paracompact hyperbolic Coxeter groups of rank 8, each generating uniform honeycombs in 7-space as permutations of rings of the Coxeter diagrams.

class=wikitable

|align=right|{\bar{P}}_7 = [3,3[7]]:
{{CDD|branch|3ab|nodes|3ab|nodes|split2|node|3|node}}

|align=right|{\bar{Q}}_7 = [31,1,32,32,1]:
{{CDD|nodea|3a|branch|3a|nodea|3a|branch|3a|nodea|3a|nodea}}

|align=right|{\bar{S}}_7 = [4,33,32,1]:
{{CDD|nodea|3a|nodea|3a|branch|3a|nodea|3a|nodea|3a|nodea|4a|nodea}}

|align=right|{\bar{T}}_7 = [33,2,2]:
{{CDD|nodes|3ab|nodes|split2|node|3|node|3|node|3|node}}

References

{{reflist}}

  • T. Gosset: On the Regular and Semi-Regular Figures in Space of n Dimensions, Messenger of Mathematics, Macmillan, 1900
  • 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
  • H.S.M. Coxeter:
  • H.S.M. Coxeter, M.S. Longuet-Higgins und J.C.P. Miller: Uniform Polyhedra, Philosophical Transactions of the Royal Society of London, Londne, 1954
  • H.S.M. Coxeter, Regular Polytopes, 3rd Edition, Dover New York, 1973
  • Kaleidoscopes: Selected Writings of H.S.M. Coxeter, edited by F. Arthur Sherk, Peter McMullen, Anthony C. Thompson, Asia Ivic Weiss, Wiley-Interscience Publication, 1995, {{ISBN|978-0-471-01003-6}} [http://www.wiley.com/WileyCDA/WileyTitle/productCd-0471010030.html Wiley::Kaleidoscopes: Selected Writings of H.S.M. Coxeter]
  • (Paper 22) H.S.M. Coxeter, Regular and Semi Regular Polytopes I, [Math. Zeit. 46 (1940) 380–407, MR 2,10]
  • (Paper 23) H.S.M. Coxeter, Regular and Semi-Regular Polytopes II, [Math. Zeit. 188 (1985) 559-591]
  • (Paper 24) H.S.M. Coxeter, Regular and Semi-Regular Polytopes III, [Math. Zeit. 200 (1988) 3-45]
  • N.W. Johnson: The Theory of Uniform Polytopes and Honeycombs, Ph.D. Dissertation, University of Toronto, 1966
  • {{KlitzingPolytopes|polyzetta.htm|8D|uniform polytopes (polyzetta)}}

External links

  • [http://www.steelpillow.com/polyhedra/ditela.html Polytope names]
  • [http://www.polytope.net/hedrondude/topes.htm Polytopes of Various Dimensions]
  • [http://tetraspace.alkaline.org/glossary.htm Multi-dimensional Glossary]

{{Polytopes}}

{{DEFAULTSORT:8-Polytope}}

Category:8-polytopes