Uniform 8-polytope#Regular and uniform honeycombs
{{short description|Polytope contained by 7-polytope facets}}
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|+ Graphs of three regular and related uniform polytopes. |
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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:
- {3,3,3,3,3,3,3} - 8-simplex
- {4,3,3,3,3,3,3} - 8-cube
- {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:
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#
!colspan=3|Coxeter group !Forms | ||||
---|---|---|---|---|
1 | A8 | [37] | {{CDD|node|3|node|3|node|3|node|3|node|3|node|3|node|3|node}} | 135 |
2 | BC8 | [4,36] | {{CDD|node|4|node|3|node|3|node|3|node|3|node|3|node|3|node}} | 255 |
3 | D8 | [35,1,1] | {{CDD|nodes|split2|node|3|node|3|node|3|node|3|node|3|node}} | 191 (64 unique) |
4 | E8 | [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:
- Simplex family: A8 [37] - {{CDD|node|3|node|3|node|3|node|3|node|3|node|3|node|3|node}}
- * 135 uniform 8-polytopes as permutations of rings in the group diagram, including one regular:
- *# {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}}
- Hypercube/orthoplex family: B8 [4,36] - {{CDD|node|4|node|3|node|3|node|3|node|3|node|3|node|3|node}}
- * 255 uniform 8-polytopes as permutations of rings in the group diagram, including two regular ones:
- *# {4,36} - 8-cube or octeract- {{CDD|node_1|4|node|3|node|3|node|3|node|3|node|3|node|3|node}}
- *# {36,4} - 8-orthoplex or octacross - {{CDD|node_1|3|node|3|node|3|node|3|node|3|node|3|node|4|node}}
- Demihypercube D8 family: [35,1,1] - {{CDD|nodea|3a|branch|3a|nodea|3a|nodea|3a|nodea|3a|nodea|3a|nodea}}
- * 191 uniform 8-polytopes as permutations of rings in the group diagram, including:
- *# {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}}.
- *# {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}}
- E-polytope family E8 family: [34,1,1] - {{CDD|nodea|3a|nodea|3a|branch|3a|nodea|3a|nodea|3a|nodea|3a|nodea}}
- * 255 uniform 8-polytopes as permutations of rings in the group diagram, including:
- *# {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}}
- *# {3,34,2} - the uniform 142, {{CDD|nodea|3a|nodea|3a|branch_01lr|3a|nodea|3a|nodea|3a|nodea|3a|nodea}},
- *# {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:
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!colspan=12|Uniform 8-polytope prism families | |||
#
!colspan=2|Coxeter group | |||
---|---|---|---|
colspan=4|7+1 | |||
1 | A7A1 | [3,3,3,3,3,3]×[ ] | {{CDD|node|3|node|3|node|3|node|3|node|3|node|3|node|2|node}} |
2 | B7A1 | [4,3,3,3,3,3]×[ ] | {{CDD|node|4|node|3|node|3|node|3|node|3|node|3|node|2|node}} |
3 | D7A1 | [34,1,1]×[ ] | {{CDD|nodes|split2|node|3|node|3|node|3|node|3|node|2|node}} |
4 | E7A1 | [33,2,1]×[ ] | {{CDD|nodea|3a|nodea|3a|branch|3a|nodea|3a|nodea|3a|nodea|2|nodea}} |
colspan=4|6+2 | |||
1 | A6I2(p) | [3,3,3,3,3]×[p] | {{CDD|node|3|node|3|node|3|node|3|node|3|node|2|node|p|node}} |
2 | B6I2(p) | [4,3,3,3,3]×[p] | {{CDD|node|4|node|3|node|3|node|3|node|3|node|2|node|p|node}} |
3 | D6I2(p) | [33,1,1]×[p] | {{CDD|nodes|split2|node|3|node|3|node|3|node|2|node|p|node}} |
4 | E6I2(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 | |||
1 | A6A1A1 | [3,3,3,3,3]×[ ]x[ ] | {{CDD|node|3|node|3|node|3|node|3|node|3|node|2|node|2|node}} |
2 | B6A1A1 | [4,3,3,3,3]×[ ]x[ ] | {{CDD|node|4|node|3|node|3|node|3|node|3|node|2|node|2|node}} |
3 | D6A1A1 | [33,1,1]×[ ]x[ ] | {{CDD|nodes|split2|node|3|node|3|node|3|node|2|node|2|node}} |
4 | E6A1A1 | [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 | |||
1 | A5A3 | [34]×[3,3] | {{CDD|node|3|node|3|node|3|node|3|node|2|node|3|node|3|node}} |
2 | B5A3 | [4,33]×[3,3] | {{CDD|node|4|node|3|node|3|node|3|node|2|node|3|node|3|node}} |
3 | D5A3 | [32,1,1]×[3,3] | {{CDD|nodes|split2|node|3|node|3|node|2|node|3|node|3|node}} |
4 | A5B3 | [34]×[4,3] | {{CDD|node|3|node|3|node|3|node|3|node|2|node|4|node|3|node}} |
5 | B5B3 | [4,33]×[4,3] | {{CDD|node|4|node|3|node|3|node|3|node|2|node|4|node|3|node}} |
6 | D5B3 | [32,1,1]×[4,3] | {{CDD|nodes|split2|node|3|node|3|node|2|node|4|node|3|node}} |
7 | A5H3 | [34]×[5,3] | {{CDD|node|3|node|3|node|3|node|3|node|2|node|5|node|3|node}} |
8 | B5H3 | [4,33]×[5,3] | {{CDD|node|4|node|3|node|3|node|3|node|2|node|5|node|3|node}} |
9 | D5H3 | [32,1,1]×[5,3] | {{CDD|nodes|split2|node|3|node|3|node|2|node|5|node|3|node}} |
colspan=4|5+2+1 | |||
1 | A5I2(p)A1 | [3,3,3]×[p]×[ ] | {{CDD|node|3|node|3|node|3|node|3|node|2|node|p|node|2|node}} |
2 | B5I2(p)A1 | [4,3,3]×[p]×[ ] | {{CDD|node|4|node|3|node|3|node|3|node|2|node|p|node|2|node}} |
3 | D5I2(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 | |||
1 | A5A1A1A1 | [3,3,3]×[ ]×[ ]×[ ] | {{CDD|node|3|node|3|node|3|node|3|node|2|node|2|node|2|node}} |
2 | B5A1A1A1 | [4,3,3]×[ ]×[ ]×[ ] | {{CDD|node|4|node|3|node|3|node|3|node|2|node|2|node|2|node}} |
3 | D5A1A1A1 | [32,1,1]×[ ]×[ ]×[ ] | {{CDD|nodes|split2|node|3|node|3|node|2|node|2|node|2|node}} |
colspan=4|4+4 | |||
1 | A4A4 | [3,3,3]×[3,3,3] | {{CDD|node|3|node|3|node|3|node|2|node|3|node|3|node|3|node}} |
2 | B4A4 | [4,3,3]×[3,3,3] | {{CDD|node|4|node|3|node|3|node|2|node|3|node|3|node|3|node}} |
3 | D4A4 | [31,1,1]×[3,3,3] | {{CDD|nodes|split2|node|3|node|2|node|3|node|3|node|3|node}} |
4 | F4A4 | [3,4,3]×[3,3,3] | {{CDD|node|3|node|4|node|3|node|2|node|3|node|3|node|3|node}} |
5 | H4A4 | [5,3,3]×[3,3,3] | {{CDD|node|5|node|3|node|3|node|2|node|3|node|3|node|3|node}} |
6 | B4B4 | [4,3,3]×[4,3,3] | {{CDD|node|4|node|3|node|3|node|2|node|4|node|3|node|3|node}} |
7 | D4B4 | [31,1,1]×[4,3,3] | {{CDD|nodes|split2|node|3|node|2|node|4|node|3|node|3|node}} |
8 | F4B4 | [3,4,3]×[4,3,3] | {{CDD|node|3|node|4|node|3|node|2|node|4|node|3|node|3|node}} |
9 | H4B4 | [5,3,3]×[4,3,3] | {{CDD|node|5|node|3|node|3|node|2|node|4|node|3|node|3|node}} |
10 | D4D4 | [31,1,1]×[31,1,1] | {{CDD|nodes|split2|node|3|node|2|nodes|split2|node|3|node}} |
11 | F4D4 | [3,4,3]×[31,1,1] | {{CDD|node|3|node|4|node|3|node|2|nodes|split2|node|3|node}} |
12 | H4D4 | [5,3,3]×[31,1,1] | {{CDD|node|5|node|3|node|3|node|2|nodes|split2|node|3|node}} |
13 | F4×F4 | [3,4,3]×[3,4,3] | {{CDD|node|3|node|4|node|3|node|2|node|3|node|4|node|3|node}} |
14 | H4×F4 | [5,3,3]×[3,4,3] | {{CDD|node|5|node|3|node|3|node|2|node|3|node|4|node|3|node}} |
15 | H4H4 | [5,3,3]×[5,3,3] | {{CDD|node|5|node|3|node|3|node|2|node|5|node|3|node|3|node}} |
colspan=4|4+3+1 | |||
1 | A4A3A1 | [3,3,3]×[3,3]×[ ] | {{CDD|node|3|node|3|node|3|node|2|node|3|node|3|node|2|node}} |
2 | A4B3A1 | [3,3,3]×[4,3]×[ ] | {{CDD|node|3|node|3|node|3|node|2|node|4|node|3|node|2|node}} |
3 | A4H3A1 | [3,3,3]×[5,3]×[ ] | {{CDD|node|3|node|3|node|3|node|2|node|5|node|3|node|2|node}} |
4 | B4A3A1 | [4,3,3]×[3,3]×[ ] | {{CDD|node|4|node|3|node|3|node|2|node|3|node|3|node|2|node}} |
5 | B4B3A1 | [4,3,3]×[4,3]×[ ] | {{CDD|node|4|node|3|node|3|node|2|node|4|node|3|node|2|node}} |
6 | B4H3A1 | [4,3,3]×[5,3]×[ ] | {{CDD|node|4|node|3|node|3|node|2|node|5|node|3|node|2|node}} |
7 | H4A3A1 | [5,3,3]×[3,3]×[ ] | {{CDD|node|5|node|3|node|3|node|2|node|3|node|3|node|2|node}} |
8 | H4B3A1 | [5,3,3]×[4,3]×[ ] | {{CDD|node|5|node|3|node|3|node|2|node|4|node|3|node|2|node}} |
9 | H4H3A1 | [5,3,3]×[5,3]×[ ] | {{CDD|node|5|node|3|node|3|node|2|node|5|node|3|node|2|node}} |
10 | F4A3A1 | [3,4,3]×[3,3]×[ ] | {{CDD|node|3|node|4|node|3|node|2|node|3|node|3|node|2|node}} |
11 | F4B3A1 | [3,4,3]×[4,3]×[ ] | {{CDD|node|3|node|4|node|3|node|2|node|4|node|3|node|2|node}} |
12 | F4H3A1 | [3,4,3]×[5,3]×[ ] | {{CDD|node|3|node|4|node|3|node|2|node|5|node|3|node|2|node}} |
13 | D4A3A1 | [31,1,1]×[3,3]×[ ] | {{CDD|nodes|split2|node|3|node|2|node|3|node|3|node|2|node}} |
14 | D4B3A1 | [31,1,1]×[4,3]×[ ] | {{CDD|nodes|split2|node|3|node|2|node|4|node|3|node|2|node}} |
15 | D4H3A1 | [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 | |||
1 | A3I2(p)I2(q)A1 | [3,3]×[p]×[q]×[ ] | {{CDD|node|3|node|3|node|2|node|p|node|2|node|q|node|2|node}} |
2 | B3I2(p)I2(q)A1 | [4,3]×[p]×[q]×[ ] | {{CDD|node|4|node|3|node|2|node|p|node|2|node|q|node|2|node}} |
3 | H3I2(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 | |||
1 | A3I2(p)A13 | [3,3]×[p]×[ ]x[ ]×[ ] | {{CDD|node|3|node|3|node|2|node|p|node|2|node|2|node|2|node}} |
2 | B3I2(p)A13 | [4,3]×[p]×[ ]x[ ]×[ ] | {{CDD|node|4|node|3|node|2|node|p|node|2|node|2|node|2|node}} |
3 | H3I2(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 | |||
1 | A3A15 | [3,3]×[ ]x[ ]×[ ]x[ ]×[ ] | {{CDD|node|3|node|3|node|2|node|2|node|2|node|2|node|2|node}} |
2 | B3A15 | [4,3]×[ ]x[ ]×[ ]x[ ]×[ ] | {{CDD|node|4|node|3|node|2|node|2|node|2|node|2|node|2|node}} |
3 | H3A15 | [5,3]×[ ]x[ ]×[ ]x[ ]×[ ] | {{CDD|node|5|node|3|node|2|node|2|node|2|node|2|node|2|node}} |
colspan=4|2+2+2+2 | |||
1 | I2(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 | |||
1 | I2(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 | |||
2 | I2(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 | |||
1 | I2(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 | |||
1 | A18 | [ ]×[ ]×[ ]×[ ]×[ ]×[ ]×[ ]×[ ] | {{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 !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) | 9 | 36 | 84 | 126 | 126 | 84 | 36 | 9 |
align=center
!2 | {{CDD|node|3|node|3|node|3|node|3|node|3|node|3|node_1|3|node}} |t1 |Rectified 8-simplex (rene) |(0,0,0,0,0,0,0,1,1) | 18 | 108 | 336 | 630 | 576 | 588 | 252 | 36 |
align=center
!3 | {{CDD|node|3|node|3|node|3|node|3|node|3|node_1|3|node|3|node}} |t2 |Birectified 8-simplex (bene) |(0,0,0,0,0,0,1,1,1) | 18 | 144 | 588 | 1386 | 2016 | 1764 | 756 | 84 |
align=center
!4 | {{CDD|node|3|node|3|node|3|node|3|node_1|3|node|3|node|3|node}} |t3 |Trirectified 8-simplex (trene) |(0,0,0,0,0,1,1,1,1) | 1260 | 126 | ||||||
align=center
!5 | {{CDD|node|3|node|3|node|3|node|3|node|3|node|3|node_1|3|node_1}} |t0,1 |Truncated 8-simplex (tene) |(0,0,0,0,0,0,0,1,2) | 288 | 72 | ||||||
align=center
!6 | {{CDD|node|3|node|3|node|3|node|3|node|3|node_1|3|node|3|node_1}} |t0,2 |(0,0,0,0,0,0,1,1,2) | 1764 | 252 | ||||||
align=center
!7 | {{CDD|node|3|node|3|node|3|node|3|node|3|node_1|3|node_1|3|node}} |t1,2 |(0,0,0,0,0,0,1,2,2) | 1008 | 252 | ||||||
align=center
!8 | {{CDD|node|3|node|3|node|3|node|3|node_1|3|node|3|node|3|node_1}} |t0,3 |(0,0,0,0,0,1,1,1,2) | 4536 | 504 | ||||||
align=center
!9 | {{CDD|node|3|node|3|node|3|node|3|node_1|3|node|3|node_1|3|node}} |t1,3 |(0,0,0,0,0,1,1,2,2) | 5292 | 756 | ||||||
align=center
!10 | {{CDD|node|3|node|3|node|3|node|3|node_1|3|node_1|3|node|3|node}} |t2,3 |(0,0,0,0,0,1,2,2,2) | 2016 | 504 | ||||||
align=center
!11 | {{CDD|node|3|node|3|node|3|node_1|3|node|3|node|3|node|3|node_1}} |t0,4 |(0,0,0,0,1,1,1,1,2) | 6300 | 630 | ||||||
align=center
!12 | {{CDD|node|3|node|3|node|3|node_1|3|node|3|node|3|node_1|3|node}} |t1,4 |(0,0,0,0,1,1,1,2,2) | 11340 | 1260 | ||||||
align=center
!13 | {{CDD|node|3|node|3|node|3|node_1|3|node|3|node_1|3|node|3|node}} |t2,4 |(0,0,0,0,1,1,2,2,2) | 8820 | 1260 | ||||||
align=center BGCOLOR="#e0f0e0"
!14 | {{CDD|node|3|node|3|node|3|node_1|3|node_1|3|node|3|node|3|node}} |t3,4 |(0,0,0,0,1,2,2,2,2) | 2520 | 630 | ||||||
align=center
!15 | {{CDD|node|3|node|3|node_1|3|node|3|node|3|node|3|node|3|node_1}} |t0,5 |(0,0,0,1,1,1,1,1,2) | 5040 | 504 | ||||||
align=center
!16 | {{CDD|node|3|node|3|node_1|3|node|3|node|3|node|3|node_1|3|node}} |t1,5 |(0,0,0,1,1,1,1,2,2) | 12600 | 1260 | ||||||
align=center BGCOLOR="#e0f0e0"
!17 | {{CDD|node|3|node|3|node_1|3|node|3|node|3|node_1|3|node|3|node}} |t2,5 |(0,0,0,1,1,1,2,2,2) | 15120 | 1680 | ||||||
align=center
!18 | {{CDD|node|3|node_1|3|node|3|node|3|node|3|node|3|node|3|node_1}} |t0,6 |(0,0,1,1,1,1,1,1,2) | 2268 | 252 | ||||||
align=center BGCOLOR="#e0f0e0"
!19 | {{CDD|node|3|node_1|3|node|3|node|3|node|3|node|3|node_1|3|node}} |t1,6 |(0,0,1,1,1,1,1,2,2) | 7560 | 756 | ||||||
align=center BGCOLOR="#e0f0e0"
!20 | {{CDD|node_1|3|node|3|node|3|node|3|node|3|node|3|node|3|node_1}} |t0,7 |(0,1,1,1,1,1,1,1,2) | 504 | 72 | ||||||
align=center
!21 | {{CDD|node|3|node|3|node|3|node|3|node|3|node_1|3|node_1|3|node_1}} |t0,1,2 |(0,0,0,0,0,0,1,2,3) | 2016 | 504 | ||||||
align=center
!22 | {{CDD|node|3|node|3|node|3|node|3|node_1|3|node|3|node_1|3|node_1}} |t0,1,3 |(0,0,0,0,0,1,1,2,3) | 9828 | 1512 | ||||||
align=center
!23 | {{CDD|node|3|node|3|node|3|node|3|node_1|3|node_1|3|node|3|node_1}} |t0,2,3 |(0,0,0,0,0,1,2,2,3) | 6804 | 1512 | ||||||
align=center
!24 | {{CDD|node|3|node|3|node|3|node|3|node_1|3|node_1|3|node_1|3|node}} |t1,2,3 |(0,0,0,0,0,1,2,3,3) | 6048 | 1512 | ||||||
align=center
!25 | {{CDD|node|3|node|3|node|3|node_1|3|node|3|node|3|node_1|3|node_1}} |t0,1,4 |(0,0,0,0,1,1,1,2,3) | 20160 | 2520 | ||||||
align=center
!26 | {{CDD|node|3|node|3|node|3|node_1|3|node|3|node_1|3|node|3|node_1}} |t0,2,4 |(0,0,0,0,1,1,2,2,3) | 26460 | 3780 | ||||||
align=center
!27 | {{CDD|node|3|node|3|node|3|node_1|3|node|3|node_1|3|node_1|3|node}} |t1,2,4 |(0,0,0,0,1,1,2,3,3) | 22680 | 3780 | ||||||
align=center
!28 | {{CDD|node|3|node|3|node|3|node_1|3|node_1|3|node|3|node|3|node_1}} |t0,3,4 |(0,0,0,0,1,2,2,2,3) | 12600 | 2520 | ||||||
align=center
!29 | {{CDD|node|3|node|3|node|3|node_1|3|node_1|3|node|3|node_1|3|node}} |t1,3,4 |(0,0,0,0,1,2,2,3,3) | 18900 | 3780 | ||||||
align=center
!30 | {{CDD|node|3|node|3|node|3|node_1|3|node_1|3|node_1|3|node|3|node}} |t2,3,4 |(0,0,0,0,1,2,3,3,3) | 10080 | 2520 | ||||||
align=center
!31 | {{CDD|node|3|node|3|node_1|3|node|3|node|3|node|3|node_1|3|node_1}} |t0,1,5 |(0,0,0,1,1,1,1,2,3) | 21420 | 2520 | ||||||
align=center
!32 | {{CDD|node|3|node|3|node_1|3|node|3|node|3|node_1|3|node|3|node_1}} |t0,2,5 |(0,0,0,1,1,1,2,2,3) | 42840 | 5040 | ||||||
align=center
!33 | {{CDD|node|3|node|3|node_1|3|node|3|node|3|node_1|3|node_1|3|node}} |t1,2,5 |(0,0,0,1,1,1,2,3,3) | 35280 | 5040 | ||||||
align=center
!34 | {{CDD|node|3|node|3|node_1|3|node|3|node_1|3|node|3|node|3|node_1}} |t0,3,5 |(0,0,0,1,1,2,2,2,3) | 37800 | 5040 | ||||||
align=center
!35 | {{CDD|node|3|node|3|node_1|3|node|3|node_1|3|node|3|node_1|3|node}} |t1,3,5 |(0,0,0,1,1,2,2,3,3) | 52920 | 7560 | ||||||
align=center
!36 | {{CDD|node|3|node|3|node_1|3|node|3|node_1|3|node_1|3|node|3|node}} |t2,3,5 |(0,0,0,1,1,2,3,3,3) | 27720 | 5040 | ||||||
align=center
!37 | {{CDD|node|3|node|3|node_1|3|node_1|3|node|3|node|3|node|3|node_1}} |t0,4,5 |(0,0,0,1,2,2,2,2,3) | 13860 | 2520 | ||||||
align=center
!38 | {{CDD|node|3|node|3|node_1|3|node_1|3|node|3|node|3|node_1|3|node}} |t1,4,5 |(0,0,0,1,2,2,2,3,3) | 30240 | 5040 | ||||||
align=center
!39 | {{CDD|node|3|node_1|3|node|3|node|3|node|3|node|3|node_1|3|node_1}} |t0,1,6 |(0,0,1,1,1,1,1,2,3) | 12096 | 1512 | ||||||
align=center
!40 | {{CDD|node|3|node_1|3|node|3|node|3|node|3|node_1|3|node|3|node_1}} |t0,2,6 |(0,0,1,1,1,1,2,2,3) | 34020 | 3780 | ||||||
align=center
!41 | {{CDD|node|3|node_1|3|node|3|node|3|node|3|node_1|3|node_1|3|node}} |t1,2,6 |(0,0,1,1,1,1,2,3,3) | 26460 | 3780 | ||||||
align=center
!42 | {{CDD|node|3|node_1|3|node|3|node|3|node_1|3|node|3|node|3|node_1}} |t0,3,6 |(0,0,1,1,1,2,2,2,3) | 45360 | 5040 | ||||||
align=center
!43 | {{CDD|node|3|node_1|3|node|3|node|3|node_1|3|node|3|node_1|3|node}} |t1,3,6 |(0,0,1,1,1,2,2,3,3) | 60480 | 7560 | ||||||
align=center
!44 | {{CDD|node|3|node_1|3|node|3|node_1|3|node|3|node|3|node|3|node_1}} |t0,4,6 |(0,0,1,1,2,2,2,2,3) | 30240 | 3780 | ||||||
align=center
!45 | {{CDD|node|3|node_1|3|node_1|3|node|3|node|3|node|3|node|3|node_1}} |t0,5,6 |(0,0,1,2,2,2,2,2,3) | 9072 | 1512 | ||||||
align=center
!46 | {{CDD|node_1|3|node|3|node|3|node|3|node|3|node|3|node_1|3|node_1}} |t0,1,7 |(0,1,1,1,1,1,1,2,3) | 3276 | 504 | ||||||
align=center
!47 | {{CDD|node_1|3|node|3|node|3|node|3|node|3|node_1|3|node|3|node_1}} |t0,2,7 |(0,1,1,1,1,1,2,2,3) | 12852 | 1512 | ||||||
align=center
!48 | {{CDD|node_1|3|node|3|node|3|node|3|node_1|3|node|3|node|3|node_1}} |t0,3,7 |(0,1,1,1,1,2,2,2,3) | 23940 | 2520 | ||||||
align=center
!49 | {{CDD|node|3|node|3|node|3|node|3|node_1|3|node_1|3|node_1|3|node_1}} |t0,1,2,3 |Runcicantitruncated 8-simplex |(0,0,0,0,0,1,2,3,4) | 12096 | 3024 | ||||||
align=center
!50 | {{CDD|node|3|node|3|node|3|node_1|3|node|3|node_1|3|node_1|3|node_1}} |t0,1,2,4 |Stericantitruncated 8-simplex |(0,0,0,0,1,1,2,3,4) | 45360 | 7560 | ||||||
align=center
!51 | {{CDD|node|3|node|3|node|3|node_1|3|node_1|3|node|3|node_1|3|node_1}} |t0,1,3,4 |Steriruncitruncated 8-simplex |(0,0,0,0,1,2,2,3,4) | 34020 | 7560 | ||||||
align=center
!52 | {{CDD|node|3|node|3|node|3|node_1|3|node_1|3|node_1|3|node|3|node_1}} |t0,2,3,4 |Steriruncicantellated 8-simplex |(0,0,0,0,1,2,3,3,4) | 34020 | 7560 | ||||||
align=center
!53 | {{CDD|node|3|node|3|node|3|node_1|3|node_1|3|node_1|3|node_1|3|node}} |t1,2,3,4 |Biruncicantitruncated 8-simplex |(0,0,0,0,1,2,3,4,4) | 30240 | 7560 | ||||||
align=center
!54 | {{CDD|node|3|node|3|node_1|3|node|3|node|3|node_1|3|node_1|3|node_1}} |t0,1,2,5 |Penticantitruncated 8-simplex |(0,0,0,1,1,1,2,3,4) | 70560 | 10080 | ||||||
align=center
!55 | {{CDD|node|3|node|3|node_1|3|node|3|node_1|3|node|3|node_1|3|node_1}} |t0,1,3,5 |Pentiruncitruncated 8-simplex |(0,0,0,1,1,2,2,3,4) | 98280 | 15120 | ||||||
align=center
!56 | {{CDD|node|3|node|3|node_1|3|node|3|node_1|3|node_1|3|node|3|node_1}} |t0,2,3,5 |Pentiruncicantellated 8-simplex |(0,0,0,1,1,2,3,3,4) | 90720 | 15120 | ||||||
align=center
!57 | {{CDD|node|3|node|3|node_1|3|node|3|node_1|3|node_1|3|node_1|3|node}} |t1,2,3,5 |Bistericantitruncated 8-simplex |(0,0,0,1,1,2,3,4,4) | 83160 | 15120 | ||||||
align=center
!58 | {{CDD|node|3|node|3|node_1|3|node_1|3|node|3|node|3|node_1|3|node_1}} |t0,1,4,5 |Pentisteritruncated 8-simplex |(0,0,0,1,2,2,2,3,4) | 50400 | 10080 | ||||||
align=center
!59 | {{CDD|node|3|node|3|node_1|3|node_1|3|node|3|node_1|3|node|3|node_1}} |t0,2,4,5 |Pentistericantellated 8-simplex |(0,0,0,1,2,2,3,3,4) | 83160 | 15120 | ||||||
align=center
!60 | {{CDD|node|3|node|3|node_1|3|node_1|3|node|3|node_1|3|node_1|3|node}} |t1,2,4,5 |Bisteriruncitruncated 8-simplex |(0,0,0,1,2,2,3,4,4) | 68040 | 15120 | ||||||
align=center
!61 | {{CDD|node|3|node|3|node_1|3|node_1|3|node_1|3|node|3|node|3|node_1}} |t0,3,4,5 |Pentisteriruncinated 8-simplex |(0,0,0,1,2,3,3,3,4) | 50400 | 10080 | ||||||
align=center
!62 | {{CDD|node|3|node|3|node_1|3|node_1|3|node_1|3|node|3|node_1|3|node}} |t1,3,4,5 |Bisteriruncicantellated 8-simplex |(0,0,0,1,2,3,3,4,4) | 75600 | 15120 | ||||||
align=center BGCOLOR="#e0f0e0"
!63 | {{CDD|node|3|node|3|node_1|3|node_1|3|node_1|3|node_1|3|node|3|node}} |t2,3,4,5 |Triruncicantitruncated 8-simplex |(0,0,0,1,2,3,4,4,4) | 40320 | 10080 | ||||||
align=center
!64 | {{CDD|node|3|node_1|3|node|3|node|3|node|3|node_1|3|node_1|3|node_1}} |t0,1,2,6 |(0,0,1,1,1,1,2,3,4) | 52920 | 7560 | ||||||
align=center
!65 | {{CDD|node|3|node_1|3|node|3|node|3|node_1|3|node|3|node_1|3|node_1}} |t0,1,3,6 |(0,0,1,1,1,2,2,3,4) | 113400 | 15120 | ||||||
align=center
!66 | {{CDD|node|3|node_1|3|node|3|node|3|node_1|3|node_1|3|node|3|node_1}} |t0,2,3,6 |Hexiruncicantellated 8-simplex |(0,0,1,1,1,2,3,3,4) | 98280 | 15120 | ||||||
align=center
!67 | {{CDD|node|3|node_1|3|node|3|node|3|node_1|3|node_1|3|node_1|3|node}} |t1,2,3,6 |Bipenticantitruncated 8-simplex |(0,0,1,1,1,2,3,4,4) | 90720 | 15120 | ||||||
align=center
!68 | {{CDD|node|3|node_1|3|node|3|node_1|3|node|3|node|3|node_1|3|node_1}} |t0,1,4,6 |(0,0,1,1,2,2,2,3,4) | 105840 | 15120 | ||||||
align=center
!69 | {{CDD|node|3|node_1|3|node|3|node_1|3|node|3|node_1|3|node|3|node_1}} |t0,2,4,6 |Hexistericantellated 8-simplex |(0,0,1,1,2,2,3,3,4) | 158760 | 22680 | ||||||
align=center
!70 | {{CDD|node|3|node_1|3|node|3|node_1|3|node|3|node_1|3|node_1|3|node}} |t1,2,4,6 |Bipentiruncitruncated 8-simplex |(0,0,1,1,2,2,3,4,4) | 136080 | 22680 | ||||||
align=center
!71 | {{CDD|node|3|node_1|3|node|3|node_1|3|node_1|3|node|3|node|3|node_1}} |t0,3,4,6 |Hexisteriruncinated 8-simplex |(0,0,1,1,2,3,3,3,4) | 90720 | 15120 | ||||||
align=center BGCOLOR="#e0f0e0"
!72 | {{CDD|node|3|node_1|3|node|3|node_1|3|node_1|3|node|3|node_1|3|node}} |t1,3,4,6 |Bipentiruncicantellated 8-simplex |(0,0,1,1,2,3,3,4,4) | 136080 | 22680 | ||||||
align=center
!73 | {{CDD|node|3|node_1|3|node_1|3|node|3|node|3|node|3|node_1|3|node_1}} |t0,1,5,6 |(0,0,1,2,2,2,2,3,4) | 41580 | 7560 | ||||||
align=center
!74 | {{CDD|node|3|node_1|3|node_1|3|node|3|node|3|node_1|3|node|3|node_1}} |t0,2,5,6 |Hexipenticantellated 8-simplex |(0,0,1,2,2,2,3,3,4) | 98280 | 15120 | ||||||
align=center BGCOLOR="#e0f0e0"
!75 | {{CDD|node|3|node_1|3|node_1|3|node|3|node|3|node_1|3|node_1|3|node}} |t1,2,5,6 |Bipentisteritruncated 8-simplex |(0,0,1,2,2,2,3,4,4) | 75600 | 15120 | ||||||
align=center
!76 | {{CDD|node|3|node_1|3|node_1|3|node|3|node_1|3|node|3|node|3|node_1}} |t0,3,5,6 |Hexipentiruncinated 8-simplex |(0,0,1,2,2,3,3,3,4) | 98280 | 15120 | ||||||
align=center
!77 | {{CDD|node|3|node_1|3|node_1|3|node_1|3|node|3|node|3|node|3|node_1}} |t0,4,5,6 |Hexipentistericated 8-simplex |(0,0,1,2,3,3,3,3,4) | 41580 | 7560 | ||||||
align=center
!78 | {{CDD|node_1|3|node|3|node|3|node|3|node|3|node_1|3|node_1|3|node_1}} |t0,1,2,7 |Hepticantitruncated 8-simplex |(0,1,1,1,1,1,2,3,4) | 18144 | 3024 | ||||||
align=center
!79 | {{CDD|node_1|3|node|3|node|3|node|3|node_1|3|node|3|node_1|3|node_1}} |t0,1,3,7 |Heptiruncitruncated 8-simplex |(0,1,1,1,1,2,2,3,4) | 56700 | 7560 | ||||||
align=center
!80 | {{CDD|node_1|3|node|3|node|3|node|3|node_1|3|node_1|3|node|3|node_1}} |t0,2,3,7 |Heptiruncicantellated 8-simplex |(0,1,1,1,1,2,3,3,4) | 45360 | 7560 | ||||||
align=center
!81 | {{CDD|node_1|3|node|3|node|3|node_1|3|node|3|node|3|node_1|3|node_1}} |t0,1,4,7 |Heptisteritruncated 8-simplex |(0,1,1,1,2,2,2,3,4) | 80640 | 10080 | ||||||
align=center
!82 | {{CDD|node_1|3|node|3|node|3|node_1|3|node|3|node_1|3|node|3|node_1}} |t0,2,4,7 |Heptistericantellated 8-simplex |(0,1,1,1,2,2,3,3,4) | 113400 | 15120 | ||||||
align=center BGCOLOR="#e0f0e0"
!83 | {{CDD|node_1|3|node|3|node|3|node_1|3|node_1|3|node|3|node|3|node_1}} |t0,3,4,7 |Heptisteriruncinated 8-simplex |(0,1,1,1,2,3,3,3,4) | 60480 | 10080 | ||||||
align=center
!84 | {{CDD|node_1|3|node|3|node_1|3|node|3|node|3|node|3|node_1|3|node_1}} |t0,1,5,7 |Heptipentitruncated 8-simplex |(0,1,1,2,2,2,2,3,4) | 56700 | 7560 | ||||||
align=center BGCOLOR="#e0f0e0"
!85 | {{CDD|node_1|3|node|3|node_1|3|node|3|node|3|node_1|3|node|3|node_1}} |t0,2,5,7 |Heptipenticantellated 8-simplex |(0,1,1,2,2,2,3,3,4) | 120960 | 15120 | ||||||
align=center BGCOLOR="#e0f0e0"
!86 | {{CDD|node_1|3|node_1|3|node|3|node|3|node|3|node|3|node_1|3|node_1}} |t0,1,6,7 |(0,1,2,2,2,2,2,3,4) | 18144 | 3024 | ||||||
align=center
!87 | {{CDD|node|3|node|3|node|3|node_1|3|node_1|3|node_1|3|node_1|3|node_1}} |t0,1,2,3,4 |Steriruncicantitruncated 8-simplex |(0,0,0,0,1,2,3,4,5) | 60480 | 15120 | ||||||
align=center
!88 | {{CDD|node|3|node|3|node_1|3|node|3|node_1|3|node_1|3|node_1|3|node_1}} |t0,1,2,3,5 |Pentiruncicantitruncated 8-simplex |(0,0,0,1,1,2,3,4,5) | 166320 | 30240 | ||||||
align=center
!89 | {{CDD|node|3|node|3|node_1|3|node_1|3|node|3|node_1|3|node_1|3|node_1}} |t0,1,2,4,5 |Pentistericantitruncated 8-simplex |(0,0,0,1,2,2,3,4,5) | 136080 | 30240 | ||||||
align=center
!90 | {{CDD|node|3|node|3|node_1|3|node_1|3|node_1|3|node|3|node_1|3|node_1}} |t0,1,3,4,5 |Pentisteriruncitruncated 8-simplex |(0,0,0,1,2,3,3,4,5) | 136080 | 30240 | ||||||
align=center
!91 | {{CDD|node|3|node|3|node_1|3|node_1|3|node_1|3|node_1|3|node|3|node_1}} |t0,2,3,4,5 |Pentisteriruncicantellated 8-simplex |(0,0,0,1,2,3,4,4,5) | 136080 | 30240 | ||||||
align=center
!92 | {{CDD|node|3|node|3|node_1|3|node_1|3|node_1|3|node_1|3|node_1|3|node}} |t1,2,3,4,5 |Bisteriruncicantitruncated 8-simplex |(0,0,0,1,2,3,4,5,5) | 120960 | 30240 | ||||||
align=center
!93 | {{CDD|node|3|node_1|3|node|3|node|3|node_1|3|node_1|3|node_1|3|node_1}} |t0,1,2,3,6 |Hexiruncicantitruncated 8-simplex |(0,0,1,1,1,2,3,4,5) | 181440 | 30240 | ||||||
align=center
!94 | {{CDD|node|3|node_1|3|node|3|node_1|3|node|3|node_1|3|node_1|3|node_1}} |t0,1,2,4,6 |Hexistericantitruncated 8-simplex |(0,0,1,1,2,2,3,4,5) | 272160 | 45360 | ||||||
align=center
!95 | {{CDD|node|3|node_1|3|node|3|node_1|3|node_1|3|node|3|node_1|3|node_1}} |t0,1,3,4,6 |Hexisteriruncitruncated 8-simplex |(0,0,1,1,2,3,3,4,5) | 249480 | 45360 | ||||||
align=center
!96 | {{CDD|node|3|node_1|3|node|3|node_1|3|node_1|3|node_1|3|node|3|node_1}} |t0,2,3,4,6 |Hexisteriruncicantellated 8-simplex |(0,0,1,1,2,3,4,4,5) | 249480 | 45360 | ||||||
align=center
!97 | {{CDD|node|3|node_1|3|node|3|node_1|3|node_1|3|node_1|3|node_1|3|node}} |t1,2,3,4,6 |Bipentiruncicantitruncated 8-simplex |(0,0,1,1,2,3,4,5,5) | 226800 | 45360 | ||||||
align=center
!98 | {{CDD|node|3|node_1|3|node_1|3|node|3|node|3|node_1|3|node_1|3|node_1}} |t0,1,2,5,6 |Hexipenticantitruncated 8-simplex |(0,0,1,2,2,2,3,4,5) | 151200 | 30240 | ||||||
align=center
!99 | {{CDD|node|3|node_1|3|node_1|3|node|3|node_1|3|node|3|node_1|3|node_1}} |t0,1,3,5,6 |Hexipentiruncitruncated 8-simplex |(0,0,1,2,2,3,3,4,5) | 249480 | 45360 | ||||||
align=center
!100 | {{CDD|node|3|node_1|3|node_1|3|node|3|node_1|3|node_1|3|node|3|node_1}} |t0,2,3,5,6 |Hexipentiruncicantellated 8-simplex |(0,0,1,2,2,3,4,4,5) | 226800 | 45360 | ||||||
align=center
!101 | {{CDD|node|3|node_1|3|node_1|3|node|3|node_1|3|node_1|3|node_1|3|node}} |t1,2,3,5,6 |Bipentistericantitruncated 8-simplex |(0,0,1,2,2,3,4,5,5) | 204120 | 45360 | ||||||
align=center
!102 | {{CDD|node|3|node_1|3|node_1|3|node_1|3|node|3|node|3|node_1|3|node_1}} |t0,1,4,5,6 |Hexipentisteritruncated 8-simplex |(0,0,1,2,3,3,3,4,5) | 151200 | 30240 | ||||||
align=center
!103 | {{CDD|node|3|node_1|3|node_1|3|node_1|3|node|3|node_1|3|node|3|node_1}} |t0,2,4,5,6 |Hexipentistericantellated 8-simplex |(0,0,1,2,3,3,4,4,5) | 249480 | 45360 | ||||||
align=center
!104 | {{CDD|node|3|node_1|3|node_1|3|node_1|3|node_1|3|node|3|node|3|node_1}} |t0,3,4,5,6 |Hexipentisteriruncinated 8-simplex |(0,0,1,2,3,4,4,4,5) | 151200 | 30240 | ||||||
align=center
!105 | {{CDD|node_1|3|node|3|node|3|node|3|node_1|3|node_1|3|node_1|3|node_1}} |t0,1,2,3,7 |Heptiruncicantitruncated 8-simplex |(0,1,1,1,1,2,3,4,5) | 83160 | 15120 | ||||||
align=center
!106 | {{CDD|node_1|3|node|3|node|3|node_1|3|node|3|node_1|3|node_1|3|node_1}} |t0,1,2,4,7 |Heptistericantitruncated 8-simplex |(0,1,1,1,2,2,3,4,5) | 196560 | 30240 | ||||||
align=center
!107 | {{CDD|node_1|3|node|3|node|3|node_1|3|node_1|3|node|3|node_1|3|node_1}} |t0,1,3,4,7 |Heptisteriruncitruncated 8-simplex |(0,1,1,1,2,3,3,4,5) | 166320 | 30240 | ||||||
align=center
!108 | {{CDD|node_1|3|node|3|node|3|node_1|3|node_1|3|node_1|3|node|3|node_1}} |t0,2,3,4,7 |Heptisteriruncicantellated 8-simplex |(0,1,1,1,2,3,4,4,5) | 166320 | 30240 | ||||||
align=center
!109 | {{CDD|node_1|3|node|3|node_1|3|node|3|node|3|node_1|3|node_1|3|node_1}} |t0,1,2,5,7 |Heptipenticantitruncated 8-simplex |(0,1,1,2,2,2,3,4,5) | 196560 | 30240 | ||||||
align=center
!110 | {{CDD|node_1|3|node|3|node_1|3|node|3|node_1|3|node|3|node_1|3|node_1}} |t0,1,3,5,7 |Heptipentiruncitruncated 8-simplex |(0,1,1,2,2,3,3,4,5) | 294840 | 45360 | ||||||
align=center
!111 | {{CDD|node_1|3|node|3|node_1|3|node|3|node_1|3|node_1|3|node|3|node_1}} |t0,2,3,5,7 |Heptipentiruncicantellated 8-simplex |(0,1,1,2,2,3,4,4,5) | 272160 | 45360 | ||||||
align=center
!112 | {{CDD|node_1|3|node|3|node_1|3|node_1|3|node|3|node|3|node_1|3|node_1}} |t0,1,4,5,7 |Heptipentisteritruncated 8-simplex |(0,1,1,2,3,3,3,4,5) | 166320 | 30240 | ||||||
align=center
!113 | {{CDD|node_1|3|node_1|3|node|3|node|3|node|3|node_1|3|node_1|3|node_1}} |t0,1,2,6,7 |Heptihexicantitruncated 8-simplex |(0,1,2,2,2,2,3,4,5) | 83160 | 15120 | ||||||
align=center
!114 | {{CDD|node_1|3|node_1|3|node|3|node|3|node_1|3|node|3|node_1|3|node_1}} |t0,1,3,6,7 |Heptihexiruncitruncated 8-simplex |(0,1,2,2,2,3,3,4,5) | 196560 | 30240 | ||||||
align=center
!115 | {{CDD|node|3|node|3|node_1|3|node_1|3|node_1|3|node_1|3|node_1|3|node_1}} |t0,1,2,3,4,5 |Pentisteriruncicantitruncated 8-simplex |(0,0,0,1,2,3,4,5,6) | 241920 | 60480 | ||||||
align=center
!116 | {{CDD|node|3|node_1|3|node|3|node_1|3|node_1|3|node_1|3|node_1|3|node_1}} |t0,1,2,3,4,6 |Hexisteriruncicantitruncated 8-simplex |(0,0,1,1,2,3,4,5,6) | 453600 | 90720 | ||||||
align=center
!117 | {{CDD|node|3|node_1|3|node_1|3|node|3|node_1|3|node_1|3|node_1|3|node_1}} |t0,1,2,3,5,6 |Hexipentiruncicantitruncated 8-simplex |(0,0,1,2,2,3,4,5,6) | 408240 | 90720 | ||||||
align=center
!118 | {{CDD|node|3|node_1|3|node_1|3|node_1|3|node|3|node_1|3|node_1|3|node_1}} |t0,1,2,4,5,6 |Hexipentistericantitruncated 8-simplex |(0,0,1,2,3,3,4,5,6) | 408240 | 90720 | ||||||
align=center
!119 | {{CDD|node|3|node_1|3|node_1|3|node_1|3|node_1|3|node|3|node_1|3|node_1}} |t0,1,3,4,5,6 |Hexipentisteriruncitruncated 8-simplex |(0,0,1,2,3,4,4,5,6) | 408240 | 90720 | ||||||
align=center
!120 | {{CDD|node|3|node_1|3|node_1|3|node_1|3|node_1|3|node_1|3|node|3|node_1}} |t0,2,3,4,5,6 |Hexipentisteriruncicantellated 8-simplex |(0,0,1,2,3,4,5,5,6) | 408240 | 90720 | ||||||
align=center BGCOLOR="#e0f0e0"
!121 | {{CDD|node|3|node_1|3|node_1|3|node_1|3|node_1|3|node_1|3|node_1|3|node}} |t1,2,3,4,5,6 |Bipentisteriruncicantitruncated 8-simplex |(0,0,1,2,3,4,5,6,6) | 362880 | 90720 | ||||||
align=center
!122 | {{CDD|node_1|3|node|3|node|3|node_1|3|node_1|3|node_1|3|node_1|3|node_1}} |t0,1,2,3,4,7 |Heptisteriruncicantitruncated 8-simplex |(0,1,1,1,2,3,4,5,6) | 302400 | 60480 | ||||||
align=center
!123 | {{CDD|node_1|3|node|3|node_1|3|node|3|node_1|3|node_1|3|node_1|3|node_1}} |t0,1,2,3,5,7 |Heptipentiruncicantitruncated 8-simplex |(0,1,1,2,2,3,4,5,6) | 498960 | 90720 | ||||||
align=center
!124 | {{CDD|node_1|3|node|3|node_1|3|node_1|3|node|3|node_1|3|node_1|3|node_1}} |t0,1,2,4,5,7 |Heptipentistericantitruncated 8-simplex |(0,1,1,2,3,3,4,5,6) | 453600 | 90720 | ||||||
align=center
!125 | {{CDD|node_1|3|node|3|node_1|3|node_1|3|node_1|3|node|3|node_1|3|node_1}} |t0,1,3,4,5,7 |Heptipentisteriruncitruncated 8-simplex |(0,1,1,2,3,4,4,5,6) | 453600 | 90720 | ||||||
align=center BGCOLOR="#e0f0e0"
!126 | {{CDD|node_1|3|node|3|node_1|3|node_1|3|node_1|3|node_1|3|node|3|node_1}} |t0,2,3,4,5,7 |Heptipentisteriruncicantellated 8-simplex |(0,1,1,2,3,4,5,5,6) | 453600 | 90720 | ||||||
align=center
!127 | {{CDD|node_1|3|node_1|3|node|3|node|3|node_1|3|node_1|3|node_1|3|node_1}} |t0,1,2,3,6,7 |Heptihexiruncicantitruncated 8-simplex |(0,1,2,2,2,3,4,5,6) | 302400 | 60480 | ||||||
align=center
!128 | {{CDD|node_1|3|node_1|3|node|3|node_1|3|node|3|node_1|3|node_1|3|node_1}} |t0,1,2,4,6,7 |Heptihexistericantitruncated 8-simplex |(0,1,2,2,3,3,4,5,6) | 498960 | 90720 | ||||||
align=center BGCOLOR="#e0f0e0"
!129 | {{CDD|node_1|3|node_1|3|node|3|node_1|3|node_1|3|node|3|node_1|3|node_1}} |t0,1,3,4,6,7 |Heptihexisteriruncitruncated 8-simplex |(0,1,2,2,3,4,4,5,6) | 453600 | 90720 | ||||||
align=center BGCOLOR="#e0f0e0"
!130 | {{CDD|node_1|3|node_1|3|node_1|3|node|3|node|3|node_1|3|node_1|3|node_1}} |t0,1,2,5,6,7 |Heptihexipenticantitruncated 8-simplex |(0,1,2,3,3,3,4,5,6) | 302400 | 60480 | ||||||
align=center
!131 | {{CDD|node|3|node_1|3|node_1|3|node_1|3|node_1|3|node_1|3|node_1|3|node_1}} |t0,1,2,3,4,5,6 |Hexipentisteriruncicantitruncated 8-simplex |(0,0,1,2,3,4,5,6,7) | 725760 | 181440 | ||||||
align=center
!132 | {{CDD|node_1|3|node|3|node_1|3|node_1|3|node_1|3|node_1|3|node_1|3|node_1}} |t0,1,2,3,4,5,7 |Heptipentisteriruncicantitruncated 8-simplex |(0,1,1,2,3,4,5,6,7) | 816480 | 181440 | ||||||
align=center
!133 | {{CDD|node_1|3|node_1|3|node|3|node_1|3|node_1|3|node_1|3|node_1|3|node_1}} |t0,1,2,3,4,6,7 |Heptihexisteriruncicantitruncated 8-simplex |(0,1,2,2,3,4,5,6,7) | 816480 | 181440 | ||||||
align=center
!134 | {{CDD|node_1|3|node_1|3|node_1|3|node|3|node_1|3|node_1|3|node_1|3|node_1}} |t0,1,2,3,5,6,7 |Heptihexipentiruncicantitruncated 8-simplex |(0,1,2,3,3,4,5,6,7) | 816480 | 181440 | ||||||
align=center BGCOLOR="#e0f0e0"
!135 | {{CDD|node_1|3|node_1|3|node_1|3|node_1|3|node_1|3|node_1|3|node_1|3|node_1}} |t0,1,2,3,4,5,6,7 |(0,1,2,3,4,5,6,7,8) | 1451520 | 362880 |
= 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 !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) | 256 | 1024 | 1792 | 1792 | 1120 | 448 | 112 | 16 |
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) | 272 | 3072 | 8960 | 12544 | 10080 | 4928 | 1344 | 112 |
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) | 272 | 3184 | 16128 | 34048 | 36960 | 22400 | 6720 | 448 |
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) | 272 | 3184 | 16576 | 48384 | 71680 | 53760 | 17920 | 1120 |
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) | 272 | 3184 | 16576 | 47712 | 80640 | 71680 | 26880 | 1792 |
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) | 272 | 3184 | 14784 | 36960 | 55552 | 50176 | 21504 | 1792 |
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) | 272 | 2160 | 7616 | 15456 | 19712 | 16128 | 7168 | 1024 |
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) | 16 | 112 | 448 | 1120 | 1792 | 1792 | 1024 | 256 |
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) | 1456 | 224 | ||||||
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) | 14784 | 1344 | ||||||
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) | 8064 | 1344 | ||||||
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) | 60480 | 4480 | ||||||
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) | 67200 | 6720 | ||||||
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) | 24640 | 4480 | ||||||
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) | 125440 | 8960 | ||||||
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) | 215040 | 17920 | ||||||
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) | 161280 | 17920 | ||||||
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) | 44800 | 8960 | ||||||
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) | 134400 | 10752 | ||||||
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) | 322560 | 26880 | ||||||
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) | 376320 | 35840 | ||||||
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) | 215040 | 26880 | ||||||
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) | 48384 | 10752 | ||||||
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) | 64512 | 7168 | ||||||
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) | 215040 | 21504 | ||||||
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) | 358400 | 35840 | ||||||
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) | 322560 | 35840 | ||||||
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) | 150528 | 21504 | ||||||
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) | 28672 | 7168 | ||||||
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) | 14336 | 2048 | ||||||
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) | 64512 | 7168 | ||||||
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) | 143360 | 14336 | ||||||
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) | 179200 | 17920 | ||||||
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) | 129024 | 14336 | ||||||
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) | 50176 | 7168 | ||||||
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) | 8192 | 2048 | ||||||
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 | 16128 | 2688 | ||||||
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 | 127680 | 13440 | ||||||
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 | 80640 | 13440 | ||||||
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 | 73920 | 13440 | ||||||
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 | 394240 | 35840 | ||||||
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 | 483840 | 53760 | ||||||
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 | 430080 | 53760 | ||||||
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 | 215040 | 35840 | ||||||
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 | 322560 | 53760 | ||||||
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 | 179200 | 35840 | ||||||
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 | 564480 | 53760 | ||||||
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 | 1075200 | 107520 | ||||||
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 | 913920 | 107520 | ||||||
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 | 913920 | 107520 | ||||||
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 | 1290240 | 161280 | ||||||
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 | 698880 | 107520 | ||||||
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 | 322560 | 53760 | ||||||
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 | 698880 | 107520 | ||||||
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 | 645120 | 107520 | ||||||
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 | 241920 | 53760 | ||||||
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 | 344064 | 43008 | ||||||
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 | 967680 | 107520 | ||||||
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 | 752640 | 107520 | ||||||
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 | 1290240 | 143360 | ||||||
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 | 1720320 | 215040 | ||||||
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 | 860160 | 143360 | ||||||
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 | 860160 | 107520 | ||||||
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 | 1720320 | 215040 | ||||||
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 | 1505280 | 215040 | ||||||
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 | 537600 | 107520 | ||||||
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 | 258048 | 43008 | ||||||
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 | 752640 | 107520 | ||||||
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 | 1003520 | 143360 | ||||||
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 | 645120 | 107520 | ||||||
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 | 172032 | 43008 | ||||||
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 | 93184 | 14336 | ||||||
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 | 365568 | 43008 | ||||||
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 | 258048 | 43008 | ||||||
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 | 680960 | 71680 | ||||||
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 | 860160 | 107520 | ||||||
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 | 394240 | 71680 | ||||||
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 | 680960 | 71680 | ||||||
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 | 1290240 | 143360 | ||||||
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 | 1075200 | 143360 | ||||||
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 | 358400 | 71680 | ||||||
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 | 365568 | 43008 | ||||||
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 | 967680 | 107520 | ||||||
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 | 1218560 | 143360 | ||||||
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 | 752640 | 107520 | ||||||
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 | 193536 | 43008 | ||||||
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 | 93184 | 14336 | ||||||
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 | 344064 | 43008 | ||||||
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 | 609280 | 71680 | ||||||
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 | 573440 | 71680 | ||||||
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 | 279552 | 43008 | ||||||
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 | 57344 | 14336 | ||||||
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 | 147840 | 26880 | ||||||
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 | 860160 | 107520 | ||||||
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 | 591360 | 107520 | ||||||
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 | 591360 | 107520 | ||||||
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 | 537600 | 107520 | ||||||
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 | 1827840 | 215040 | ||||||
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 | 2419200 | 322560 | ||||||
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 | 2257920 | 322560 | ||||||
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 | 2096640 | 322560 | ||||||
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 | 1182720 | 215040 | ||||||
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 | 1935360 | 322560 | ||||||
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 | 1612800 | 322560 | ||||||
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 | 1182720 | 215040 | ||||||
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 | 1774080 | 322560 | ||||||
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 | 967680 | 215040 | ||||||
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 | 1505280 | 215040 | ||||||
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 | 3225600 | 430080 | ||||||
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 | 2795520 | 430080 | ||||||
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 | 2580480 | 430080 | ||||||
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 | 3010560 | 430080 | ||||||
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 | 4515840 | 645120 | ||||||
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 | 3870720 | 645120 | ||||||
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 | 2580480 | 430080 | ||||||
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 | 3870720 | 645120 | ||||||
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 | 2150400 | 430080 | ||||||
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 | 1182720 | 215040 | ||||||
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 | 2795520 | 430080 | ||||||
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 | 2150400 | 430080 | ||||||
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 | 2795520 | 430080 | ||||||
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 | 3870720 | 645120 | ||||||
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 | 1935360 | 430080 | ||||||
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 | 1182720 | 215040 | ||||||
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 | 2580480 | 430080 | ||||||
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 | 2365440 | 430080 | ||||||
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 | 860160 | 215040 | ||||||
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 | 516096 | 86016 | ||||||
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 | 1612800 | 215040 | ||||||
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 | 1290240 | 215040 | ||||||
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 | 1182720 | 215040 | ||||||
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 | 2293760 | 286720 | ||||||
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 | 3225600 | 430080 | ||||||
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 | 2795520 | 430080 | ||||||
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 | 1720320 | 286720 | ||||||
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 | 2580480 | 430080 | ||||||
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 | 1433600 | 286720 | ||||||
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 | 1612800 | 215040 | ||||||
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 | 3440640 | 430080 | ||||||
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 | 2795520 | 430080 | ||||||
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 | 3225600 | 430080 | ||||||
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 | 4515840 | 645120 | ||||||
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 | 2365440 | 430080 | ||||||
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 | 1290240 | 215040 | ||||||
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 | 2795520 | 430080 | ||||||
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 | 2580480 | 430080 | ||||||
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 | 967680 | 215040 | ||||||
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 | 516096 | 86016 | ||||||
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 | 1612800 | 215040 | ||||||
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 | 1182720 | 215040 | ||||||
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 | 2293760 | 286720 | ||||||
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 | 3010560 | 430080 | ||||||
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 | 1433600 | 286720 | ||||||
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 | 1612800 | 215040 | ||||||
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 | 3225600 | 430080 | ||||||
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 | 2795520 | 430080 | ||||||
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 | 967680 | 215040 | ||||||
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 | 516096 | 86016 | ||||||
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 | 1505280 | 215040 | ||||||
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 | 2007040 | 286720 | ||||||
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 | 1290240 | 215040 | ||||||
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 | 344064 | 86016 | ||||||
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 | 1075200 | 215040 | ||||||
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 | 4193280 | 645120 | ||||||
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 | 3225600 | 645120 | ||||||
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 | 3225600 | 645120 | ||||||
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 | 3225600 | 645120 | ||||||
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 | 2903040 | 645120 | ||||||
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 | 5160960 | 860160 | ||||||
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 | 7741440 | 1290240 | ||||||
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 | 7096320 | 1290240 | ||||||
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 | 7096320 | 1290240 | ||||||
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 | 6451200 | 1290240 | ||||||
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 | 4300800 | 860160 | ||||||
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 | 7096320 | 1290240 | ||||||
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 | 6451200 | 1290240 | ||||||
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 | 5806080 | 1290240 | ||||||
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 | 4300800 | 860160 | ||||||
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 | 7096320 | 1290240 | ||||||
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 | 5806080 | 1290240 | ||||||
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 | 4300800 | 860160 | ||||||
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 | 6451200 | 1290240 | ||||||
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 | 3440640 | 860160 | ||||||
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 | 2365440 | 430080 | ||||||
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 | 5591040 | 860160 | ||||||
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 | 4730880 | 860160 | ||||||
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 | 4730880 | 860160 | ||||||
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 | 4300800 | 860160 | ||||||
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 | 5591040 | 860160 | ||||||
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 | 8386560 | 1290240 | ||||||
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 | 7741440 | 1290240 | ||||||
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 | 7096320 | 1290240 | ||||||
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 | 4730880 | 860160 | ||||||
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 | 7741440 | 1290240 | ||||||
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 | 6451200 | 1290240 | ||||||
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 | 4730880 | 860160 | ||||||
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 | 7096320 | 1290240 | ||||||
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 | 3870720 | 860160 | ||||||
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 | 2365440 | 430080 | ||||||
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 | 5591040 | 860160 | ||||||
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 | 4730880 | 860160 | ||||||
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 | 4300800 | 860160 | ||||||
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 | 5591040 | 860160 | ||||||
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 | 8386560 | 1290240 | ||||||
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 | 7096320 | 1290240 | ||||||
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 | 4730880 | 860160 | ||||||
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 | 7096320 | 1290240 | ||||||
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 | 3870720 | 860160 | ||||||
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 | 2365440 | 430080 | ||||||
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 | 5591040 | 860160 | ||||||
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 | 4300800 | 860160 | ||||||
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 | 5591040 | 860160 | ||||||
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 | 7741440 | 1290240 | ||||||
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 | 3870720 | 860160 | ||||||
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 | 2365440 | 430080 | ||||||
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 | 5160960 | 860160 | ||||||
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 | 4730880 | 860160 | ||||||
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 | 1720320 | 430080 | ||||||
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 | 5806080 | 1290240 | ||||||
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 | 12902400 | 2580480 | ||||||
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 | 11612160 | 2580480 | ||||||
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 | 11612160 | 2580480 | ||||||
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 | 11612160 | 2580480 | ||||||
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 | 11612160 | 2580480 | ||||||
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 | 10321920 | 2580480 | ||||||
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 | 8601600 | 1720320 | ||||||
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 | 14192640 | 2580480 | ||||||
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 | 12902400 | 2580480 | ||||||
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 | 12902400 | 2580480 | ||||||
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 | 12902400 | 2580480 | ||||||
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 | 11612160 | 2580480 | ||||||
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 | 8601600 | 1720320 | ||||||
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 | 14192640 | 2580480 | ||||||
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 | 12902400 | 2580480 | ||||||
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 | 12902400 | 2580480 | ||||||
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 | 11612160 | 2580480 | ||||||
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 | 8601600 | 1720320 | ||||||
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 | 14192640 | 2580480 | ||||||
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 | 12902400 | 2580480 | ||||||
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 | 11612160 | 2580480 | ||||||
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 | 8601600 | 1720320 | ||||||
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 | 14192640 | 2580480 | ||||||
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 | 11612160 | 2580480 | ||||||
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 | 8601600 | 1720320 | ||||||
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 | 12902400 | 2580480 | ||||||
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 | 6881280 | 1720320 | ||||||
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 | 20643840 | 5160960 | ||||||
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 | 23224320 | 5160960 | ||||||
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 | 23224320 | 5160960 | ||||||
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 | 23224320 | 5160960 | ||||||
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 | 23224320 | 5160960 | ||||||
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 | 23224320 | 5160960 | ||||||
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 | 23224320 | 5160960 | ||||||
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 | 20643840 | 5160960 | ||||||
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 | 41287680 | 10321920 |
= 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 !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) | 144 | 1136 | 4032 | 8288 | 10752 | 7168 | 1792 | 128 | 1.0000000 |
align=center
!2 | {{CDD|nodes_10ru|split2|node_1|3|node|3|node|3|node|3|node|3|node}} = {{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) | 23296 | 3584 | 2.6457512 | ||||||
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) | 64512 | 7168 | 2.4494896 | ||||||
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) | 98560 | 8960 | 2.2360678 | ||||||
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) | 89600 | 7168 | 1.9999999 | ||||||
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) | 48384 | 3584 | 1.7320508 | ||||||
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) | 14336 | 1024 | 1.4142135 | ||||||
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) | 86016 | 21504 | 4.1231055 | ||||||
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) | 349440 | 53760 | 3.8729835 | ||||||
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) | 179200 | 35840 | 3.7416575 | ||||||
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) | 573440 | 71680 | 3.6055512 | ||||||
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) | 537600 | 71680 | 3.4641016 | ||||||
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) | 232960 | 35840 | 3.3166249 | ||||||
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) | 456960 | 53760 | 3.3166249 | ||||||
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) | 645120 | 71680 | 3.1622777 | ||||||
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) | 483840 | 53760 | 3 | ||||||
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) | 182784 | 21504 | 2.8284271 | ||||||
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) | 172032 | 21504 | 3 | ||||||
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) | 340480 | 35840 | 2.8284271 | ||||||
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) | 376320 | 35840 | 2.6457512 | ||||||
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) | 236544 | 21504 | 2.4494898 | ||||||
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) | 78848 | 7168 | 2.236068 | ||||||
align=center
!23 | {{CDD|nodes_10ru|split2|node_1|3|node_1|3|node_1|3|node|3|node|3|node}} = {{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) | 430080 | 107520 | 5.3851647 | ||||||
align=center
!24 | {{CDD|nodes_10ru|split2|node_1|3|node_1|3|node|3|node_1|3|node|3|node}} = {{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) | 1182720 | 215040 | 5.0990195 | ||||||
align=center
!25 | {{CDD|nodes_10ru|split2|node_1|3|node|3|node_1|3|node_1|3|node|3|node}} = {{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) | 1075200 | 215040 | 4.8989797 | ||||||
align=center
!26 | {{CDD|nodes_10ru|split2|node|3|node_1|3|node_1|3|node_1|3|node|3|node}} = {{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) | 716800 | 143360 | 4.7958317 | ||||||
align=center
!27 | {{CDD|nodes_10ru|split2|node_1|3|node_1|3|node|3|node|3|node_1|3|node}} = {{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) | 1290240 | 215040 | 4.7958317 | ||||||
align=center
!28 | {{CDD|nodes_10ru|split2|node_1|3|node|3|node_1|3|node|3|node_1|3|node}} = {{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) | 2096640 | 322560 | 4.5825758 | ||||||
align=center
!29 | {{CDD|nodes_10ru|split2|node|3|node_1|3|node_1|3|node|3|node_1|3|node}} = {{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) | 1290240 | 215040 | 4.472136 | ||||||
align=center
!30 | {{CDD|nodes_10ru|split2|node_1|3|node|3|node|3|node_1|3|node_1|3|node}} = {{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) | 1290240 | 215040 | 4.3588991 | ||||||
align=center
!31 | {{CDD|nodes_10ru|split2|node|3|node_1|3|node|3|node_1|3|node_1|3|node}} = {{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) | 1397760 | 215040 | 4.2426405 | ||||||
align=center
!32 | {{CDD|nodes_10ru|split2|node|3|node|3|node_1|3|node_1|3|node_1|3|node}} = {{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) | 698880 | 107520 | 4.1231055 | ||||||
align=center
!33 | {{CDD|nodes_10ru|split2|node_1|3|node_1|3|node|3|node|3|node|3|node_1}} = {{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) | 591360 | 107520 | 4.472136 | ||||||
align=center
!34 | {{CDD|nodes_10ru|split2|node_1|3|node|3|node_1|3|node|3|node|3|node_1}} = {{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) | 1505280 | 215040 | 4.2426405 | ||||||
align=center
!35 | {{CDD|nodes_10ru|split2|node|3|node_1|3|node_1|3|node|3|node|3|node_1}} = {{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) | 860160 | 143360 | 4.1231055 | ||||||
align=center
!36 | {{CDD|nodes_10ru|split2|node_1|3|node|3|node|3|node_1|3|node|3|node_1}} = {{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) | 1612800 | 215040 | 4 | ||||||
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) | 1612800 | 215040 | 3.8729835 | ||||||
align=center
!38 | {{CDD|nodes_10ru|split2|node|3|node|3|node_1|3|node_1|3|node|3|node_1}} = {{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) | 752640 | 107520 | 3.7416575 | ||||||
align=center
!39 | {{CDD|nodes_10ru|split2|node_1|3|node|3|node|3|node|3|node_1|3|node_1}} = {{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) | 752640 | 107520 | 3.7416575 | ||||||
align=center
!40 | {{CDD|nodes_10ru|split2|node|3|node_1|3|node|3|node|3|node_1|3|node_1}} = {{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) | 1146880 | 143360 | 3.6055512 | ||||||
align=center
!41 | {{CDD|nodes_10ru|split2|node|3|node|3|node_1|3|node|3|node_1|3|node_1}} = {{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) | 913920 | 107520 | 3.4641016 | ||||||
align=center
!42 | {{CDD|nodes_10ru|split2|node|3|node|3|node|3|node_1|3|node_1|3|node_1}} = {{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) | 365568 | 43008 | 3.3166249 | ||||||
align=center
!43 | {{CDD|nodes_10ru|split2|node_1|3|node_1|3|node_1|3|node_1|3|node|3|node}} = {{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) | 1720320 | 430080 | 6.4031243 | ||||||
align=center
!44 | {{CDD|nodes_10ru|split2|node_1|3|node_1|3|node_1|3|node|3|node_1|3|node}} = {{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) | 3225600 | 645120 | 6.0827627 | ||||||
align=center
!45 | {{CDD|nodes_10ru|split2|node_1|3|node_1|3|node|3|node_1|3|node_1|3|node}} = {{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) | 2903040 | 645120 | 5.8309517 | ||||||
align=center
!46 | {{CDD|nodes_10ru|split2|node_1|3|node|3|node_1|3|node_1|3|node_1|3|node}} = {{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) | 3225600 | 645120 | 5.6568542 | ||||||
align=center
!47 | {{CDD|nodes_10ru|split2|node|3|node_1|3|node_1|3|node_1|3|node_1|3|node}} = {{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) | 2150400 | 430080 | 5.5677648 | ||||||
align=center
!48 | {{CDD|nodes_10ru|split2|node_1|3|node_1|3|node_1|3|node|3|node|3|node_1}} = {{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) | 2150400 | 430080 | 5.7445626 | ||||||
align=center
!49 | {{CDD|nodes_10ru|split2|node_1|3|node_1|3|node|3|node_1|3|node|3|node_1}} = {{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) | 3548160 | 645120 | 5.4772258 | ||||||
align=center
!50 | {{CDD|nodes_10ru|split2|node_1|3|node|3|node_1|3|node_1|3|node|3|node_1}} = {{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) | 3548160 | 645120 | 5.291503 | ||||||
align=center
!51 | {{CDD|nodes_10ru|split2|node|3|node_1|3|node_1|3|node_1|3|node|3|node_1}} = {{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) | 2365440 | 430080 | 5.1961527 | ||||||
align=center
!52 | {{CDD|nodes_10ru|split2|node_1|3|node_1|3|node|3|node|3|node_1|3|node_1}} = {{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) | 2150400 | 430080 | 5.1961527 | ||||||
align=center
!53 | {{CDD|nodes_10ru|split2|node_1|3|node|3|node_1|3|node|3|node_1|3|node_1}} = {{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) | 3870720 | 645120 | 5 | ||||||
align=center
!54 | {{CDD|nodes_10ru|split2|node|3|node_1|3|node_1|3|node|3|node_1|3|node_1}} = {{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) | 2365440 | 430080 | 4.8989797 | ||||||
align=center
!55 | {{CDD|nodes_10ru|split2|node_1|3|node|3|node|3|node_1|3|node_1|3|node_1}} = {{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) | 2580480 | 430080 | 4.7958317 | ||||||
align=center
!56 | {{CDD|nodes_10ru|split2|node|3|node_1|3|node|3|node_1|3|node_1|3|node_1}} = {{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) | 2795520 | 430080 | 4.6904159 | ||||||
align=center
!57 | {{CDD|nodes_10ru|split2|node|3|node|3|node_1|3|node_1|3|node_1|3|node_1}} = {{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) | 1397760 | 215040 | 4.5825758 | ||||||
align=center
!58 | {{CDD|nodes_10ru|split2|node_1|3|node_1|3|node_1|3|node_1|3|node_1|3|node}} = {{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) | 5160960 | 1290240 | 7.1414285 | ||||||
align=center
!59 | {{CDD|nodes_10ru|split2|node_1|3|node_1|3|node_1|3|node_1|3|node|3|node_1}} = {{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) | 5806080 | 1290240 | 6.78233 | ||||||
align=center
!60 | {{CDD|nodes_10ru|split2|node_1|3|node_1|3|node_1|3|node|3|node_1|3|node_1}} = {{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) | 5806080 | 1290240 | 6.480741 | ||||||
align=center
!61 | {{CDD|nodes_10ru|split2|node_1|3|node_1|3|node|3|node_1|3|node_1|3|node_1}} = {{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) | 5806080 | 1290240 | 6.244998 | ||||||
align=center
!62 | {{CDD|nodes_10ru|split2|node_1|3|node|3|node_1|3|node_1|3|node_1|3|node_1}} = {{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) | 6451200 | 1290240 | 6.0827627 | ||||||
align=center
!63 | {{CDD|nodes_10ru|split2|node|3|node_1|3|node_1|3|node_1|3|node_1|3|node_1}} = {{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) | 4300800 | 860160 | 6.0000000 | ||||||
align=center
!64 | {{CDD|nodes_10ru|split2|node_1|3|node_1|3|node_1|3|node_1|3|node_1|3|node_1}} = {{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) | 2580480 | 10321920 | 7.5498347 |
= 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 | 207360 | 483840 | 483840 | 241920 | 60480 | 6720 | 240 |
align=center
|2 | {{CDD|nodea_1|3a|nodea_1|3a|nodea|3a|nodea|3a|branch|3a|nodea|3a|nodea}} | Truncated 421 (tiffy)
| | 188160 | 13440 | |||||
align=center
|3 | {{CDD|nodea|3a|nodea_1|3a|nodea|3a|nodea|3a|branch|3a|nodea|3a|nodea}} | Rectified 421 (riffy)
|19680 | 375840 | 1935360 | 3386880 | 2661120 | 1028160 | 181440 | 6720 |
align=center
|4 | {{CDD|nodea|3a|nodea|3a|nodea_1|3a|nodea|3a|branch|3a|nodea|3a|nodea}} | Birectified 421 (borfy)
|19680 | 382560 | 2600640 | 7741440 | 9918720 | 5806080 | 1451520 | 60480 |
align=center
|5 | {{CDD|nodea|3a|nodea|3a|nodea|3a|nodea_1|3a|branch|3a|nodea|3a|nodea}} | Trirectified 421 (torfy)
|19680 | 382560 | 2661120 | 9313920 | 16934400 | 14515200 | 4838400 | 241920 |
align=center
|6 | {{CDD|nodea|3a|nodea|3a|nodea|3a|nodea|3a|branch_10|3a|nodea|3a|nodea}} | Rectified 142 (buffy)
|19680 | 382560 | 2661120 | 9072000 | 16934400 | 16934400 | 7257600 | 483840 |
align=center
|7 | {{CDD|nodea|3a|nodea|3a|nodea|3a|nodea|3a|branch|3a|nodea_1|3a|nodea}} | Rectified 241 (robay)
|19680 | 313440 | 1693440 | 4717440 | 7257600 | 5322240 | 1451520 | 69120 |
align=center
|8 | {{CDD|nodea|3a|nodea|3a|nodea|3a|nodea|3a|branch|3a|nodea|3a|nodea_1}} | 241 (bay)
|17520 | 144960 | 544320 | 1209600 | 1209600 | 483840 | 69120 | 2160 |
align=center
|9 | {{CDD|nodea|3a|nodea|3a|nodea|3a|nodea|3a|branch|3a|nodea_1|3a|nodea_1}} | Truncated 241
| | 138240 | ||||||
align=center
|10 | {{CDD|nodea|3a|nodea|3a|nodea|3a|nodea|3a|branch_01lr|3a|nodea|3a|nodea}} | 142 (bif)
|2400 | 106080 | 725760 | 2298240 | 3628800 | 2419200 | 483840 | 17280 |
align=center
|11 | {{CDD|nodea|3a|nodea|3a|nodea|3a|nodea|3a|branch_11|3a|nodea|3a|nodea}} | Truncated 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 !Forms | ||||
---|---|---|---|---|
align=center
|1 | [3[8]] | {{CDD|node|split1|nodes|3ab|nodes|3ab|nodes|split2|node}} | 29 | |
align=center
|2 | [4,35,4] | {{CDD|node|4|node|3|node|3|node|3|node|3|node|3|node|4|node}} | 135 | |
align=center
|3 | [4,34,31,1] | {{CDD|nodes|split2|node|3|node|3|node|3|node|3|node|4|node}} | 191 (64 new) | |
align=center
|4 | [31,1,33,31,1] | {{CDD|nodes|split2|node|3|node|3|node|3|node|split1|nodes}} | 77 (10 new) | |
align=center
|5 | [33,3,1] | {{CDD|nodes|3ab|nodes|3ab|nodes|split2|node|3|node}} | 143 |
Regular and uniform tessellations include:
- 29 uniquely ringed forms, including:
- 7-simplex honeycomb: {3[8]} {{CDD|node_1|split1|nodes|3ab|nodes|3ab|nodes|split2|node}}
- 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}}
- 191 uniquely ringed forms, 127 shared with , 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}}
- , [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}}
- 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| = [3,3[7]]: |align=right| = [31,1,32,32,1]: |align=right| = [4,33,32,1]: |align=right| = [33,2,2]: |
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}}