Uniform 8-polytope
8-simplex |
Rectified 8-simplex
|
Truncated 8-simplex
| |||||||||
Cantellated 8-simplex
|
Runcinated 8-simplex
|
Stericated 8-simplex
| |||||||||
Pentellated 8-simplex
|
Hexicated 8-simplex
|
Heptellated 8-simplex
| |||||||||
8-orthoplex |
Rectified 8-orthoplex
|
Truncated 8-orthoplex
| |||||||||
Cantellated 8-orthoplex
|
Runcinated 8-orthoplex | ||||||||||
Hexicated 8-orthoplex |
Cantellated 8-cube | ||||||||||
Runcinated 8-cube |
Stericated 8-cube |
Pentellated 8-cube | |||||||||
Hexicated 8-cube |
Heptellated 8-cube | ||||||||||
8-cube |
Rectified 8-cube
|
Truncated 8-cube
| |||||||||
8-demicube |
Truncated 8-demicube
|
Cantellated 8-demicube | |||||||||
Runcinated 8-demicube |
Stericated 8-demicube | ||||||||||
Pentellated 8-demicube |
Hexicated 8-demicube | ||||||||||
421 |
142 |
241 |
In
A uniform 8-polytope is one which is
Regular 8-polytopes
Regular 8-polytopes can be represented by the
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
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.[1]
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.[1]
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 group | Forms | ||
---|---|---|---|---|
1 | A8 | [37] | 135 | |
2 | BC8 | [4,36] | 255 | |
3 | D8 | [35,1,1] | 191 (64 unique) | |
4 | E8 | [34,2,1] | 255 |
Selected regular and uniform 8-polytopes from each family include:
- Simplex family: A8 [37] -
- 135 uniform 8-polytopes as permutations of rings in the group diagram, including one regular:
- {37} - 8-simplex or ennea-9-tope or enneazetton -
- 135 uniform 8-polytopes as permutations of rings in the group diagram, including one regular:
- orthoplexfamily: B8 [4,36] -
- 255 uniform 8-polytopes as permutations of rings in the group diagram, including two regular ones:
- {4,36} - 8-cube or octeract-
- {36,4} - 8-orthoplex or octacross -
- 255 uniform 8-polytopes as permutations of rings in the group diagram, including two regular ones:
- Demihypercube D8 family: [35,1,1] -
- 191 uniform 8-polytopes as permutations of rings in the group diagram, including:
- {3,35,1} - 8-demicube or demiocteract, 151 - ; also as h{4,36} .
- {3,3,3,3,3,31,1} - 8-orthoplex, 511 -
- 191 uniform 8-polytopes as permutations of rings in the group diagram, including:
- E-polytope familyE8 family: [34,1,1] -
- 255 uniform 8-polytopes as permutations of rings in the group diagram, including:
- {3,3,3,3,32,1} - 421,
- {3,34,2} - the uniform 142, ,
- {3,3,34,1} - the uniform 241,
- {3,3,3,3,32,1} -
- 255 uniform 8-polytopes as permutations of rings in the group diagram, including:
Uniform prismatic forms
There are many
Uniform 8-polytope prism families | |||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|
# | Coxeter group | Coxeter-Dynkin diagram
| |||||||||
7+1 | |||||||||||
1 | A7A1 | [3,3,3,3,3,3]×[ ] | |||||||||
2 | B7A1 | [4,3,3,3,3,3]×[ ] | |||||||||
3 | D7A1 | [34,1,1]×[ ] | |||||||||
4 | E7A1 | [33,2,1]×[ ] | |||||||||
6+2 | |||||||||||
1 | A6I2(p) | [3,3,3,3,3]×[p] | |||||||||
2 | B6I2(p) | [4,3,3,3,3]×[p] | |||||||||
3 | D6I2(p) | [33,1,1]×[p] | |||||||||
4 | E6I2(p) | [3,3,3,3,3]×[p] | |||||||||
6+1+1 | |||||||||||
1 | A6A1A1 | [3,3,3,3,3]×[ ]x[ ] | |||||||||
2 | B6A1A1 | [4,3,3,3,3]×[ ]x[ ] | |||||||||
3 | D6A1A1 | [33,1,1]×[ ]x[ ] | |||||||||
4 | E6A1A1 | [3,3,3,3,3]×[ ]x[ ] | |||||||||
5+3 | |||||||||||
1 | A5A3 | [34]×[3,3] | |||||||||
2 | B5A3 | [4,33]×[3,3] | |||||||||
3 | D5A3 | [32,1,1]×[3,3] | |||||||||
4 | A5B3 | [34]×[4,3] | |||||||||
5 | B5B3 | [4,33]×[4,3] | |||||||||
6 | D5B3 | [32,1,1]×[4,3] | |||||||||
7 | A5H3 | [34]×[5,3] | |||||||||
8 | B5H3 | [4,33]×[5,3] | |||||||||
9 | D5H3 | [32,1,1]×[5,3] | |||||||||
5+2+1 | |||||||||||
1 | A5I2(p)A1 | [3,3,3]×[p]×[ ] | |||||||||
2 | B5I2(p)A1 | [4,3,3]×[p]×[ ] | |||||||||
3 | D5I2(p)A1 | [32,1,1]×[p]×[ ] | |||||||||
5+1+1+1 | |||||||||||
1 | A5A1A1A1 | [3,3,3]×[ ]×[ ]×[ ] | |||||||||
2 | B5A1A1A1 | [4,3,3]×[ ]×[ ]×[ ] | |||||||||
3 | D5A1A1A1 | [32,1,1]×[ ]×[ ]×[ ] | |||||||||
4+4 | |||||||||||
1 | A4A4 | [3,3,3]×[3,3,3] | |||||||||
2 | B4A4 | [4,3,3]×[3,3,3] | |||||||||
3 | D4A4 | [31,1,1]×[3,3,3] | |||||||||
4 | F4A4 | [3,4,3]×[3,3,3] | |||||||||
5 | H4A4 | [5,3,3]×[3,3,3] | |||||||||
6 | B4B4 | [4,3,3]×[4,3,3] | |||||||||
7 | D4B4 | [31,1,1]×[4,3,3] | |||||||||
8 | F4B4 | [3,4,3]×[4,3,3] | |||||||||
9 | H4B4 | [5,3,3]×[4,3,3] | |||||||||
10 | D4D4 | [31,1,1]×[31,1,1] | |||||||||
11 | F4D4 | [3,4,3]×[31,1,1] | |||||||||
12 | H4D4 | [5,3,3]×[31,1,1] | |||||||||
13 | F4×F4 | [3,4,3]×[3,4,3] | |||||||||
14 | H4×F4 | [5,3,3]×[3,4,3] | |||||||||
15 | H4H4 | [5,3,3]×[5,3,3] | |||||||||
4+3+1 | |||||||||||
1 | A4A3A1 | [3,3,3]×[3,3]×[ ] | |||||||||
2 | A4B3A1 | [3,3,3]×[4,3]×[ ] | |||||||||
3 | A4H3A1 | [3,3,3]×[5,3]×[ ] | |||||||||
4 | B4A3A1 | [4,3,3]×[3,3]×[ ] | |||||||||
5 | B4B3A1 | [4,3,3]×[4,3]×[ ] | |||||||||
6 | B4H3A1 | [4,3,3]×[5,3]×[ ] | |||||||||
7 | H4A3A1 | [5,3,3]×[3,3]×[ ] | |||||||||
8 | H4B3A1 | [5,3,3]×[4,3]×[ ] | |||||||||
9 | H4H3A1 | [5,3,3]×[5,3]×[ ] | |||||||||
10 | F4A3A1 | [3,4,3]×[3,3]×[ ] | |||||||||
11 | F4B3A1 | [3,4,3]×[4,3]×[ ] | |||||||||
12 | F4H3A1 | [3,4,3]×[5,3]×[ ] | |||||||||
13 | D4A3A1 | [31,1,1]×[3,3]×[ ] | |||||||||
14 | D4B3A1 | [31,1,1]×[4,3]×[ ] | |||||||||
15 | D4H3A1 | [31,1,1]×[5,3]×[ ] | |||||||||
4+2+2 | |||||||||||
... | |||||||||||
4+2+1+1 | |||||||||||
... | |||||||||||
4+1+1+1+1 | |||||||||||
... | |||||||||||
3+3+2 | |||||||||||
1 | A3A3I2(p) | [3,3]×[3,3]×[p] | |||||||||
2 | B3A3I2(p) | [4,3]×[3,3]×[p] | |||||||||
3 | H3A3I2(p) | [5,3]×[3,3]×[p] | |||||||||
4 | B3B3I2(p) | [4,3]×[4,3]×[p] | |||||||||
5 | H3B3I2(p) | [5,3]×[4,3]×[p] | |||||||||
6 | H3H3I2(p) | [5,3]×[5,3]×[p] | |||||||||
3+3+1+1 | |||||||||||
1 | A32A12 | [3,3]×[3,3]×[ ]×[ ] | |||||||||
2 | B3A3A12 | [4,3]×[3,3]×[ ]×[ ] | |||||||||
3 | H3A3A12 | [5,3]×[3,3]×[ ]×[ ] | |||||||||
4 | B3B3A12 | [4,3]×[4,3]×[ ]×[ ] | |||||||||
5 | H3B3A12 | [5,3]×[4,3]×[ ]×[ ] | |||||||||
6 | H3H3A12 | [5,3]×[5,3]×[ ]×[ ] | |||||||||
3+2+2+1 | |||||||||||
1 | A3I2(p)I2(q)A1 | [3,3]×[p]×[q]×[ ] | |||||||||
2 | B3I2(p)I2(q)A1 | [4,3]×[p]×[q]×[ ] | |||||||||
3 | H3I2(p)I2(q)A1 | [5,3]×[p]×[q]×[ ] | |||||||||
3+2+1+1+1 | |||||||||||
1 | A3I2(p)A13 | [3,3]×[p]×[ ]x[ ]×[ ] | |||||||||
2 | B3I2(p)A13 | [4,3]×[p]×[ ]x[ ]×[ ] | |||||||||
3 | H3I2(p)A13 | [5,3]×[p]×[ ]x[ ]×[ ] | |||||||||
3+1+1+1+1+1 | |||||||||||
1 | A3A15 | [3,3]×[ ]x[ ]×[ ]x[ ]×[ ] | |||||||||
2 | B3A15 | [4,3]×[ ]x[ ]×[ ]x[ ]×[ ] | |||||||||
3 | H3A15 | [5,3]×[ ]x[ ]×[ ]x[ ]×[ ] | |||||||||
2+2+2+2 | |||||||||||
1 | I2(p)I2(q)I2(r)I2(s) | [p]×[q]×[r]×[s] | |||||||||
2+2+2+1+1 | |||||||||||
1 | I2(p)I2(q)I2(r)A12 | [p]×[q]×[r]×[ ]×[ ] | |||||||||
2+2+1+1+1+1 | |||||||||||
2 | I2(p)I2(q)A14 | [p]×[q]×[ ]×[ ]×[ ]×[ ] | |||||||||
2+1+1+1+1+1+1 | |||||||||||
1 | I2(p)A16 | [p]×[ ]×[ ]×[ ]×[ ]×[ ]×[ ] | |||||||||
1+1+1+1+1+1+1+1 | |||||||||||
1 | A18 | [ ]×[ ]×[ ]×[ ]×[ ]×[ ]×[ ]×[ ] |
The A8 family
The A8 family has symmetry of order 362880 (9 factorial).
There are 135 forms based on all permutations of the
See also a
A8 uniform polytopes | ||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|
# | Coxeter-Dynkin diagram
|
Truncation indices |
Johnson name | Basepoint | Element counts | |||||||
7 | 6 | 5 | 4 | 3 | 2 | 1 | 0 | |||||
1 |
|
t0 | 8-simplex (ene) | (0,0,0,0,0,0,0,0,1) | 9 | 36 | 84 | 126 | 126 | 84 | 36 | 9 |
2 |
|
t1 | Rectified 8-simplex (rene)
|
(0,0,0,0,0,0,0,1,1) | 18 | 108 | 336 | 630 | 576 | 588 | 252 | 36 |
3 |
|
t2 | Birectified 8-simplex (bene)
|
(0,0,0,0,0,0,1,1,1) | 18 | 144 | 588 | 1386 | 2016 | 1764 | 756 | 84 |
4 |
|
t3 | Trirectified 8-simplex (trene)
|
(0,0,0,0,0,1,1,1,1) | 1260 | 126 | ||||||
5 |
|
t0,1 | Truncated 8-simplex (tene)
|
(0,0,0,0,0,0,0,1,2) | 288 | 72 | ||||||
6 |
|
t0,2 | Cantellated 8-simplex
|
(0,0,0,0,0,0,1,1,2) | 1764 | 252 | ||||||
7 |
|
t1,2 | Bitruncated 8-simplex
|
(0,0,0,0,0,0,1,2,2) | 1008 | 252 | ||||||
8 |
|
t0,3 | Runcinated 8-simplex
|
(0,0,0,0,0,1,1,1,2) | 4536 | 504 | ||||||
9 |
|
t1,3 | Bicantellated 8-simplex
|
(0,0,0,0,0,1,1,2,2) | 5292 | 756 | ||||||
10 |
|
t2,3 | Tritruncated 8-simplex
|
(0,0,0,0,0,1,2,2,2) | 2016 | 504 | ||||||
11 |
|
t0,4 | Stericated 8-simplex
|
(0,0,0,0,1,1,1,1,2) | 6300 | 630 | ||||||
12 |
|
t1,4 | Biruncinated 8-simplex
|
(0,0,0,0,1,1,1,2,2) | 11340 | 1260 | ||||||
13 |
|
t2,4 | Tricantellated 8-simplex
|
(0,0,0,0,1,1,2,2,2) | 8820 | 1260 | ||||||
14 |
|
t3,4 | Quadritruncated 8-simplex
|
(0,0,0,0,1,2,2,2,2) | 2520 | 630 | ||||||
15 |
|
t0,5 | Pentellated 8-simplex
|
(0,0,0,1,1,1,1,1,2) | 5040 | 504 | ||||||
16 |
|
t1,5 | Bistericated 8-simplex
|
(0,0,0,1,1,1,1,2,2) | 12600 | 1260 | ||||||
17 |
|
t2,5 | Triruncinated 8-simplex
|
(0,0,0,1,1,1,2,2,2) | 15120 | 1680 | ||||||
18 |
|
t0,6 | Hexicated 8-simplex
|
(0,0,1,1,1,1,1,1,2) | 2268 | 252 | ||||||
19 |
|
t1,6 | Bipentellated 8-simplex
|
(0,0,1,1,1,1,1,2,2) | 7560 | 756 | ||||||
20 |
|
t0,7 | Heptellated 8-simplex
|
(0,1,1,1,1,1,1,1,2) | 504 | 72 | ||||||
21 |
|
t0,1,2 | Cantitruncated 8-simplex
|
(0,0,0,0,0,0,1,2,3) | 2016 | 504 | ||||||
22 |
|
t0,1,3 | Runcitruncated 8-simplex
|
(0,0,0,0,0,1,1,2,3) | 9828 | 1512 | ||||||
23 |
|
t0,2,3 | Runcicantellated 8-simplex
|
(0,0,0,0,0,1,2,2,3) | 6804 | 1512 | ||||||
24 |
|
t1,2,3 | Bicantitruncated 8-simplex
|
(0,0,0,0,0,1,2,3,3) | 6048 | 1512 | ||||||
25 |
|
t0,1,4 | Steritruncated 8-simplex
|
(0,0,0,0,1,1,1,2,3) | 20160 | 2520 | ||||||
26 |
|
t0,2,4 | Stericantellated 8-simplex
|
(0,0,0,0,1,1,2,2,3) | 26460 | 3780 | ||||||
27 |
|
t1,2,4 | Biruncitruncated 8-simplex
|
(0,0,0,0,1,1,2,3,3) | 22680 | 3780 | ||||||
28 |
|
t0,3,4 | Steriruncinated 8-simplex
|
(0,0,0,0,1,2,2,2,3) | 12600 | 2520 | ||||||
29 |
|
t1,3,4 | Biruncicantellated 8-simplex
|
(0,0,0,0,1,2,2,3,3) | 18900 | 3780 | ||||||
30 |
|
t2,3,4 | Tricantitruncated 8-simplex
|
(0,0,0,0,1,2,3,3,3) | 10080 | 2520 | ||||||
31 |
|
t0,1,5 | Pentitruncated 8-simplex | (0,0,0,1,1,1,1,2,3) | 21420 | 2520 | ||||||
32 |
|
t0,2,5 | Penticantellated 8-simplex | (0,0,0,1,1,1,2,2,3) | 42840 | 5040 | ||||||
33 |
|
t1,2,5 | Bisteritruncated 8-simplex
|
(0,0,0,1,1,1,2,3,3) | 35280 | 5040 | ||||||
34 |
|
t0,3,5 | Pentiruncinated 8-simplex | (0,0,0,1,1,2,2,2,3) | 37800 | 5040 | ||||||
35 |
|
t1,3,5 | Bistericantellated 8-simplex
|
(0,0,0,1,1,2,2,3,3) | 52920 | 7560 | ||||||
36 |
|
t2,3,5 | Triruncitruncated 8-simplex | (0,0,0,1,1,2,3,3,3) | 27720 | 5040 | ||||||
37 |
|
t0,4,5 | Pentistericated 8-simplex | (0,0,0,1,2,2,2,2,3) | 13860 | 2520 | ||||||
38 |
|
t1,4,5 | Bisteriruncinated 8-simplex
|
(0,0,0,1,2,2,2,3,3) | 30240 | 5040 | ||||||
39 |
|
t0,1,6 | Hexitruncated 8-simplex | (0,0,1,1,1,1,1,2,3) | 12096 | 1512 | ||||||
40 |
|
t0,2,6 | Hexicantellated 8-simplex | (0,0,1,1,1,1,2,2,3) | 34020 | 3780 | ||||||
41 |
|
t1,2,6 | Bipentitruncated 8-simplex | (0,0,1,1,1,1,2,3,3) | 26460 | 3780 | ||||||
42 |
|
t0,3,6 | Hexiruncinated 8-simplex | (0,0,1,1,1,2,2,2,3) | 45360 | 5040 | ||||||
43 |
|
t1,3,6 | Bipenticantellated 8-simplex | (0,0,1,1,1,2,2,3,3) | 60480 | 7560 | ||||||
44 |
|
t0,4,6 | Hexistericated 8-simplex | (0,0,1,1,2,2,2,2,3) | 30240 | 3780 | ||||||
45 |
|
t0,5,6 | Hexipentellated 8-simplex | (0,0,1,2,2,2,2,2,3) | 9072 | 1512 | ||||||
46 |
|
t0,1,7 | Heptitruncated 8-simplex | (0,1,1,1,1,1,1,2,3) | 3276 | 504 | ||||||
47 |
|
t0,2,7 | Hepticantellated 8-simplex | (0,1,1,1,1,1,2,2,3) | 12852 | 1512 | ||||||
48 |
|
t0,3,7 | Heptiruncinated 8-simplex | (0,1,1,1,1,2,2,2,3) | 23940 | 2520 | ||||||
49 |
|
t0,1,2,3 | Runcicantitruncated 8-simplex
|
(0,0,0,0,0,1,2,3,4) | 12096 | 3024 | ||||||
50 |
|
t0,1,2,4 | Stericantitruncated 8-simplex
|
(0,0,0,0,1,1,2,3,4) | 45360 | 7560 | ||||||
51 |
|
t0,1,3,4 | Steriruncitruncated 8-simplex
|
(0,0,0,0,1,2,2,3,4) | 34020 | 7560 | ||||||
52 |
|
t0,2,3,4 | Steriruncicantellated 8-simplex
|
(0,0,0,0,1,2,3,3,4) | 34020 | 7560 | ||||||
53 |
|
t1,2,3,4 | Biruncicantitruncated 8-simplex
|
(0,0,0,0,1,2,3,4,4) | 30240 | 7560 | ||||||
54 |
|
t0,1,2,5 | Penticantitruncated 8-simplex | (0,0,0,1,1,1,2,3,4) | 70560 | 10080 | ||||||
55 |
|
t0,1,3,5 | Pentiruncitruncated 8-simplex | (0,0,0,1,1,2,2,3,4) | 98280 | 15120 | ||||||
56 |
|
t0,2,3,5 | Pentiruncicantellated 8-simplex | (0,0,0,1,1,2,3,3,4) | 90720 | 15120 | ||||||
57 |
|
t1,2,3,5 | Bistericantitruncated 8-simplex
|
(0,0,0,1,1,2,3,4,4) | 83160 | 15120 | ||||||
58 |
|
t0,1,4,5 | Pentisteritruncated 8-simplex | (0,0,0,1,2,2,2,3,4) | 50400 | 10080 | ||||||
59 |
|
t0,2,4,5 | Pentistericantellated 8-simplex | (0,0,0,1,2,2,3,3,4) | 83160 | 15120 | ||||||
60 |
|
t1,2,4,5 | Bisteriruncitruncated 8-simplex
|
(0,0,0,1,2,2,3,4,4) | 68040 | 15120 | ||||||
61 |
|
t0,3,4,5 | Pentisteriruncinated 8-simplex | (0,0,0,1,2,3,3,3,4) | 50400 | 10080 | ||||||
62 |
|
t1,3,4,5 | Bisteriruncicantellated 8-simplex
|
(0,0,0,1,2,3,3,4,4) | 75600 | 15120 | ||||||
63 |
|
t2,3,4,5 | Triruncicantitruncated 8-simplex
|
(0,0,0,1,2,3,4,4,4) | 40320 | 10080 | ||||||
64 |
|
t0,1,2,6 | Hexicantitruncated 8-simplex | (0,0,1,1,1,1,2,3,4) | 52920 | 7560 | ||||||
65 |
|
t0,1,3,6 | Hexiruncitruncated 8-simplex | (0,0,1,1,1,2,2,3,4) | 113400 | 15120 | ||||||
66 |
|
t0,2,3,6 | Hexiruncicantellated 8-simplex | (0,0,1,1,1,2,3,3,4) | 98280 | 15120 | ||||||
67 |
|
t1,2,3,6 | Bipenticantitruncated 8-simplex | (0,0,1,1,1,2,3,4,4) | 90720 | 15120 | ||||||
68 |
|
t0,1,4,6 | Hexisteritruncated 8-simplex | (0,0,1,1,2,2,2,3,4) | 105840 | 15120 | ||||||
69 |
|
t0,2,4,6 | Hexistericantellated 8-simplex | (0,0,1,1,2,2,3,3,4) | 158760 | 22680 | ||||||
70 |
|
t1,2,4,6 | Bipentiruncitruncated 8-simplex | (0,0,1,1,2,2,3,4,4) | 136080 | 22680 | ||||||
71 |
|
t0,3,4,6 | Hexisteriruncinated 8-simplex | (0,0,1,1,2,3,3,3,4) | 90720 | 15120 | ||||||
72 |
|
t1,3,4,6 | Bipentiruncicantellated 8-simplex | (0,0,1,1,2,3,3,4,4) | 136080 | 22680 | ||||||
73 |
|
t0,1,5,6 | Hexipentitruncated 8-simplex | (0,0,1,2,2,2,2,3,4) | 41580 | 7560 | ||||||
74 |
|
t0,2,5,6 | Hexipenticantellated 8-simplex | (0,0,1,2,2,2,3,3,4) | 98280 | 15120 | ||||||
75 |
|
t1,2,5,6 | Bipentisteritruncated 8-simplex | (0,0,1,2,2,2,3,4,4) | 75600 | 15120 | ||||||
76 |
|
t0,3,5,6 | Hexipentiruncinated 8-simplex | (0,0,1,2,2,3,3,3,4) | 98280 | 15120 | ||||||
77 |
|
t0,4,5,6 | Hexipentistericated 8-simplex | (0,0,1,2,3,3,3,3,4) | 41580 | 7560 | ||||||
78 |
|
t0,1,2,7 | Hepticantitruncated 8-simplex | (0,1,1,1,1,1,2,3,4) | 18144 | 3024 | ||||||
79 |
|
t0,1,3,7 | Heptiruncitruncated 8-simplex | (0,1,1,1,1,2,2,3,4) | 56700 | 7560 | ||||||
80 |
|
t0,2,3,7 | Heptiruncicantellated 8-simplex | (0,1,1,1,1,2,3,3,4) | 45360 | 7560 | ||||||
81 |
|
t0,1,4,7 | Heptisteritruncated 8-simplex | (0,1,1,1,2,2,2,3,4) | 80640 | 10080 | ||||||
82 |
|
t0,2,4,7 | Heptistericantellated 8-simplex | (0,1,1,1,2,2,3,3,4) | 113400 | 15120 | ||||||
83 |
|
t0,3,4,7 | Heptisteriruncinated 8-simplex | (0,1,1,1,2,3,3,3,4) | 60480 | 10080 | ||||||
84 |
|
t0,1,5,7 | Heptipentitruncated 8-simplex | (0,1,1,2,2,2,2,3,4) | 56700 | 7560 | ||||||
85 |
|
t0,2,5,7 | Heptipenticantellated 8-simplex | (0,1,1,2,2,2,3,3,4) | 120960 | 15120 | ||||||
86 |
|
t0,1,6,7 | Heptihexitruncated 8-simplex | (0,1,2,2,2,2,2,3,4) | 18144 | 3024 | ||||||
87 |
|
t0,1,2,3,4 | Steriruncicantitruncated 8-simplex
|
(0,0,0,0,1,2,3,4,5) | 60480 | 15120 | ||||||
88 |
|
t0,1,2,3,5 | Pentiruncicantitruncated 8-simplex | (0,0,0,1,1,2,3,4,5) | 166320 | 30240 | ||||||
89 |
|
t0,1,2,4,5 | Pentistericantitruncated 8-simplex | (0,0,0,1,2,2,3,4,5) | 136080 | 30240 | ||||||
90 |
|
t0,1,3,4,5 | Pentisteriruncitruncated 8-simplex | (0,0,0,1,2,3,3,4,5) | 136080 | 30240 | ||||||
91 |
|
t0,2,3,4,5 | Pentisteriruncicantellated 8-simplex | (0,0,0,1,2,3,4,4,5) | 136080 | 30240 | ||||||
92 |
|
t1,2,3,4,5 | Bisteriruncicantitruncated 8-simplex
|
(0,0,0,1,2,3,4,5,5) | 120960 | 30240 | ||||||
93 |
|
t0,1,2,3,6 | Hexiruncicantitruncated 8-simplex | (0,0,1,1,1,2,3,4,5) | 181440 | 30240 | ||||||
94 |
|
t0,1,2,4,6 | Hexistericantitruncated 8-simplex | (0,0,1,1,2,2,3,4,5) | 272160 | 45360 | ||||||
95 |
|
t0,1,3,4,6 | Hexisteriruncitruncated 8-simplex | (0,0,1,1,2,3,3,4,5) | 249480 | 45360 | ||||||
96 |
|
t0,2,3,4,6 | Hexisteriruncicantellated 8-simplex | (0,0,1,1,2,3,4,4,5) | 249480 | 45360 | ||||||
97 |
|
t1,2,3,4,6 | Bipentiruncicantitruncated 8-simplex | (0,0,1,1,2,3,4,5,5) | 226800 | 45360 | ||||||
98 |
|
t0,1,2,5,6 | Hexipenticantitruncated 8-simplex | (0,0,1,2,2,2,3,4,5) | 151200 | 30240 | ||||||
99 |
|
t0,1,3,5,6 | Hexipentiruncitruncated 8-simplex | (0,0,1,2,2,3,3,4,5) | 249480 | 45360 | ||||||
100 |
|
t0,2,3,5,6 | Hexipentiruncicantellated 8-simplex | (0,0,1,2,2,3,4,4,5) | 226800 | 45360 | ||||||
101 |
|
t1,2,3,5,6 | Bipentistericantitruncated 8-simplex | (0,0,1,2,2,3,4,5,5) | 204120 | 45360 | ||||||
102 |
|
t0,1,4,5,6 | Hexipentisteritruncated 8-simplex | (0,0,1,2,3,3,3,4,5) | 151200 | 30240 | ||||||
103 |
|
t0,2,4,5,6 | Hexipentistericantellated 8-simplex | (0,0,1,2,3,3,4,4,5) | 249480 | 45360 | ||||||
104 |
|
t0,3,4,5,6 | Hexipentisteriruncinated 8-simplex | (0,0,1,2,3,4,4,4,5) | 151200 | 30240 | ||||||
105 |
|
t0,1,2,3,7 | Heptiruncicantitruncated 8-simplex | (0,1,1,1,1,2,3,4,5) | 83160 | 15120 | ||||||
106 |
|
t0,1,2,4,7 | Heptistericantitruncated 8-simplex | (0,1,1,1,2,2,3,4,5) | 196560 | 30240 | ||||||
107 |
|
t0,1,3,4,7 | Heptisteriruncitruncated 8-simplex | (0,1,1,1,2,3,3,4,5) | 166320 | 30240 | ||||||
108 |
|
t0,2,3,4,7 | Heptisteriruncicantellated 8-simplex | (0,1,1,1,2,3,4,4,5) | 166320 | 30240 | ||||||
109 |
|
t0,1,2,5,7 | Heptipenticantitruncated 8-simplex | (0,1,1,2,2,2,3,4,5) | 196560 | 30240 | ||||||
110 |
|
t0,1,3,5,7 | Heptipentiruncitruncated 8-simplex | (0,1,1,2,2,3,3,4,5) | 294840 | 45360 | ||||||
111 |
|
t0,2,3,5,7 | Heptipentiruncicantellated 8-simplex | (0,1,1,2,2,3,4,4,5) | 272160 | 45360 | ||||||
112 |
|
t0,1,4,5,7 | Heptipentisteritruncated 8-simplex | (0,1,1,2,3,3,3,4,5) | 166320 | 30240 | ||||||
113 |
|
t0,1,2,6,7 | Heptihexicantitruncated 8-simplex | (0,1,2,2,2,2,3,4,5) | 83160 | 15120 | ||||||
114 |
|
t0,1,3,6,7 | Heptihexiruncitruncated 8-simplex | (0,1,2,2,2,3,3,4,5) | 196560 | 30240 | ||||||
115 |
|
t0,1,2,3,4,5 | Pentisteriruncicantitruncated 8-simplex | (0,0,0,1,2,3,4,5,6) | 241920 | 60480 | ||||||
116 |
|
t0,1,2,3,4,6 | Hexisteriruncicantitruncated 8-simplex | (0,0,1,1,2,3,4,5,6) | 453600 | 90720 | ||||||
117 |
|
t0,1,2,3,5,6 | Hexipentiruncicantitruncated 8-simplex | (0,0,1,2,2,3,4,5,6) | 408240 | 90720 | ||||||
118 |
|
t0,1,2,4,5,6 | Hexipentistericantitruncated 8-simplex | (0,0,1,2,3,3,4,5,6) | 408240 | 90720 | ||||||
119 |
|
t0,1,3,4,5,6 | Hexipentisteriruncitruncated 8-simplex | (0,0,1,2,3,4,4,5,6) | 408240 | 90720 | ||||||
120 |
|
t0,2,3,4,5,6 | Hexipentisteriruncicantellated 8-simplex | (0,0,1,2,3,4,5,5,6) | 408240 | 90720 | ||||||
121 |
|
t1,2,3,4,5,6 | Bipentisteriruncicantitruncated 8-simplex | (0,0,1,2,3,4,5,6,6) | 362880 | 90720 | ||||||
122 |
|
t0,1,2,3,4,7 | Heptisteriruncicantitruncated 8-simplex | (0,1,1,1,2,3,4,5,6) | 302400 | 60480 | ||||||
123 |
|
t0,1,2,3,5,7 | Heptipentiruncicantitruncated 8-simplex | (0,1,1,2,2,3,4,5,6) | 498960 | 90720 | ||||||
124 |
|
t0,1,2,4,5,7 | Heptipentistericantitruncated 8-simplex | (0,1,1,2,3,3,4,5,6) | 453600 | 90720 | ||||||
125 |
|
t0,1,3,4,5,7 | Heptipentisteriruncitruncated 8-simplex | (0,1,1,2,3,4,4,5,6) | 453600 | 90720 | ||||||
126 |
|
t0,2,3,4,5,7 | Heptipentisteriruncicantellated 8-simplex | (0,1,1,2,3,4,5,5,6) | 453600 | 90720 | ||||||
127 |
|
t0,1,2,3,6,7 | Heptihexiruncicantitruncated 8-simplex | (0,1,2,2,2,3,4,5,6) | 302400 | 60480 | ||||||
128 |
|
t0,1,2,4,6,7 | Heptihexistericantitruncated 8-simplex | (0,1,2,2,3,3,4,5,6) | 498960 | 90720 | ||||||
129 |
|
t0,1,3,4,6,7 | Heptihexisteriruncitruncated 8-simplex | (0,1,2,2,3,4,4,5,6) | 453600 | 90720 | ||||||
130 |
|
t0,1,2,5,6,7 | Heptihexipenticantitruncated 8-simplex | (0,1,2,3,3,3,4,5,6) | 302400 | 60480 | ||||||
131 |
|
t0,1,2,3,4,5,6 | Hexipentisteriruncicantitruncated 8-simplex | (0,0,1,2,3,4,5,6,7) | 725760 | 181440 | ||||||
132 |
|
t0,1,2,3,4,5,7 | Heptipentisteriruncicantitruncated 8-simplex | (0,1,1,2,3,4,5,6,7) | 816480 | 181440 | ||||||
133 |
|
t0,1,2,3,4,6,7 | Heptihexisteriruncicantitruncated 8-simplex | (0,1,2,2,3,4,5,6,7) | 816480 | 181440 | ||||||
134 |
|
t0,1,2,3,5,6,7 | Heptihexipentiruncicantitruncated 8-simplex | (0,1,2,3,3,4,5,6,7) | 816480 | 181440 | ||||||
135 |
|
t0,1,2,3,4,5,6,7 | Omnitruncated 8-simplex
|
(0,1,2,3,4,5,6,7,8) | 1451520 | 362880 |
The B8 family
The B8 family has symmetry of order 10321920 (8
See also a
B8 uniform polytopes | ||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|
# | Coxeter-Dynkin diagram
|
Schläfli symbol |
Name | Element counts | ||||||||
7 | 6 | 5 | 4 | 3 | 2 | 1 | 0 | |||||
1 | t0{36,4} | 8-orthoplex Diacosipentacontahexazetton (ek) |
256 | 1024 | 1792 | 1792 | 1120 | 448 | 112 | 16 | ||
2 | t1{36,4} | Rectified 8-orthoplex Rectified diacosipentacontahexazetton (rek) |
272 | 3072 | 8960 | 12544 | 10080 | 4928 | 1344 | 112 | ||
3 | t2{36,4} | Birectified 8-orthoplex Birectified diacosipentacontahexazetton (bark) |
272 | 3184 | 16128 | 34048 | 36960 | 22400 | 6720 | 448 | ||
4 | t3{36,4} | Trirectified 8-orthoplex Trirectified diacosipentacontahexazetton (tark) |
272 | 3184 | 16576 | 48384 | 71680 | 53760 | 17920 | 1120 | ||
5 | t3{4,36} | Trirectified 8-cube Trirectified octeract (tro) |
272 | 3184 | 16576 | 47712 | 80640 | 71680 | 26880 | 1792 | ||
6 | t2{4,36} | Birectified 8-cube Birectified octeract (bro) |
272 | 3184 | 14784 | 36960 | 55552 | 50176 | 21504 | 1792 | ||
7 | t1{4,36} | Rectified 8-cube Rectified octeract (recto) |
272 | 2160 | 7616 | 15456 | 19712 | 16128 | 7168 | 1024 | ||
8 | t0{4,36} | 8-cube Octeract (octo) |
16 | 112 | 448 | 1120 | 1792 | 1792 | 1024 | 256 | ||
9 | t0,1{36,4} | Truncated 8-orthoplex Truncated diacosipentacontahexazetton (tek) |
1456 | 224 | ||||||||
10 | t0,2{36,4} | Cantellated 8-orthoplex Small rhombated diacosipentacontahexazetton (srek) |
14784 | 1344 | ||||||||
11 | t1,2{36,4} | Bitruncated 8-orthoplex Bitruncated diacosipentacontahexazetton (batek) |
8064 | 1344 | ||||||||
12 | t0,3{36,4} | Runcinated 8-orthoplex Small prismated diacosipentacontahexazetton (spek) |
60480 | 4480 | ||||||||
13 | t1,3{36,4} | Bicantellated 8-orthoplex Small birhombated diacosipentacontahexazetton (sabork) |
67200 | 6720 | ||||||||
14 | t2,3{36,4} | Tritruncated 8-orthoplex Tritruncated diacosipentacontahexazetton (tatek) |
24640 | 4480 | ||||||||
15 | t0,4{36,4} | Stericated 8-orthoplex Small cellated diacosipentacontahexazetton (scak) |
125440 | 8960 | ||||||||
16 | t1,4{36,4} | Biruncinated 8-orthoplex Small biprismated diacosipentacontahexazetton (sabpek) |
215040 | 17920 | ||||||||
17 | t2,4{36,4} | Tricantellated 8-orthoplex Small trirhombated diacosipentacontahexazetton (satrek) |
161280 | 17920 | ||||||||
18 | t3,4{4,36} | Quadritruncated 8-cube Octeractidiacosipentacontahexazetton (oke) |
44800 | 8960 | ||||||||
19 | t0,5{36,4} | Pentellated 8-orthoplex Small terated diacosipentacontahexazetton (setek) |
134400 | 10752 | ||||||||
20 | t1,5{36,4} | Bistericated 8-orthoplex Small bicellated diacosipentacontahexazetton (sibcak) |
322560 | 26880 | ||||||||
21 | t2,5{4,36} | Triruncinated 8-cube Small triprismato-octeractidiacosipentacontahexazetton (sitpoke) |
376320 | 35840 | ||||||||
22 | t2,4{4,36} | Tricantellated 8-cube Small trirhombated octeract (satro) |
215040 | 26880 | ||||||||
23 | t2,3{4,36} | Tritruncated 8-cube Tritruncated octeract (tato) |
48384 | 10752 | ||||||||
24 | t0,6{36,4} | Hexicated 8-orthoplex Small petated diacosipentacontahexazetton (supek) |
64512 | 7168 | ||||||||
25 | t1,6{4,36} | Bipentellated 8-cube Small biteri-octeractidiacosipentacontahexazetton (sabtoke) |
215040 | 21504 | ||||||||
26 | t1,5{4,36} | Bistericated 8-cube Small bicellated octeract (sobco) |
358400 | 35840 | ||||||||
27 | t1,4{4,36} | Biruncinated 8-cube Small biprismated octeract (sabepo) |
322560 | 35840 | ||||||||
28 | t1,3{4,36} | Bicantellated 8-cube Small birhombated octeract (subro) |
150528 | 21504 | ||||||||
29 | t1,2{4,36} | Bitruncated 8-cube Bitruncated octeract (bato) |
28672 | 7168 | ||||||||
30 | t0,7{4,36} | Heptellated 8-cube Small exi-octeractidiacosipentacontahexazetton (saxoke) |
14336 | 2048 | ||||||||
31 | t0,6{4,36} | Hexicated 8-cube Small petated octeract (supo) |
64512 | 7168 | ||||||||
32 | t0,5{4,36} | Pentellated 8-cube Small terated octeract (soto) |
143360 | 14336 | ||||||||
33 | t0,4{4,36} | Stericated 8-cube Small cellated octeract (soco) |
179200 | 17920 | ||||||||
34 | t0,3{4,36} | Runcinated 8-cube Small prismated octeract (sopo) |
129024 | 14336 | ||||||||
35 | t0,2{4,36} | Cantellated 8-cube Small rhombated octeract (soro) |
50176 | 7168 | ||||||||
36 | t0,1{4,36} | Truncated 8-cube Truncated octeract (tocto) |
8192 | 2048 | ||||||||
37 | t0,1,2{36,4} | Cantitruncated 8-orthoplex Great rhombated diacosipentacontahexazetton |
16128 | 2688 | ||||||||
38 | t0,1,3{36,4} | Runcitruncated 8-orthoplex Prismatotruncated diacosipentacontahexazetton |
127680 | 13440 | ||||||||
39 | t0,2,3{36,4} | Runcicantellated 8-orthoplex Prismatorhombated diacosipentacontahexazetton |
80640 | 13440 | ||||||||
40 | t1,2,3{36,4} | Bicantitruncated 8-orthoplex Great birhombated diacosipentacontahexazetton |
73920 | 13440 | ||||||||
41 | t0,1,4{36,4} | Steritruncated 8-orthoplex Cellitruncated diacosipentacontahexazetton |
394240 | 35840 | ||||||||
42 | t0,2,4{36,4} | Stericantellated 8-orthoplex Cellirhombated diacosipentacontahexazetton |
483840 | 53760 | ||||||||
43 | t1,2,4{36,4} | Biruncitruncated 8-orthoplex Biprismatotruncated diacosipentacontahexazetton |
430080 | 53760 | ||||||||
44 | t0,3,4{36,4} | Steriruncinated 8-orthoplex Celliprismated diacosipentacontahexazetton |
215040 | 35840 | ||||||||
45 | t1,3,4{36,4} | Biruncicantellated 8-orthoplex Biprismatorhombated diacosipentacontahexazetton |
322560 | 53760 | ||||||||
46 | t2,3,4{36,4} | Tricantitruncated 8-orthoplex Great trirhombated diacosipentacontahexazetton |
179200 | 35840 | ||||||||
47 | t0,1,5{36,4} | Pentitruncated 8-orthoplex Teritruncated diacosipentacontahexazetton |
564480 | 53760 | ||||||||
48 | t0,2,5{36,4} | Penticantellated 8-orthoplex Terirhombated diacosipentacontahexazetton |
1075200 | 107520 | ||||||||
49 | t1,2,5{36,4} | Bisteritruncated 8-orthoplex Bicellitruncated diacosipentacontahexazetton |
913920 | 107520 | ||||||||
50 | t0,3,5{36,4} | Pentiruncinated 8-orthoplex Teriprismated diacosipentacontahexazetton |
913920 | 107520 | ||||||||
51 | t1,3,5{36,4} | Bistericantellated 8-orthoplex Bicellirhombated diacosipentacontahexazetton |
1290240 | 161280 | ||||||||
52 | t2,3,5{36,4} | Triruncitruncated 8-orthoplex Triprismatotruncated diacosipentacontahexazetton |
698880 | 107520 | ||||||||
53 | t0,4,5{36,4} | Pentistericated 8-orthoplex Tericellated diacosipentacontahexazetton |
322560 | 53760 | ||||||||
54 | t1,4,5{36,4} | Bisteriruncinated 8-orthoplex Bicelliprismated diacosipentacontahexazetton |
698880 | 107520 | ||||||||
55 | t2,3,5{4,36} | Triruncitruncated 8-cube Triprismatotruncated octeract |
645120 | 107520 | ||||||||
56 | t2,3,4{4,36} | Tricantitruncated 8-cube Great trirhombated octeract |
241920 | 53760 | ||||||||
57 | t0,1,6{36,4} | Hexitruncated 8-orthoplex Petitruncated diacosipentacontahexazetton |
344064 | 43008 | ||||||||
58 | t0,2,6{36,4} | Hexicantellated 8-orthoplex Petirhombated diacosipentacontahexazetton |
967680 | 107520 | ||||||||
59 | t1,2,6{36,4} | Bipentitruncated 8-orthoplex Biteritruncated diacosipentacontahexazetton |
752640 | 107520 | ||||||||
60 | t0,3,6{36,4} | Hexiruncinated 8-orthoplex Petiprismated diacosipentacontahexazetton |
1290240 | 143360 | ||||||||
61 | t1,3,6{36,4} | Bipenticantellated 8-orthoplex Biterirhombated diacosipentacontahexazetton |
1720320 | 215040 | ||||||||
62 | t1,4,5{4,36} | Bisteriruncinated 8-cube Bicelliprismated octeract |
860160 | 143360 | ||||||||
63 | t0,4,6{36,4} | Hexistericated 8-orthoplex Peticellated diacosipentacontahexazetton |
860160 | 107520 | ||||||||
64 | t1,3,6{4,36} | Bipenticantellated 8-cube Biterirhombated octeract |
1720320 | 215040 | ||||||||
65 | t1,3,5{4,36} | Bistericantellated 8-cube Bicellirhombated octeract |
1505280 | 215040 | ||||||||
66 | t1,3,4{4,36} | Biruncicantellated 8-cube Biprismatorhombated octeract |
537600 | 107520 | ||||||||
67 | t0,5,6{36,4} | Hexipentellated 8-orthoplex Petiterated diacosipentacontahexazetton |
258048 | 43008 | ||||||||
68 | t1,2,6{4,36} | Bipentitruncated 8-cube Biteritruncated octeract |
752640 | 107520 | ||||||||
69 | t1,2,5{4,36} | Bisteritruncated 8-cube Bicellitruncated octeract |
1003520 | 143360 | ||||||||
70 | t1,2,4{4,36} | Biruncitruncated 8-cube Biprismatotruncated octeract |
645120 | 107520 | ||||||||
71 | t1,2,3{4,36} | Bicantitruncated 8-cube Great birhombated octeract |
172032 | 43008 | ||||||||
72 | t0,1,7{36,4} | Heptitruncated 8-orthoplex Exitruncated diacosipentacontahexazetton |
93184 | 14336 | ||||||||
73 | t0,2,7{36,4} | Hepticantellated 8-orthoplex Exirhombated diacosipentacontahexazetton |
365568 | 43008 | ||||||||
74 | t0,5,6{4,36} | Hexipentellated 8-cube Petiterated octeract |
258048 | 43008 | ||||||||
75 | t0,3,7{36,4} | Heptiruncinated 8-orthoplex Exiprismated diacosipentacontahexazetton |
680960 | 71680 | ||||||||
76 | t0,4,6{4,36} | Hexistericated 8-cube Peticellated octeract |
860160 | 107520 | ||||||||
77 | t0,4,5{4,36} | Pentistericated 8-cube Tericellated octeract |
394240 | 71680 | ||||||||
78 | t0,3,7{4,36} | Heptiruncinated 8-cube Exiprismated octeract |
680960 | 71680 | ||||||||
79 | t0,3,6{4,36} | Hexiruncinated 8-cube Petiprismated octeract |
1290240 | 143360 | ||||||||
80 | t0,3,5{4,36} | Pentiruncinated 8-cube Teriprismated octeract |
1075200 | 143360 | ||||||||
81 | t0,3,4{4,36} | Steriruncinated 8-cube Celliprismated octeract |
358400 | 71680 | ||||||||
82 | t0,2,7{4,36} | Hepticantellated 8-cube Exirhombated octeract |
365568 | 43008 | ||||||||
83 | t0,2,6{4,36} | Hexicantellated 8-cube Petirhombated octeract |
967680 | 107520 | ||||||||
84 | t0,2,5{4,36} | Penticantellated 8-cube Terirhombated octeract |
1218560 | 143360 | ||||||||
85 | t0,2,4{4,36} | Stericantellated 8-cube Cellirhombated octeract |
752640 | 107520 | ||||||||
86 | t0,2,3{4,36} | Runcicantellated 8-cube Prismatorhombated octeract |
193536 | 43008 | ||||||||
87 | t0,1,7{4,36} | Heptitruncated 8-cube Exitruncated octeract |
93184 | 14336 | ||||||||
88 | t0,1,6{4,36} | Hexitruncated 8-cube Petitruncated octeract |
344064 | 43008 | ||||||||
89 | t0,1,5{4,36} | Pentitruncated 8-cube Teritruncated octeract |
609280 | 71680 | ||||||||
90 | t0,1,4{4,36} | Steritruncated 8-cube Cellitruncated octeract |
573440 | 71680 | ||||||||
91 | t0,1,3{4,36} | Runcitruncated 8-cube Prismatotruncated octeract |
279552 | 43008 | ||||||||
92 | t0,1,2{4,36} | Cantitruncated 8-cube Great rhombated octeract |
57344 | 14336 | ||||||||
93 | t0,1,2,3{36,4} | Runcicantitruncated 8-orthoplex Great prismated diacosipentacontahexazetton |
147840 | 26880 | ||||||||
94 | t0,1,2,4{36,4} | Stericantitruncated 8-orthoplex Celligreatorhombated diacosipentacontahexazetton |
860160 | 107520 | ||||||||
95 | t0,1,3,4{36,4} | Steriruncitruncated 8-orthoplex Celliprismatotruncated diacosipentacontahexazetton |
591360 | 107520 | ||||||||
96 | t0,2,3,4{36,4} | Steriruncicantellated 8-orthoplex Celliprismatorhombated diacosipentacontahexazetton |
591360 | 107520 | ||||||||
97 | t1,2,3,4{36,4} | Biruncicantitruncated 8-orthoplex Great biprismated diacosipentacontahexazetton |
537600 | 107520 | ||||||||
98 | t0,1,2,5{36,4} | Penticantitruncated 8-orthoplex Terigreatorhombated diacosipentacontahexazetton |
1827840 | 215040 | ||||||||
99 | t0,1,3,5{36,4} | Pentiruncitruncated 8-orthoplex Teriprismatotruncated diacosipentacontahexazetton |
2419200 | 322560 | ||||||||
100 | t0,2,3,5{36,4} | Pentiruncicantellated 8-orthoplex Teriprismatorhombated diacosipentacontahexazetton |
2257920 | 322560 | ||||||||
101 | t1,2,3,5{36,4} | Bistericantitruncated 8-orthoplex Bicelligreatorhombated diacosipentacontahexazetton |
2096640 | 322560 | ||||||||
102 | t0,1,4,5{36,4} | Pentisteritruncated 8-orthoplex Tericellitruncated diacosipentacontahexazetton |
1182720 | 215040 | ||||||||
103 | t0,2,4,5{36,4} | Pentistericantellated 8-orthoplex Tericellirhombated diacosipentacontahexazetton |
1935360 | 322560 | ||||||||
104 | t1,2,4,5{36,4} | Bisteriruncitruncated 8-orthoplex Bicelliprismatotruncated diacosipentacontahexazetton |
1612800 | 322560 | ||||||||
105 | t0,3,4,5{36,4} | Pentisteriruncinated 8-orthoplex Tericelliprismated diacosipentacontahexazetton |
1182720 | 215040 | ||||||||
106 | t1,3,4,5{36,4} | Bisteriruncicantellated 8-orthoplex Bicelliprismatorhombated diacosipentacontahexazetton |
1774080 | 322560 | ||||||||
107 | t2,3,4,5{4,36} | Triruncicantitruncated 8-cube Great triprismato-octeractidiacosipentacontahexazetton |
967680 | 215040 | ||||||||
108 | t0,1,2,6{36,4} | Hexicantitruncated 8-orthoplex Petigreatorhombated diacosipentacontahexazetton |
1505280 | 215040 | ||||||||
109 | t0,1,3,6{36,4} | Hexiruncitruncated 8-orthoplex Petiprismatotruncated diacosipentacontahexazetton |
3225600 | 430080 | ||||||||
110 | t0,2,3,6{36,4} | Hexiruncicantellated 8-orthoplex Petiprismatorhombated diacosipentacontahexazetton |
2795520 | 430080 | ||||||||
111 | t1,2,3,6{36,4} | Bipenticantitruncated 8-orthoplex Biterigreatorhombated diacosipentacontahexazetton |
2580480 | 430080 | ||||||||
112 | t0,1,4,6{36,4} | Hexisteritruncated 8-orthoplex Peticellitruncated diacosipentacontahexazetton |
3010560 | 430080 | ||||||||
113 | t0,2,4,6{36,4} | Hexistericantellated 8-orthoplex Peticellirhombated diacosipentacontahexazetton |
4515840 | 645120 | ||||||||
114 | t1,2,4,6{36,4} | Bipentiruncitruncated 8-orthoplex Biteriprismatotruncated diacosipentacontahexazetton |
3870720 | 645120 | ||||||||
115 | t0,3,4,6{36,4} | Hexisteriruncinated 8-orthoplex Peticelliprismated diacosipentacontahexazetton |
2580480 | 430080 | ||||||||
116 | t1,3,4,6{4,36} | Bipentiruncicantellated 8-cube Biteriprismatorhombi-octeractidiacosipentacontahexazetton |
3870720 | 645120 | ||||||||
117 | t1,3,4,5{4,36} | Bisteriruncicantellated 8-cube Bicelliprismatorhombated octeract |
2150400 | 430080 | ||||||||
118 | t0,1,5,6{36,4} | Hexipentitruncated 8-orthoplex Petiteritruncated diacosipentacontahexazetton |
1182720 | 215040 | ||||||||
119 | t0,2,5,6{36,4} | Hexipenticantellated 8-orthoplex Petiterirhombated diacosipentacontahexazetton |
2795520 | 430080 | ||||||||
120 | t1,2,5,6{4,36} | Bipentisteritruncated 8-cube Bitericellitrunki-octeractidiacosipentacontahexazetton |
2150400 | 430080 | ||||||||
121 | t0,3,5,6{36,4} | Hexipentiruncinated 8-orthoplex Petiteriprismated diacosipentacontahexazetton |
2795520 | 430080 | ||||||||
122 | t1,2,4,6{4,36} | Bipentiruncitruncated 8-cube Biteriprismatotruncated octeract |
3870720 | 645120 | ||||||||
123 | t1,2,4,5{4,36} | Bisteriruncitruncated 8-cube Bicelliprismatotruncated octeract |
1935360 | 430080 | ||||||||
124 | t0,4,5,6{36,4} | Hexipentistericated 8-orthoplex Petitericellated diacosipentacontahexazetton |
1182720 | 215040 | ||||||||
125 | t1,2,3,6{4,36} | Bipenticantitruncated 8-cube Biterigreatorhombated octeract |
2580480 | 430080 | ||||||||
126 | t1,2,3,5{4,36} | Bistericantitruncated 8-cube Bicelligreatorhombated octeract |
2365440 | 430080 | ||||||||
127 | t1,2,3,4{4,36} | Biruncicantitruncated 8-cube Great biprismated octeract |
860160 | 215040 | ||||||||
128 | t0,1,2,7{36,4} | Hepticantitruncated 8-orthoplex Exigreatorhombated diacosipentacontahexazetton |
516096 | 86016 | ||||||||
129 | t0,1,3,7{36,4} | Heptiruncitruncated 8-orthoplex Exiprismatotruncated diacosipentacontahexazetton |
1612800 | 215040 | ||||||||
130 | t0,2,3,7{36,4} | Heptiruncicantellated 8-orthoplex Exiprismatorhombated diacosipentacontahexazetton |
1290240 | 215040 | ||||||||
131 | t0,4,5,6{4,36} | Hexipentistericated 8-cube Petitericellated octeract |
1182720 | 215040 | ||||||||
132 | t0,1,4,7{36,4} | Heptisteritruncated 8-orthoplex Exicellitruncated diacosipentacontahexazetton |
2293760 | 286720 | ||||||||
133 | t0,2,4,7{36,4} | Heptistericantellated 8-orthoplex Exicellirhombated diacosipentacontahexazetton |
3225600 | 430080 | ||||||||
134 | t0,3,5,6{4,36} | Hexipentiruncinated 8-cube Petiteriprismated octeract |
2795520 | 430080 | ||||||||
135 | t0,3,4,7{4,36} | Heptisteriruncinated 8-cube Exicelliprismato-octeractidiacosipentacontahexazetton |
1720320 | 286720 | ||||||||
136 | t0,3,4,6{4,36} | Hexisteriruncinated 8-cube Peticelliprismated octeract |
2580480 | 430080 | ||||||||
137 | t0,3,4,5{4,36} | Pentisteriruncinated 8-cube Tericelliprismated octeract |
1433600 | 286720 | ||||||||
138 | t0,1,5,7{36,4} | Heptipentitruncated 8-orthoplex Exiteritruncated diacosipentacontahexazetton |
1612800 | 215040 | ||||||||
139 | t0,2,5,7{4,36} | Heptipenticantellated 8-cube Exiterirhombi-octeractidiacosipentacontahexazetton |
3440640 | 430080 | ||||||||
140 | t0,2,5,6{4,36} | Hexipenticantellated 8-cube Petiterirhombated octeract |
2795520 | 430080 | ||||||||
141 | t0,2,4,7{4,36} | Heptistericantellated 8-cube Exicellirhombated octeract |
3225600 | 430080 | ||||||||
142 | t0,2,4,6{4,36} | Hexistericantellated 8-cube Peticellirhombated octeract |
4515840 | 645120 | ||||||||
143 | t0,2,4,5{4,36} | Pentistericantellated 8-cube Tericellirhombated octeract |
2365440 | 430080 | ||||||||
144 | t0,2,3,7{4,36} | Heptiruncicantellated 8-cube Exiprismatorhombated octeract |
1290240 | 215040 | ||||||||
145 | t0,2,3,6{4,36} | Hexiruncicantellated 8-cube Petiprismatorhombated octeract |
2795520 | 430080 | ||||||||
146 | t0,2,3,5{4,36} | Pentiruncicantellated 8-cube Teriprismatorhombated octeract |
2580480 | 430080 | ||||||||
147 | t0,2,3,4{4,36} | Steriruncicantellated 8-cube Celliprismatorhombated octeract |
967680 | 215040 | ||||||||
148 | t0,1,6,7{4,36} | Heptihexitruncated 8-cube Exipetitrunki-octeractidiacosipentacontahexazetton |
516096 | 86016 | ||||||||
149 | t0,1,5,7{4,36} | Heptipentitruncated 8-cube Exiteritruncated octeract |
1612800 | 215040 | ||||||||
150 | t0,1,5,6{4,36} | Hexipentitruncated 8-cube Petiteritruncated octeract |
1182720 | 215040 | ||||||||
151 | t0,1,4,7{4,36} | Heptisteritruncated 8-cube Exicellitruncated octeract |
2293760 | 286720 | ||||||||
152 | t0,1,4,6{4,36} | Hexisteritruncated 8-cube Peticellitruncated octeract |
3010560 | 430080 | ||||||||
153 | t0,1,4,5{4,36} | Pentisteritruncated 8-cube Tericellitruncated octeract |
1433600 | 286720 | ||||||||
154 | t0,1,3,7{4,36} | Heptiruncitruncated 8-cube Exiprismatotruncated octeract |
1612800 | 215040 | ||||||||
155 | t0,1,3,6{4,36} | Hexiruncitruncated 8-cube Petiprismatotruncated octeract |
3225600 | 430080 | ||||||||
156 | t0,1,3,5{4,36} | Pentiruncitruncated 8-cube Teriprismatotruncated octeract |
2795520 | 430080 | ||||||||
157 | t0,1,3,4{4,36} | Steriruncitruncated 8-cube Celliprismatotruncated octeract |
967680 | 215040 | ||||||||
158 | t0,1,2,7{4,36} | Hepticantitruncated 8-cube Exigreatorhombated octeract |
516096 | 86016 | ||||||||
159 | t0,1,2,6{4,36} | Hexicantitruncated 8-cube Petigreatorhombated octeract |
1505280 | 215040 | ||||||||
160 | t0,1,2,5{4,36} | Penticantitruncated 8-cube Terigreatorhombated octeract |
2007040 | 286720 | ||||||||
161 | t0,1,2,4{4,36} | Stericantitruncated 8-cube Celligreatorhombated octeract |
1290240 | 215040 | ||||||||
162 | t0,1,2,3{4,36} | Runcicantitruncated 8-cube Great prismated octeract |
344064 | 86016 | ||||||||
163 | t0,1,2,3,4{36,4} | Steriruncicantitruncated 8-orthoplex Great cellated diacosipentacontahexazetton |
1075200 | 215040 | ||||||||
164 | t0,1,2,3,5{36,4} | Pentiruncicantitruncated 8-orthoplex Terigreatoprismated diacosipentacontahexazetton |
4193280 | 645120 | ||||||||
165 | t0,1,2,4,5{36,4} | Pentistericantitruncated 8-orthoplex Tericelligreatorhombated diacosipentacontahexazetton |
3225600 | 645120 | ||||||||
166 | t0,1,3,4,5{36,4} | Pentisteriruncitruncated 8-orthoplex Tericelliprismatotruncated diacosipentacontahexazetton |
3225600 | 645120 | ||||||||
167 | t0,2,3,4,5{36,4} | Pentisteriruncicantellated 8-orthoplex Tericelliprismatorhombated diacosipentacontahexazetton |
3225600 | 645120 | ||||||||
168 | t1,2,3,4,5{36,4} | Bisteriruncicantitruncated 8-orthoplex Great bicellated diacosipentacontahexazetton |
2903040 | 645120 | ||||||||
169 | t0,1,2,3,6{36,4} | Hexiruncicantitruncated 8-orthoplex Petigreatoprismated diacosipentacontahexazetton |
5160960 | 860160 | ||||||||
170 | t0,1,2,4,6{36,4} | Hexistericantitruncated 8-orthoplex Peticelligreatorhombated diacosipentacontahexazetton |
7741440 | 1290240 | ||||||||
171 | t0,1,3,4,6{36,4} | Hexisteriruncitruncated 8-orthoplex Peticelliprismatotruncated diacosipentacontahexazetton |
7096320 | 1290240 | ||||||||
172 | t0,2,3,4,6{36,4} | Hexisteriruncicantellated 8-orthoplex Peticelliprismatorhombated diacosipentacontahexazetton |
7096320 | 1290240 | ||||||||
173 | t1,2,3,4,6{36,4} | Bipentiruncicantitruncated 8-orthoplex Biterigreatoprismated diacosipentacontahexazetton |
6451200 | 1290240 | ||||||||
174 | t0,1,2,5,6{36,4} | Hexipenticantitruncated 8-orthoplex Petiterigreatorhombated diacosipentacontahexazetton |
4300800 | 860160 | ||||||||
175 | t0,1,3,5,6{36,4} | Hexipentiruncitruncated 8-orthoplex Petiteriprismatotruncated diacosipentacontahexazetton |
7096320 | 1290240 | ||||||||
176 | t0,2,3,5,6{36,4} | Hexipentiruncicantellated 8-orthoplex Petiteriprismatorhombated diacosipentacontahexazetton |
6451200 | 1290240 | ||||||||
177 | t1,2,3,5,6{36,4} | Bipentistericantitruncated 8-orthoplex Bitericelligreatorhombated diacosipentacontahexazetton |
5806080 | 1290240 | ||||||||
178 | t0,1,4,5,6{36,4} | Hexipentisteritruncated 8-orthoplex Petitericellitruncated diacosipentacontahexazetton |
4300800 | 860160 | ||||||||
179 | t0,2,4,5,6{36,4} | Hexipentistericantellated 8-orthoplex Petitericellirhombated diacosipentacontahexazetton |
7096320 | 1290240 | ||||||||
180 | t1,2,3,5,6{4,36} | Bipentistericantitruncated 8-cube Bitericelligreatorhombated octeract |
5806080 | 1290240 | ||||||||
181 | t0,3,4,5,6{36,4} | Hexipentisteriruncinated 8-orthoplex Petitericelliprismated diacosipentacontahexazetton |
4300800 | 860160 | ||||||||
182 | t1,2,3,4,6{4,36} | Bipentiruncicantitruncated 8-cube Biterigreatoprismated octeract |
6451200 | 1290240 | ||||||||
183 | t1,2,3,4,5{4,36} | Bisteriruncicantitruncated 8-cube Great bicellated octeract |
3440640 | 860160 | ||||||||
184 | t0,1,2,3,7{36,4} | Heptiruncicantitruncated 8-orthoplex Exigreatoprismated diacosipentacontahexazetton |
2365440 | 430080 | ||||||||
185 | t0,1,2,4,7{36,4} | Heptistericantitruncated 8-orthoplex Exicelligreatorhombated diacosipentacontahexazetton |
5591040 | 860160 | ||||||||
186 | t0,1,3,4,7{36,4} | Heptisteriruncitruncated 8-orthoplex Exicelliprismatotruncated diacosipentacontahexazetton |
4730880 | 860160 | ||||||||
187 | t0,2,3,4,7{36,4} | Heptisteriruncicantellated 8-orthoplex Exicelliprismatorhombated diacosipentacontahexazetton |
4730880 | 860160 | ||||||||
188 | t0,3,4,5,6{4,36} | Hexipentisteriruncinated 8-cube Petitericelliprismated octeract |
4300800 | 860160 | ||||||||
189 | t0,1,2,5,7{36,4} | Heptipenticantitruncated 8-orthoplex Exiterigreatorhombated diacosipentacontahexazetton |
5591040 | 860160 | ||||||||
190 | t0,1,3,5,7{36,4} | Heptipentiruncitruncated 8-orthoplex Exiteriprismatotruncated diacosipentacontahexazetton |
8386560 | 1290240 | ||||||||
191 | t0,2,3,5,7{36,4} | Heptipentiruncicantellated 8-orthoplex Exiteriprismatorhombated diacosipentacontahexazetton |
7741440 | 1290240 | ||||||||
192 | t0,2,4,5,6{4,36} | Hexipentistericantellated 8-cube Petitericellirhombated octeract |
7096320 | 1290240 | ||||||||
193 | t0,1,4,5,7{36,4} | Heptipentisteritruncated 8-orthoplex Exitericellitruncated diacosipentacontahexazetton |
4730880 | 860160 | ||||||||
194 | t0,2,3,5,7{4,36} | Heptipentiruncicantellated 8-cube Exiteriprismatorhombated octeract |
7741440 | 1290240 | ||||||||
195 | t0,2,3,5,6{4,36} | Hexipentiruncicantellated 8-cube Petiteriprismatorhombated octeract |
6451200 | 1290240 | ||||||||
196 | t0,2,3,4,7{4,36} | Heptisteriruncicantellated 8-cube Exicelliprismatorhombated octeract |
4730880 | 860160 | ||||||||
197 | t0,2,3,4,6{4,36} | Hexisteriruncicantellated 8-cube Peticelliprismatorhombated octeract |
7096320 | 1290240 | ||||||||
198 | t0,2,3,4,5{4,36} | Pentisteriruncicantellated 8-cube Tericelliprismatorhombated octeract |
3870720 | 860160 | ||||||||
199 | t0,1,2,6,7{36,4} | Heptihexicantitruncated 8-orthoplex Exipetigreatorhombated diacosipentacontahexazetton |
2365440 | 430080 | ||||||||
200 | t0,1,3,6,7{36,4} | Heptihexiruncitruncated 8-orthoplex Exipetiprismatotruncated diacosipentacontahexazetton |
5591040 | 860160 | ||||||||
201 | t0,1,4,5,7{4,36} | Heptipentisteritruncated 8-cube Exitericellitruncated octeract |
4730880 | 860160 | ||||||||
202 | t0,1,4,5,6{4,36} | Hexipentisteritruncated 8-cube Petitericellitruncated octeract |
4300800 | 860160 | ||||||||
203 | t0,1,3,6,7{4,36} | Heptihexiruncitruncated 8-cube Exipetiprismatotruncated octeract |
5591040 | 860160 | ||||||||
204 | t0,1,3,5,7{4,36} | Heptipentiruncitruncated 8-cube Exiteriprismatotruncated octeract |
8386560 | 1290240 | ||||||||
205 | t0,1,3,5,6{4,36} | Hexipentiruncitruncated 8-cube Petiteriprismatotruncated octeract |
7096320 | 1290240 | ||||||||
206 | t0,1,3,4,7{4,36} | Heptisteriruncitruncated 8-cube Exicelliprismatotruncated octeract |
4730880 | 860160 | ||||||||
207 | t0,1,3,4,6{4,36} | Hexisteriruncitruncated 8-cube Peticelliprismatotruncated octeract |
7096320 | 1290240 | ||||||||
208 | t0,1,3,4,5{4,36} | Pentisteriruncitruncated 8-cube Tericelliprismatotruncated octeract |
3870720 | 860160 | ||||||||
209 | t0,1,2,6,7{4,36} | Heptihexicantitruncated 8-cube Exipetigreatorhombated octeract |
2365440 | 430080 | ||||||||
210 | t0,1,2,5,7{4,36} | Heptipenticantitruncated 8-cube Exiterigreatorhombated octeract |
5591040 | 860160 | ||||||||
211 | t0,1,2,5,6{4,36} | Hexipenticantitruncated 8-cube Petiterigreatorhombated octeract |
4300800 | 860160 | ||||||||
212 | t0,1,2,4,7{4,36} | Heptistericantitruncated 8-cube Exicelligreatorhombated octeract |
5591040 | 860160 | ||||||||
213 | t0,1,2,4,6{4,36} | Hexistericantitruncated 8-cube Peticelligreatorhombated octeract |
7741440 | 1290240 | ||||||||
214 | t0,1,2,4,5{4,36} | Pentistericantitruncated 8-cube Tericelligreatorhombated octeract |
3870720 | 860160 | ||||||||
215 | t0,1,2,3,7{4,36} | Heptiruncicantitruncated 8-cube Exigreatoprismated octeract |
2365440 | 430080 | ||||||||
216 | t0,1,2,3,6{4,36} | Hexiruncicantitruncated 8-cube Petigreatoprismated octeract |
5160960 | 860160 | ||||||||
217 | t0,1,2,3,5{4,36} | Pentiruncicantitruncated 8-cube Terigreatoprismated octeract |
4730880 | 860160 | ||||||||
218 | t0,1,2,3,4{4,36} | Steriruncicantitruncated 8-cube Great cellated octeract |
1720320 | 430080 | ||||||||
219 | t0,1,2,3,4,5{36,4} | Pentisteriruncicantitruncated 8-orthoplex Great terated diacosipentacontahexazetton |
5806080 | 1290240 | ||||||||
220 | t0,1,2,3,4,6{36,4} | Hexisteriruncicantitruncated 8-orthoplex Petigreatocellated diacosipentacontahexazetton |
12902400 | 2580480 | ||||||||
221 | t0,1,2,3,5,6{36,4} | Hexipentiruncicantitruncated 8-orthoplex Petiterigreatoprismated diacosipentacontahexazetton |
11612160 | 2580480 | ||||||||
222 | t0,1,2,4,5,6{36,4} | Hexipentistericantitruncated 8-orthoplex Petitericelligreatorhombated diacosipentacontahexazetton |
11612160 | 2580480 | ||||||||
223 | t0,1,3,4,5,6{36,4} | Hexipentisteriruncitruncated 8-orthoplex Petitericelliprismatotruncated diacosipentacontahexazetton |
11612160 | 2580480 | ||||||||
224 | t0,2,3,4,5,6{36,4} | Hexipentisteriruncicantellated 8-orthoplex Petitericelliprismatorhombated diacosipentacontahexazetton |
11612160 | 2580480 | ||||||||
225 | t1,2,3,4,5,6{4,36} | Bipentisteriruncicantitruncated 8-cube Great biteri-octeractidiacosipentacontahexazetton |
10321920 | 2580480 | ||||||||
226 | t0,1,2,3,4,7{36,4} | Heptisteriruncicantitruncated 8-orthoplex Exigreatocellated diacosipentacontahexazetton |
8601600 | 1720320 | ||||||||
227 | t0,1,2,3,5,7{36,4} | Heptipentiruncicantitruncated 8-orthoplex Exiterigreatoprismated diacosipentacontahexazetton |
14192640 | 2580480 | ||||||||
228 | t0,1,2,4,5,7{36,4} | Heptipentistericantitruncated 8-orthoplex Exitericelligreatorhombated diacosipentacontahexazetton |
12902400 | 2580480 | ||||||||
229 | t0,1,3,4,5,7{36,4} | Heptipentisteriruncitruncated 8-orthoplex Exitericelliprismatotruncated diacosipentacontahexazetton |
12902400 | 2580480 | ||||||||
230 | t0,2,3,4,5,7{4,36} | Heptipentisteriruncicantellated 8-cube Exitericelliprismatorhombi-octeractidiacosipentacontahexazetton |
12902400 | 2580480 | ||||||||
231 | t0,2,3,4,5,6{4,36} | Hexipentisteriruncicantellated 8-cube Petitericelliprismatorhombated octeract |
11612160 | 2580480 | ||||||||
232 | t0,1,2,3,6,7{36,4} | Heptihexiruncicantitruncated 8-orthoplex Exipetigreatoprismated diacosipentacontahexazetton |
8601600 | 1720320 | ||||||||
233 | t0,1,2,4,6,7{36,4} | Heptihexistericantitruncated 8-orthoplex Exipeticelligreatorhombated diacosipentacontahexazetton |
14192640 | 2580480 | ||||||||
234 | t0,1,3,4,6,7{4,36} | Heptihexisteriruncitruncated 8-cube Exipeticelliprismatotrunki-octeractidiacosipentacontahexazetton |
12902400 | 2580480 | ||||||||
235 | t0,1,3,4,5,7{4,36} | Heptipentisteriruncitruncated 8-cube Exitericelliprismatotruncated octeract |
12902400 | 2580480 | ||||||||
236 | t0,1,3,4,5,6{4,36} | Hexipentisteriruncitruncated 8-cube Petitericelliprismatotruncated octeract |
11612160 | 2580480 | ||||||||
237 | t0,1,2,5,6,7{4,36} | Heptihexipenticantitruncated 8-cube Exipetiterigreatorhombi-octeractidiacosipentacontahexazetton |
8601600 | 1720320 | ||||||||
238 | t0,1,2,4,6,7{4,36} | Heptihexistericantitruncated 8-cube Exipeticelligreatorhombated octeract |
14192640 | 2580480 | ||||||||
239 | t0,1,2,4,5,7{4,36} | Heptipentistericantitruncated 8-cube Exitericelligreatorhombated octeract |
12902400 | 2580480 | ||||||||
240 | t0,1,2,4,5,6{4,36} | Hexipentistericantitruncated 8-cube Petitericelligreatorhombated octeract |
11612160 | 2580480 | ||||||||
241 | t0,1,2,3,6,7{4,36} | Heptihexiruncicantitruncated 8-cube Exipetigreatoprismated octeract |
8601600 | 1720320 | ||||||||
242 | t0,1,2,3,5,7{4,36} | Heptipentiruncicantitruncated 8-cube Exiterigreatoprismated octeract |
14192640 | 2580480 | ||||||||
243 | t0,1,2,3,5,6{4,36} | Hexipentiruncicantitruncated 8-cube Petiterigreatoprismated octeract |
11612160 | 2580480 | ||||||||
244 | t0,1,2,3,4,7{4,36} | Heptisteriruncicantitruncated 8-cube Exigreatocellated octeract |
8601600 | 1720320 | ||||||||
245 | t0,1,2,3,4,6{4,36} | Hexisteriruncicantitruncated 8-cube Petigreatocellated octeract |
12902400 | 2580480 | ||||||||
246 | t0,1,2,3,4,5{4,36} | Pentisteriruncicantitruncated 8-cube Great terated octeract |
6881280 | 1720320 | ||||||||
247 | t0,1,2,3,4,5,6{36,4} | Hexipentisteriruncicantitruncated 8-orthoplex Great petated diacosipentacontahexazetton |
20643840 | 5160960 | ||||||||
248 | t0,1,2,3,4,5,7{36,4} | Heptipentisteriruncicantitruncated 8-orthoplex Exigreatoterated diacosipentacontahexazetton |
23224320 | 5160960 | ||||||||
249 | t0,1,2,3,4,6,7{36,4} | Heptihexisteriruncicantitruncated 8-orthoplex Exipetigreatocellated diacosipentacontahexazetton |
23224320 | 5160960 | ||||||||
250 | t0,1,2,3,5,6,7{36,4} | Heptihexipentiruncicantitruncated 8-orthoplex Exipetiterigreatoprismated diacosipentacontahexazetton |
23224320 | 5160960 | ||||||||
251 | t0,1,2,3,5,6,7{4,36} | Heptihexipentiruncicantitruncated 8-cube Exipetiterigreatoprismated octeract |
23224320 | 5160960 | ||||||||
252 | t0,1,2,3,4,6,7{4,36} | Heptihexisteriruncicantitruncated 8-cube Exipetigreatocellated octeract |
23224320 | 5160960 | ||||||||
253 | t0,1,2,3,4,5,7{4,36} | Heptipentisteriruncicantitruncated 8-cube Exigreatoterated octeract |
23224320 | 5160960 | ||||||||
254 | t0,1,2,3,4,5,6{4,36} | Hexipentisteriruncicantitruncated 8-cube Great petated octeract |
20643840 | 5160960 | ||||||||
255 | t0,1,2,3,4,5,6,7{4,36} | Omnitruncated 8-cube Great exi-octeractidiacosipentacontahexazetton |
41287680 | 10321920 |
The D8 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
See
D8 uniform polytopes | ||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
# | Coxeter-Dynkin diagram
|
Name | Base point (Alternately signed) |
Element counts | Circumrad | |||||||||
7 | 6 | 5 | 4 | 3 | 2 | 1 | 0 | |||||||
1 | = |
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 | ||
2 | = |
cantic 8-cube h2{4,3,3,3,3,3,3} |
(1,1,3,3,3,3,3,3) | 23296 | 3584 | 2.6457512 | ||||||||
3 | = |
runcic 8-cube h3{4,3,3,3,3,3,3} |
(1,1,1,3,3,3,3,3) | 64512 | 7168 | 2.4494896 | ||||||||
4 | = |
steric 8-cube h4{4,3,3,3,3,3,3} |
(1,1,1,1,3,3,3,3) | 98560 | 8960 | 2.2360678 | ||||||||
5 | = |
pentic 8-cube h5{4,3,3,3,3,3,3} |
(1,1,1,1,1,3,3,3) | 89600 | 7168 | 1.9999999 | ||||||||
6 | = |
hexic 8-cube h6{4,3,3,3,3,3,3} |
(1,1,1,1,1,1,3,3) | 48384 | 3584 | 1.7320508 | ||||||||
7 | = |
heptic 8-cube h7{4,3,3,3,3,3,3} |
(1,1,1,1,1,1,1,3) | 14336 | 1024 | 1.4142135 | ||||||||
8 | = |
runcicantic 8-cube h2,3{4,3,3,3,3,3,3} |
(1,1,3,5,5,5,5,5) | 86016 | 21504 | 4.1231055 | ||||||||
9 | = |
stericantic 8-cube h2,4{4,3,3,3,3,3,3} |
(1,1,3,3,5,5,5,5) | 349440 | 53760 | 3.8729835 | ||||||||
10 | = |
steriruncic 8-cube h3,4{4,3,3,3,3,3,3} |
(1,1,1,3,5,5,5,5) | 179200 | 35840 | 3.7416575 | ||||||||
11 | = |
penticantic 8-cube h2,5{4,3,3,3,3,3,3} |
(1,1,3,3,3,5,5,5) | 573440 | 71680 | 3.6055512 | ||||||||
12 | = |
pentiruncic 8-cube h3,5{4,3,3,3,3,3,3} |
(1,1,1,3,3,5,5,5) | 537600 | 71680 | 3.4641016 | ||||||||
13 | = |
pentisteric 8-cube h4,5{4,3,3,3,3,3,3} |
(1,1,1,1,3,5,5,5) | 232960 | 35840 | 3.3166249 | ||||||||
14 | = |
hexicantic 8-cube h2,6{4,3,3,3,3,3,3} |
(1,1,3,3,3,3,5,5) | 456960 | 53760 | 3.3166249 | ||||||||
15 | = |
hexicruncic 8-cube h3,6{4,3,3,3,3,3,3} |
(1,1,1,3,3,3,5,5) | 645120 | 71680 | 3.1622777 | ||||||||
16 | = |
hexisteric 8-cube h4,6{4,3,3,3,3,3,3} |
(1,1,1,1,3,3,5,5) | 483840 | 53760 | 3 | ||||||||
17 | = |
hexipentic 8-cube h5,6{4,3,3,3,3,3,3} |
(1,1,1,1,1,3,5,5) | 182784 | 21504 | 2.8284271 | ||||||||
18 | = |
hepticantic 8-cube h2,7{4,3,3,3,3,3,3} |
(1,1,3,3,3,3,3,5) | 172032 | 21504 | 3 | ||||||||
19 | = |
heptiruncic 8-cube h3,7{4,3,3,3,3,3,3} |
(1,1,1,3,3,3,3,5) | 340480 | 35840 | 2.8284271 | ||||||||
20 | = |
heptsteric 8-cube h4,7{4,3,3,3,3,3,3} |
(1,1,1,1,3,3,3,5) | 376320 | 35840 | 2.6457512 | ||||||||
21 | = |
heptipentic 8-cube h5,7{4,3,3,3,3,3,3} |
(1,1,1,1,1,3,3,5) | 236544 | 21504 | 2.4494898 | ||||||||
22 | = |
heptihexic 8-cube h6,7{4,3,3,3,3,3,3} |
(1,1,1,1,1,1,3,5) | 78848 | 7168 | 2.236068 | ||||||||
23 | = |
steriruncicantic 8-cube h2,3,4{4,36} |
(1,1,3,5,7,7,7,7) | 430080 | 107520 | 5.3851647 | ||||||||
24 | = |
pentiruncicantic 8-cube h2,3,5{4,36} |
(1,1,3,5,5,7,7,7) | 1182720 | 215040 | 5.0990195 | ||||||||
25 | = |
pentistericantic 8-cube h2,4,5{4,36} |
(1,1,3,3,5,7,7,7) | 1075200 | 215040 | 4.8989797 | ||||||||
26 | = |
pentisterirunic 8-cube h3,4,5{4,36} |
(1,1,1,3,5,7,7,7) | 716800 | 143360 | 4.7958317 | ||||||||
27 | = |
hexiruncicantic 8-cube h2,3,6{4,36} |
(1,1,3,5,5,5,7,7) | 1290240 | 215040 | 4.7958317 | ||||||||
28 | = |
hexistericantic 8-cube h2,4,6{4,36} |
(1,1,3,3,5,5,7,7) | 2096640 | 322560 | 4.5825758 | ||||||||
29 | = |
hexisterirunic 8-cube h3,4,6{4,36} |
(1,1,1,3,5,5,7,7) | 1290240 | 215040 | 4.472136 | ||||||||
30 | = |
hexipenticantic 8-cube h2,5,6{4,36} |
(1,1,3,3,3,5,7,7) | 1290240 | 215040 | 4.3588991 | ||||||||
31 | = |
hexipentirunic 8-cube h3,5,6{4,36} |
(1,1,1,3,3,5,7,7) | 1397760 | 215040 | 4.2426405 | ||||||||
32 | = |
hexipentisteric 8-cube h4,5,6{4,36} |
(1,1,1,1,3,5,7,7) | 698880 | 107520 | 4.1231055 | ||||||||
33 | = |
heptiruncicantic 8-cube h2,3,7{4,36} |
(1,1,3,5,5,5,5,7) | 591360 | 107520 | 4.472136 | ||||||||
34 | = |
heptistericantic 8-cube h2,4,7{4,36} |
(1,1,3,3,5,5,5,7) | 1505280 | 215040 | 4.2426405 | ||||||||
35 | = |
heptisterruncic 8-cube h3,4,7{4,36} |
(1,1,1,3,5,5,5,7) | 860160 | 143360 | 4.1231055 | ||||||||
36 | = |
heptipenticantic 8-cube h2,5,7{4,36} |
(1,1,3,3,3,5,5,7) | 1612800 | 215040 | 4 | ||||||||
37 | = |
heptipentiruncic 8-cube h3,5,7{4,36} |
(1,1,1,3,3,5,5,7) | 1612800 | 215040 | 3.8729835 | ||||||||
38 | = |
heptipentisteric 8-cube h4,5,7{4,36} |
(1,1,1,1,3,5,5,7) | 752640 | 107520 | 3.7416575 | ||||||||
39 | = |
heptihexicantic 8-cube h2,6,7{4,36} |
(1,1,3,3,3,3,5,7) | 752640 | 107520 | 3.7416575 | ||||||||
40 | = |
heptihexiruncic 8-cube h3,6,7{4,36} |
(1,1,1,3,3,3,5,7) | 1146880 | 143360 | 3.6055512 | ||||||||
41 | = |
heptihexisteric 8-cube h4,6,7{4,36} |
(1,1,1,1,3,3,5,7) | 913920 | 107520 | 3.4641016 | ||||||||
42 | = |
heptihexipentic 8-cube h5,6,7{4,36} |
(1,1,1,1,1,3,5,7) | 365568 | 43008 | 3.3166249 | ||||||||
43 | = |
pentisteriruncicantic 8-cube h2,3,4,5{4,36} |
(1,1,3,5,7,9,9,9) | 1720320 | 430080 | 6.4031243 | ||||||||
44 | = |
hexisteriruncicantic 8-cube h2,3,4,6{4,36} |
(1,1,3,5,7,7,9,9) | 3225600 | 645120 | 6.0827627 | ||||||||
45 | = |
hexipentiruncicantic 8-cube h2,3,5,6{4,36} |
(1,1,3,5,5,7,9,9) | 2903040 | 645120 | 5.8309517 | ||||||||
46 | = |
hexipentistericantic 8-cube h2,4,5,6{4,36} |
(1,1,3,3,5,7,9,9) | 3225600 | 645120 | 5.6568542 | ||||||||
47 | = |
hexipentisteriruncic 8-cube h3,4,5,6{4,36} |
(1,1,1,3,5,7,9,9) | 2150400 | 430080 | 5.5677648 | ||||||||
48 | = |
heptsteriruncicantic 8-cube h2,3,4,7{4,36} |
(1,1,3,5,7,7,7,9) | 2150400 | 430080 | 5.7445626 | ||||||||
49 | = |
heptipentiruncicantic 8-cube h2,3,5,7{4,36} |
(1,1,3,5,5,7,7,9) | 3548160 | 645120 | 5.4772258 | ||||||||
50 | = |
heptipentistericantic 8-cube h2,4,5,7{4,36} |
(1,1,3,3,5,7,7,9) | 3548160 | 645120 | 5.291503 | ||||||||
51 | = |
heptipentisteriruncic 8-cube h3,4,5,7{4,36} |
(1,1,1,3,5,7,7,9) | 2365440 | 430080 | 5.1961527 | ||||||||
52 | = |
heptihexiruncicantic 8-cube h2,3,6,7{4,36} |
(1,1,3,5,5,5,7,9) | 2150400 | 430080 | 5.1961527 | ||||||||
53 | = |
heptihexistericantic 8-cube h2,4,6,7{4,36} |
(1,1,3,3,5,5,7,9) | 3870720 | 645120 | 5 | ||||||||
54 | = |
heptihexisteriruncic 8-cube h3,4,6,7{4,36} |
(1,1,1,3,5,5,7,9) | 2365440 | 430080 | 4.8989797 | ||||||||
55 | = |
heptihexipenticantic 8-cube h2,5,6,7{4,36} |
(1,1,3,3,3,5,7,9) | 2580480 | 430080 | 4.7958317 | ||||||||
56 | = |
heptihexipentiruncic 8-cube h3,5,6,7{4,36} |
(1,1,1,3,3,5,7,9) | 2795520 | 430080 | 4.6904159 | ||||||||
57 | = |
heptihexipentisteric 8-cube h4,5,6,7{4,36} |
(1,1,1,1,3,5,7,9) | 1397760 | 215040 | 4.5825758 | ||||||||
58 | = |
hexipentisteriruncicantic 8-cube h2,3,4,5,6{4,36} |
(1,1,3,5,7,9,11,11) | 5160960 | 1290240 | 7.1414285 | ||||||||
59 | = |
heptipentisteriruncicantic 8-cube h2,3,4,5,7{4,36} |
(1,1,3,5,7,9,9,11) | 5806080 | 1290240 | 6.78233 | ||||||||
60 | = |
heptihexisteriruncicantic 8-cube h2,3,4,6,7{4,36} |
(1,1,3,5,7,7,9,11) | 5806080 | 1290240 | 6.480741 | ||||||||
61 | = |
heptihexipentiruncicantic 8-cube h2,3,5,6,7{4,36} |
(1,1,3,5,5,7,9,11) | 5806080 | 1290240 | 6.244998 | ||||||||
62 | = |
heptihexipentistericantic 8-cube h2,4,5,6,7{4,36} |
(1,1,3,3,5,7,9,11) | 6451200 | 1290240 | 6.0827627 | ||||||||
63 | = |
heptihexipentisteriruncic 8-cube h3,4,5,6,7{4,36} |
(1,1,1,3,5,7,9,11) | 4300800 | 860160 | 6.0000000 | ||||||||
64 | = |
heptihexipentisteriruncicantic 8-cube h2,3,4,5,6,7{4,36} |
(1,1,3,5,7,9,11,13) | 2580480 | 10321920 | 7.5498347 |
The E8 family
The E8 family has symmetry order 696,729,600.
There are 255 forms based on all permutations of the
See also
E8 uniform polytopes | ||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
# | Coxeter-Dynkin diagram |
Names | Element counts | |||||||||||
7-faces | 6-faces | 5-faces | 4-faces | Cells | Faces | Edges | Vertices | |||||||
1 | 421 (fy)
|
19440 | 207360 | 483840 | 483840 | 241920 | 60480 | 6720 | 240 | |||||
2 | Truncated 421 (tiffy) | 188160 | 13440 | |||||||||||
3 | Rectified 421 (riffy)
|
19680 | 375840 | 1935360 | 3386880 | 2661120 | 1028160 | 181440 | 6720 | |||||
4 | Birectified 421 (borfy)
|
19680 | 382560 | 2600640 | 7741440 | 9918720 | 5806080 | 1451520 | 60480 | |||||
5 | Trirectified 421 (torfy)
|
19680 | 382560 | 2661120 | 9313920 | 16934400 | 14515200 | 4838400 | 241920 | |||||
6 | Rectified 142 (buffy)
|
19680 | 382560 | 2661120 | 9072000 | 16934400 | 16934400 | 7257600 | 483840 | |||||
7 | Rectified 241 (robay)
|
19680 | 313440 | 1693440 | 4717440 | 7257600 | 5322240 | 1451520 | 69120 | |||||
8 | 241 (bay) | 17520 | 144960 | 544320 | 1209600 | 1209600 | 483840 | 69120 | 2160 | |||||
9 | Truncated 241 | 138240 | ||||||||||||
10 | 142 (bif) | 2400 | 106080 | 725760 | 2298240 | 3628800 | 2419200 | 483840 | 17280 | |||||
11 | Truncated 142 | 967680 | ||||||||||||
12 | Omnitruncated 421 | 696729600 |
Regular and uniform honeycombs
There are five fundamental affine
# | Coxeter group | Coxeter diagram
|
Forms | |
---|---|---|---|---|
1 | [3[8]] | 29 | ||
2 | [4,35,4] | 135 | ||
3 | [4,34,31,1] | 191 (64 new) | ||
4 | [31,1,33,31,1] | 77 (10 new) | ||
5 | [33,3,1] | 143 |
Regular and uniform tessellations include:
- 29 uniquely ringed forms, including:
- 7-simplex honeycomb: {3[8]}
- 135 uniquely ringed forms, including:
- Regular 7-cube honeycomb: {4,34,4} = {4,34,31,1}, =
- Regular
- 191 uniquely ringed forms, 127 shared with , and 64 new, including:
- 7-demicube honeycomb: h{4,34,4} = {31,1,34,4}, =
- , [31,1,33,31,1]: 77 unique ring permutations, and 10 are new, the first Coxeter called a quarter 7-cubic honeycomb.
- , , , , , , , , ,
- 143 uniquely ringed forms, including:
- 133 honeycomb: {3,33,3},
- 331 honeycomb: {3,3,3,33,1},
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
= [3,3[7]]: |
= [31,1,32,32,1]: |
= [4,33,32,1]: |
= [33,2,2]: |
References
- 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,
- (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
- Klitzing, Richard. "8D uniform polytopes (polyzetta)".
External links
Family | An | Bn | I2(p) / Dn | E6 / E7 / E8 / F4 / G2 | Hn
| |||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|
Regular polygon | Triangle | Square | p-gon | Hexagon | Pentagon | |||||||
Uniform polyhedron | Tetrahedron | Octahedron • Cube | Demicube | Dodecahedron • Icosahedron | ||||||||
Uniform polychoron
|
Pentachoron | 16-cell • Tesseract | Demitesseract | 24-cell | 120-cell • 600-cell | |||||||
Uniform 5-polytope | 5-simplex | 5-orthoplex • 5-cube | 5-demicube | |||||||||
Uniform 6-polytope | 6-simplex | 6-orthoplex • 6-cube | 6-demicube | 122 • 221 | ||||||||
Uniform 7-polytope | 7-simplex | 7-orthoplex • 7-cube | 7-demicube | 132 • 231 • 321 | ||||||||
Uniform 8-polytope | 8-simplex | 8-orthoplex • 8-cube | 8-demicube | 142 • 241 • 421 | ||||||||
Uniform 9-polytope | 9-simplex | 9-orthoplex • 9-cube | 9-demicube | |||||||||
Uniform 10-polytope | 10-simplex | 10-orthoplex • 10-cube | 10-demicube | |||||||||
Uniform n-polytope | n-simplex | n-orthoplex • n-cube | n-demicube | 1k2 • 2k1 • k21 | n-pentagonal polytope | |||||||
Topics: List of regular polytopes and compounds
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