The A10 Family
The A10 family has symmetry of order 39,916,800 (11 factorial).
There are 512+16-1=527 forms based on all permutations of the Coxeter-Dynkin diagrams with one or more rings. 31 are shown below: all one and two ringed forms, and the final omnitruncated form. Bowers-style acronym names are given in parentheses for cross-referencing.
| # | Graph | Coxeter-Dynkin diagram Schläfli symbol Name |
Element counts | |||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 9-faces | 8-faces | 7-faces | 6-faces | 5-faces | 4-faces | Cells | Faces | Edges | Vertices | |||
| 1 |
|
11 | 55 | 165 | 330 | 462 | 462 | 330 | 165 | 55 | 11 | |
| 2 |
|
495 | 55 | |||||||||
| 3 |
|
1980 | 165 | |||||||||
| 4 |
|
4620 | 330 | |||||||||
| 5 |
|
6930 | 462 | |||||||||
| 6 |
|
550 | 110 | |||||||||
| 7 |
|
4455 | 495 | |||||||||
| 8 |
|
2475 | 495 | |||||||||
| 9 |
|
15840 | 1320 | |||||||||
| 10 |
|
17820 | 1980 | |||||||||
| 11 |
|
6600 | 1320 | |||||||||
| 12 |
|
32340 | 2310 | |||||||||
| 13 |
|
55440 | 4620 | |||||||||
| 14 |
|
41580 | 4620 | |||||||||
| 15 |
|
11550 | 2310 | |||||||||
| 16 |
|
41580 | 2772 | |||||||||
| 17 |
|
97020 | 6930 | |||||||||
| 18 |
|
110880 | 9240 | |||||||||
| 19 |
|
62370 | 6930 | |||||||||
| 20 |
|
13860 | 2772 | |||||||||
| 21 |
|
34650 | 2310 | |||||||||
| 22 |
|
103950 | 6930 | |||||||||
| 23 |
|
161700 | 11550 | |||||||||
| 24 |
|
138600 | 11550 | |||||||||
| 25 |
|
18480 | 1320 | |||||||||
| 26 |
|
69300 | 4620 | |||||||||
| 27 |
|
138600 | 9240 | |||||||||
| 28 |
|
5940 | 495 | |||||||||
| 29 |
|
27720 | 1980 | |||||||||
| 30 |
|
990 | 110 | |||||||||
| 31 | t{3,3,3,3,3,3,3,3,3} Omnitruncated 10-simplex |
199584000 | 39916800 | |||||||||
Read more about this topic: Uniform 10-polytope
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