The B10 Family
There are 1023 forms based on all permutations of the Coxeter-Dynkin diagrams with one or more rings.
Twelve cases are shown below: ten single-ring (rectified) forms, and two truncations. 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 | t{4,3,3,3,3,3,3,3,3} 10-cube (deker) |
20 | 180 | 960 | 3360 | 8064 | 13440 | 15360 | 11520 | 5120 | 1024 | |
| 2 | t{4,3,3,3,3,3,3,3,3} Truncated 10-cube (tade) |
51200 | 10240 | |||||||||
| 3 | t{4,3,3,3,3,3,3,3,3} Rectified 10-cube (rade) |
46080 | 5120 | |||||||||
| 4 | t{4,3,3,3,3,3,3,3,3} Birectified 10-cube (brade) |
184320 | 11520 | |||||||||
| 5 | t{4,3,3,3,3,3,3,3,3} Trirectified 10-cube (trade) |
322560 | 15360 | |||||||||
| 6 | t{4,3,3,3,3,3,3,3,3} Quadrirectified 10-cube (terade) |
322560 | 13440 | |||||||||
| 7 | t{3,3,3,3,3,3,3,3,4} Quadrirectified 10-orthoplex (terake) |
201600 | 8064 | |||||||||
| 8 | t{3,3,3,3,3,3,3,4} Trirectified 10-orthoplex (trake) |
80640 | 3360 | |||||||||
| 9 | t{3,3,3,3,3,3,3,3,4} Birectified 10-orthoplex (brake) |
20160 | 960 | |||||||||
| 10 | t{3,3,3,3,3,3,3,3,4} Rectified 10-orthoplex (rake) |
2880 | 180 | |||||||||
| 11 | t{3,3,3,3,3,3,3,3,4} Truncated 10-orthoplex (take) |
3060 | 360 | |||||||||
| 12 | t{3,3,3,3,3,3,3,3,4} 10-orthoplex (ka) |
1024 | 5120 | 11520 | 15360 | 13440 | 8064 | 3360 | 960 | 180 | 20 | |
Read more about this topic: Uniform 10-polytope
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