- general polytopal classes:
- Wythoffian polypeta
links
| Acronym | catax |
| Name | cellitruncated hexeract |
| Circumradius | sqrt[(14+7 sqrt(2))/2] = 3.456841 |
| Coordinates | ((1+2 sqrt(2))/2, (1+2 sqrt(2))/2, (1+sqrt(2))/2, (1+sqrt(2))/2, (1+sqrt(2))/2, 1/2) & all permutations, all changes of sign |
| Face vector | 3840, 19200, 34080, 25440, 7388, 668 |
| Confer |
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External links |
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As abstract polytope catax is isomorphic to quactix, thereby replacing octagons by octagrams, resp. tic by quith and op by stop, resp. tat by quitit, ticcup by quithip and todip by tistodip, resp capt by quacpot, tratic by traquith and owoct by stowoct.
Incidence matrix according to Dynkin symbol
o3x3o3o3x4x . . . . . . | 3840 | 6 3 1 | 3 6 12 6 3 3 | 3 6 3 2 6 6 6 12 1 3 | 1 3 3 3 6 2 2 6 6 1 | 1 1 3 3 2 ------------+------+-----------------+--------------------------------+-------------------------------------------------+-----------------------------------------+------------------ . x . . . . | 2 | 11520 * * | 1 2 2 1 0 0 | 2 2 1 1 2 2 1 2 0 0 | 1 2 2 1 2 1 1 2 1 0 | 1 1 2 1 1 . . . . x . | 2 | * 5760 * | 0 0 4 0 2 1 | 0 2 0 0 2 0 4 4 1 2 | 0 1 0 2 2 2 0 2 4 1 | 1 0 1 2 2 . . . . . x | 2 | * * 1920 | 0 0 0 6 0 3 | 0 0 3 0 0 6 0 12 0 4 | 0 0 3 0 6 0 2 6 6 1 | 0 1 3 3 2 ------------+------+-----------------+--------------------------------+-------------------------------------------------+-----------------------------------------+------------------ o3x . . . . | 3 | 3 0 0 | 3840 * * * * * | 2 2 1 0 0 0 0 0 0 0 | 1 2 2 1 2 0 0 0 0 0 | 1 1 2 1 0 . x3o . . . | 3 | 3 0 0 | * 7680 * * * * | 1 0 0 1 1 1 0 0 0 0 | 1 1 1 0 0 1 1 1 0 0 | 1 1 1 0 1 . x . . x . | 4 | 2 2 0 | * * 11520 * * * | 0 1 0 0 1 0 1 1 0 0 | 0 1 0 1 1 1 0 1 1 0 | 1 0 1 1 1 . x . . . x | 4 | 2 0 2 | * * * 5760 * * | 0 0 1 0 0 2 0 2 0 0 | 0 0 2 0 2 0 1 2 1 0 | 0 1 2 1 1 . . . o3x . | 3 | 0 3 0 | * * * * 3840 * | 0 0 0 0 0 0 2 0 1 1 | 0 0 0 1 0 2 0 0 2 1 | 1 0 0 1 2 . . . . x4x | 8 | 0 4 4 | * * * * * 1440 | 0 0 0 0 0 0 0 4 0 2 | 0 0 0 0 2 0 0 2 4 1 | 0 0 1 2 2 ------------+------+-----------------+--------------------------------+-------------------------------------------------+-----------------------------------------+------------------ o3x3o . . . ♦ 6 | 12 0 0 | 4 4 0 0 0 0 | 1920 * * * * * * * * * | 1 1 1 0 0 0 0 0 0 0 | 1 1 1 0 0 o3x . . x . ♦ 6 | 6 3 0 | 2 0 3 0 0 0 | * 3840 * * * * * * * * | 0 1 0 1 1 0 0 0 0 0 | 1 0 1 1 0 o3x . . . x ♦ 6 | 6 0 3 | 2 0 0 3 0 0 | * * 1920 * * * * * * * | 0 0 2 0 2 0 0 0 0 0 | 0 1 2 1 0 . x3o3o . . ♦ 4 | 6 0 0 | 0 4 0 0 0 0 | * * * 1920 * * * * * * | 1 0 0 0 0 1 1 0 0 0 | 1 1 0 0 1 . x3o . x . ♦ 6 | 6 3 0 | 0 2 3 0 0 0 | * * * * 3840 * * * * * | 0 1 0 0 0 1 0 1 0 0 | 1 0 1 0 1 . x3o . . x ♦ 6 | 6 0 3 | 0 2 0 3 0 0 | * * * * * 3840 * * * * | 0 0 1 0 0 0 1 1 0 0 | 0 1 1 0 1 . x . o3x . ♦ 6 | 3 6 0 | 0 0 3 0 2 0 | * * * * * * 3840 * * * | 0 0 0 1 0 1 0 0 1 0 | 1 0 0 1 1 . x . . x4x ♦ 16 | 8 8 8 | 0 0 4 4 0 2 | * * * * * * * 2880 * * | 0 0 0 0 1 0 0 1 1 0 | 0 0 1 1 1 . . o3o3x . ♦ 4 | 0 6 0 | 0 0 0 0 4 0 | * * * * * * * * 960 * | 0 0 0 0 0 2 0 0 0 1 | 1 0 0 0 2 . . . o3x4x ♦ 24 | 0 24 12 | 0 0 0 0 8 6 | * * * * * * * * * 480 | 0 0 0 0 0 0 0 0 2 1 | 0 0 0 1 2 ------------+------+-----------------+--------------------------------+-------------------------------------------------+-----------------------------------------+------------------ o3x3o3o . . ♦ 10 | 30 0 0 | 10 20 0 0 0 0 | 5 0 0 5 0 0 0 0 0 0 | 384 * * * * * * * * * | 1 1 0 0 0 o3x3o . x . ♦ 12 | 24 6 0 | 8 8 12 0 0 0 | 2 4 0 0 4 0 0 0 0 0 | * 960 * * * * * * * * | 1 0 1 0 0 o3x3o . . x ♦ 12 | 24 0 6 | 8 8 0 12 0 0 | 2 0 4 0 0 4 0 0 0 0 | * * 960 * * * * * * * | 0 1 1 0 0 o3x . o3x . ♦ 9 | 9 9 0 | 3 0 9 0 3 0 | 0 3 0 0 0 0 3 0 0 0 | * * * 1280 * * * * * * | 1 0 0 1 0 o3x . . x4x ♦ 24 | 24 12 12 | 8 0 12 12 0 3 | 0 4 4 0 0 0 0 3 0 0 | * * * * 960 * * * * * | 0 0 1 1 0 . x3o3o3x . ♦ 20 | 30 30 0 | 0 20 30 0 20 0 | 0 0 0 5 10 0 10 0 5 0 | * * * * * 384 * * * * | 1 0 0 0 1 . x3o3o . x ♦ 8 | 12 0 4 | 0 8 0 6 0 0 | 0 0 0 2 0 4 0 0 0 0 | * * * * * * 960 * * * | 0 1 0 0 1 . x3o . x4x ♦ 24 | 24 12 12 | 0 8 12 12 0 3 | 0 0 0 0 4 4 0 3 0 0 | * * * * * * * 960 * * | 0 0 1 0 1 . x . o3x4x ♦ 48 | 24 48 24 | 0 0 24 12 16 12 | 0 0 0 0 0 0 8 6 0 2 | * * * * * * * * 480 * | 0 0 0 1 1 . . o3o3x4x ♦ 64 | 0 96 32 | 0 0 0 0 64 24 | 0 0 0 0 0 0 0 0 16 8 | * * * * * * * * * 60 | 0 0 0 0 2 ------------+------+-----------------+--------------------------------+-------------------------------------------------+-----------------------------------------+------------------ o3x3o3o3x . ♦ 60 | 180 90 0 | 60 120 180 0 60 0 | 30 60 0 30 60 0 60 0 15 0 | 6 15 0 20 0 6 0 0 0 0 | 64 * * * * o3x3o3o . x ♦ 20 | 60 0 10 | 20 40 0 30 0 0 | 10 0 10 10 0 20 0 0 0 0 | 2 0 5 0 0 0 5 0 0 0 | * 192 * * * o3x3o . x4x ♦ 48 | 96 24 24 | 32 32 48 48 0 6 | 8 16 16 0 16 16 0 12 0 0 | 0 4 4 0 4 0 0 4 0 0 | * * 240 * * o3x . o3x4x ♦ 72 | 72 72 36 | 24 0 72 36 24 18 | 0 24 12 0 0 0 24 18 0 3 | 0 0 0 8 6 0 0 0 3 0 | * * * 160 * . x3o3o3x4x ♦ 640 | 960 960 320 | 0 640 960 480 640 240 | 0 0 0 160 320 320 320 240 160 80 | 0 0 0 0 0 32 80 80 40 10 | * * * * 12
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