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- general polytopal classes:
- Wythoffian polytera
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| Acronym | quiprin |
| Name | quasiprismatorhombated penteract |
| Circumradius | sqrt[23-10 sqrt(2)]/2 = 1.488108 |
| Vertex figure |
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| Coordinates | (2 sqrt(2)-1, 2 sqrt(2)-1, sqrt(2)-1, 1, 1)/2 & all permutations, all changes of sign |
| Colonel of regiment | gibtadin |
| Face vector | 960, 2880, 2960, 1240, 202 |
| Confer |
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External links |
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As abstract polyteron quiprin is isomorph to prin, thereby replacing retrograde by prograde squares, resp. querco by sirco, resp. paqrit by prit.
Incidence matrix according to Dynkin symbol
o3x3x3o4/3x . . . . . | 960 | 2 2 2 | 1 4 4 1 2 1 | 2 2 2 4 2 1 | 1 2 1 2 ------------+-----+-------------+-------------------------+------------------------+------------ . x . . . | 2 | 960 * * | 1 2 2 0 0 0 | 2 2 1 2 1 0 | 1 2 1 1 . . x . . | 2 | * 960 * | 0 2 0 1 1 0 | 1 0 2 2 0 1 | 1 1 0 2 . . . . x | 2 | * * 960 | 0 0 2 0 1 1 | 0 1 0 2 2 1 | 0 1 1 2 ------------+-----+-------------+-------------------------+------------------------+------------ o3x . . . | 3 | 3 0 0 | 320 * * * * * | 2 2 0 0 0 0 | 1 2 1 0 . x3x . . | 6 | 3 3 0 | * 640 * * * * | 1 0 1 1 0 0 | 1 1 0 1 . x . . x | 4 | 2 0 2 | * * 960 * * * | 0 1 0 1 1 0 | 0 1 1 1 . . x3o . | 3 | 0 3 0 | * * * 320 * * | 0 0 2 0 0 1 | 1 0 0 2 . . x . x | 4 | 0 2 2 | * * * * 480 * | 0 0 0 2 0 1 | 0 1 0 2 . . . o4/3x | 4 | 0 0 4 | * * * * * 240 | 0 0 0 0 2 1 | 0 0 1 2 ------------+-----+-------------+-------------------------+------------------------+------------ o3x3x . . ♦ 12 | 12 6 0 | 4 4 0 0 0 0 | 160 * * * * * | 1 1 0 0 o3x . . x ♦ 6 | 6 0 3 | 2 0 3 0 0 0 | * 320 * * * * | 0 1 1 0 . x3x3o . ♦ 12 | 6 12 0 | 0 4 0 4 0 0 | * * 160 * * * | 1 0 0 1 . x3x . x ♦ 12 | 6 6 6 | 0 2 3 0 3 0 | * * * 320 * * | 0 1 0 1 . x . o4/3x ♦ 8 | 4 0 8 | 0 0 4 0 0 2 | * * * * 240 * | 0 0 1 1 . . x3o4/3x ♦ 24 | 0 24 24 | 0 0 0 8 12 6 | * * * * * 40 | 0 0 0 2 ------------+-----+-------------+-------------------------+------------------------+------------ o3x3x3o . ♦ 30 | 30 30 0 | 10 20 0 10 0 0 | 5 0 5 0 0 0 | 32 * * * o3x3x . x ♦ 24 | 24 12 12 | 8 8 12 0 6 0 | 2 4 0 4 0 0 | * 80 * * o3x . o4/3x ♦ 12 | 12 0 12 | 4 0 12 0 0 3 | 0 4 0 0 3 0 | * * 80 * . x3x3o4/3x ♦ 192 | 96 192 192 | 0 64 96 64 96 48 | 0 0 16 32 24 8 | * * * 10
o3x3x3/2o4x . . . . . | 960 | 2 2 2 | 1 4 4 1 2 1 | 2 2 2 4 2 1 | 1 2 1 2 ------------+-----+-------------+-------------------------+------------------------+------------ . x . . . | 2 | 960 * * | 1 2 2 0 0 0 | 2 2 1 2 1 0 | 1 2 1 1 . . x . . | 2 | * 960 * | 0 2 0 1 1 0 | 1 0 2 2 0 1 | 1 1 0 2 . . . . x | 2 | * * 960 | 0 0 2 0 1 1 | 0 1 0 2 2 1 | 0 1 1 2 ------------+-----+-------------+-------------------------+------------------------+------------ o3x . . . | 3 | 3 0 0 | 320 * * * * * | 2 2 0 0 0 0 | 1 2 1 0 . x3x . . | 6 | 3 3 0 | * 640 * * * * | 1 0 1 1 0 0 | 1 1 0 1 . x . . x | 4 | 2 0 2 | * * 960 * * * | 0 1 0 1 1 0 | 0 1 1 1 . . x3/2o . | 3 | 0 3 0 | * * * 320 * * | 0 0 2 0 0 1 | 1 0 0 2 . . x . x | 4 | 0 2 2 | * * * * 480 * | 0 0 0 2 0 1 | 0 1 0 2 . . . o4x | 4 | 0 0 4 | * * * * * 240 | 0 0 0 0 2 1 | 0 0 1 2 ------------+-----+-------------+-------------------------+------------------------+------------ o3x3x . . ♦ 12 | 12 6 0 | 4 4 0 0 0 0 | 160 * * * * * | 1 1 0 0 o3x . . x ♦ 6 | 6 0 3 | 2 0 3 0 0 0 | * 320 * * * * | 0 1 1 0 . x3x3/2o . ♦ 12 | 6 12 0 | 0 4 0 4 0 0 | * * 160 * * * | 1 0 0 1 . x3x . x ♦ 12 | 6 6 6 | 0 2 3 0 3 0 | * * * 320 * * | 0 1 0 1 . x . o4x ♦ 8 | 4 0 8 | 0 0 4 0 0 2 | * * * * 240 * | 0 0 1 1 . . x3/2o4x ♦ 24 | 0 24 24 | 0 0 0 8 12 6 | * * * * * 40 | 0 0 0 2 ------------+-----+-------------+-------------------------+------------------------+------------ o3x3x3/2o . ♦ 30 | 30 30 0 | 10 20 0 10 0 0 | 5 0 5 0 0 0 | 32 * * * o3x3x . x ♦ 24 | 24 12 12 | 8 8 12 0 6 0 | 2 4 0 4 0 0 | * 80 * * o3x . o4x ♦ 12 | 12 0 12 | 4 0 12 0 0 3 | 0 4 0 0 3 0 | * * 80 * . x3x3/2o4x ♦ 192 | 96 192 192 | 0 64 96 64 96 48 | 0 0 16 32 24 8 | * * * 10
o3/2x3x3o4/3x . . . . . | 960 | 2 2 2 | 1 4 4 1 2 1 | 2 2 2 4 2 1 | 1 2 1 2 --------------+-----+-------------+-------------------------+------------------------+------------ . x . . . | 2 | 960 * * | 1 2 2 0 0 0 | 2 2 1 2 1 0 | 1 2 1 1 . . x . . | 2 | * 960 * | 0 2 0 1 1 0 | 1 0 2 2 0 1 | 1 1 0 2 . . . . x | 2 | * * 960 | 0 0 2 0 1 1 | 0 1 0 2 2 1 | 0 1 1 2 --------------+-----+-------------+-------------------------+------------------------+------------ o3/2x . . . | 3 | 3 0 0 | 320 * * * * * | 2 2 0 0 0 0 | 1 2 1 0 . x3x . . | 6 | 3 3 0 | * 640 * * * * | 1 0 1 1 0 0 | 1 1 0 1 . x . . x | 4 | 2 0 2 | * * 960 * * * | 0 1 0 1 1 0 | 0 1 1 1 . . x3o . | 3 | 0 3 0 | * * * 320 * * | 0 0 2 0 0 1 | 1 0 0 2 . . x . x | 4 | 0 2 2 | * * * * 480 * | 0 0 0 2 0 1 | 0 1 0 2 . . . o4/3x | 4 | 0 0 4 | * * * * * 240 | 0 0 0 0 2 1 | 0 0 1 2 --------------+-----+-------------+-------------------------+------------------------+------------ o3/2x3x . . ♦ 12 | 12 6 0 | 4 4 0 0 0 0 | 160 * * * * * | 1 1 0 0 o3/2x . . x ♦ 6 | 6 0 3 | 2 0 3 0 0 0 | * 320 * * * * | 0 1 1 0 . x3x3o . ♦ 12 | 6 12 0 | 0 4 0 4 0 0 | * * 160 * * * | 1 0 0 1 . x3x . x ♦ 12 | 6 6 6 | 0 2 3 0 3 0 | * * * 320 * * | 0 1 0 1 . x . o4/3x ♦ 8 | 4 0 8 | 0 0 4 0 0 2 | * * * * 240 * | 0 0 1 1 . . x3o4/3x ♦ 24 | 0 24 24 | 0 0 0 8 12 6 | * * * * * 40 | 0 0 0 2 --------------+-----+-------------+-------------------------+------------------------+------------ o3/2x3x3o . ♦ 30 | 30 30 0 | 10 20 0 10 0 0 | 5 0 5 0 0 0 | 32 * * * o3/2x3x . x ♦ 24 | 24 12 12 | 8 8 12 0 6 0 | 2 4 0 4 0 0 | * 80 * * o3/2x . o4/3x ♦ 12 | 12 0 12 | 4 0 12 0 0 3 | 0 4 0 0 3 0 | * * 80 * . x3x3o4/3x ♦ 192 | 96 192 192 | 0 64 96 64 96 48 | 0 0 16 32 24 8 | * * * 10
o3/2x3x3/2o4x . . . . . | 960 | 2 2 2 | 1 4 4 1 2 1 | 2 2 2 4 2 1 | 1 2 1 2 --------------+-----+-------------+-------------------------+------------------------+------------ . x . . . | 2 | 960 * * | 1 2 2 0 0 0 | 2 2 1 2 1 0 | 1 2 1 1 . . x . . | 2 | * 960 * | 0 2 0 1 1 0 | 1 0 2 2 0 1 | 1 1 0 2 . . . . x | 2 | * * 960 | 0 0 2 0 1 1 | 0 1 0 2 2 1 | 0 1 1 2 --------------+-----+-------------+-------------------------+------------------------+------------ o3/2x . . . | 3 | 3 0 0 | 320 * * * * * | 2 2 0 0 0 0 | 1 2 1 0 . x3x . . | 6 | 3 3 0 | * 640 * * * * | 1 0 1 1 0 0 | 1 1 0 1 . x . . x | 4 | 2 0 2 | * * 960 * * * | 0 1 0 1 1 0 | 0 1 1 1 . . x3/2o . | 3 | 0 3 0 | * * * 320 * * | 0 0 2 0 0 1 | 1 0 0 2 . . x . x | 4 | 0 2 2 | * * * * 480 * | 0 0 0 2 0 1 | 0 1 0 2 . . . o4x | 4 | 0 0 4 | * * * * * 240 | 0 0 0 0 2 1 | 0 0 1 2 -------------+-----+-------------+-------------------------+------------------------+------------ o3/2x3x . . ♦ 12 | 12 6 0 | 4 4 0 0 0 0 | 160 * * * * * | 1 1 0 0 o3/2x . . x ♦ 6 | 6 0 3 | 2 0 3 0 0 0 | * 320 * * * * | 0 1 1 0 . x3x3/2o . ♦ 12 | 6 12 0 | 0 4 0 4 0 0 | * * 160 * * * | 1 0 0 1 . x3x . x ♦ 12 | 6 6 6 | 0 2 3 0 3 0 | * * * 320 * * | 0 1 0 1 . x . o4x ♦ 8 | 4 0 8 | 0 0 4 0 0 2 | * * * * 240 * | 0 0 1 1 . . x3/2o4x ♦ 24 | 0 24 24 | 0 0 0 8 12 6 | * * * * * 40 | 0 0 0 2 --------------+-----+-------------+-------------------------+------------------------+------------ o3/2x3x3/2o . ♦ 30 | 30 30 0 | 10 20 0 10 0 0 | 5 0 5 0 0 0 | 32 * * * o3/2x3x . x ♦ 24 | 24 12 12 | 8 8 12 0 6 0 | 2 4 0 4 0 0 | * 80 * * o3/2x . o4x ♦ 12 | 12 0 12 | 4 0 12 0 0 3 | 0 4 0 0 3 0 | * * 80 * . x3x3/2o4x ♦ 192 | 96 192 192 | 0 64 96 64 96 48 | 0 0 16 32 24 8 | * * * 10
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