- general polytopal classes:
- Wythoffian polytera
links
| Acronym | brewahen |
| Name | biretrosphenary demipenteract |
| Circumradius | sqrt(5) = 2.236068 |
| Coordinates | (2, 2, 1, 1, 0)/sqrt(2) & all permutations, all changes of sign |
| Colonel of regiment | sibrant |
| Face vector | 480, 1920, 1920, 600, 58 |
| Confer |
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External links |
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Incidence matrix according to Dynkin symbol
o
3 \ 3
x---o
3 \ / \ 3
x---x
3/2 3
o3x3x3x3o3*b *c3/2*e . . . . . | 480 | 4 2 2 | 2 4 4 2 2 1 1 | 2 2 1 4 2 2 1 | 2 1 1 2 ---------------------+-----+-------------+-----------------------------+-----------------------+------------ . x . . . | 2 | 960 * * | 1 1 1 1 0 0 0 | 1 1 1 1 1 1 0 | 1 1 1 1 . . x . . | 2 | * 480 * | 0 2 0 0 1 1 0 | 1 0 0 2 2 0 1 | 1 1 0 2 . . . x . | 2 | * * 480 | 0 0 2 0 1 0 1 | 0 1 0 2 0 2 1 | 1 0 1 2 ---------------------+-----+-------------+-----------------------------+-----------------------+------------ o3x . . . | 3 | 3 0 0 | 320 * * * * * * | 1 1 1 0 0 0 0 | 1 1 1 0 . x3x . . | 6 | 3 3 0 | * 320 * * * * * | 1 0 0 1 1 0 0 | 1 1 0 1 . x . x . | 4 | 2 0 2 | * * 480 * * * * | 0 1 0 1 0 1 0 | 1 0 1 1 . x . . o3*b | 3 | 3 0 0 | * * * 320 * * * | 0 0 1 0 1 1 0 | 0 1 1 1 . . x3x . | 6 | 0 3 3 | * * * * 160 * * | 0 0 0 2 0 0 1 | 1 0 0 2 . . x . o *c3/2*e | 3 | 0 3 0 | * * * * * 160 * | 0 0 0 0 2 0 1 | 0 1 0 2 . . . x3o | 3 | 0 0 3 | * * * * * * 160 | 0 0 0 0 0 2 1 | 0 0 1 2 ---------------------+-----+-------------+-----------------------------+-----------------------+------------ o3x3x . . ♦ 12 | 12 6 0 | 4 4 0 0 0 0 0 | 80 * * * * * * | 1 1 0 0 o3x . x . ♦ 6 | 6 0 3 | 2 0 3 0 0 0 0 | * 160 * * * * * | 1 0 1 0 o3x . . o3*b ♦ 6 | 12 0 0 | 4 0 0 4 0 0 0 | * * 80 * * * * | 0 1 1 0 . x3x3x . ♦ 24 | 12 12 12 | 0 4 6 0 4 0 0 | * * * 80 * * * | 1 0 0 1 . x3x . o3*b *c3/2*e ♦ 12 | 12 12 0 | 0 4 0 4 0 4 0 | * * * * 80 * * | 0 1 0 1 . x . x3o3*b ♦ 12 | 12 0 12 | 0 0 6 4 0 0 4 | * * * * * 80 * | 0 0 1 1 . . x3x3o *c3/2*e ♦ 12 | 0 12 12 | 0 0 0 0 4 4 4 | * * * * * * 40 | 0 0 0 2 ---------------------+-----+-------------+-----------------------------+-----------------------+------------ o3x3x3x . ♦ 60 | 60 30 30 | 20 20 30 0 10 0 0 | 5 10 0 5 0 0 0 | 16 * * * o3x3x . o3*b *c3/2*e ♦ 30 | 60 30 0 | 20 20 0 20 0 10 0 | 5 0 5 0 5 0 0 | * 16 * * o3x . x3o3*b ♦ 30 | 60 0 30 | 20 0 30 20 0 0 10 | 0 10 5 0 0 5 0 | * * 16 * . x3x3x3o3*b *c3/2*e ♦ 96 | 96 96 96 | 0 32 48 32 32 32 32 | 0 0 0 8 8 8 8 | * * * 10
o
3/2 \ 3
x---o
3 \ / \ 3
x---x
3/2 3
o3/2x3x3x3o3*b *c3/2*e . . . . . | 480 | 4 2 2 | 2 4 4 2 2 1 1 | 2 2 1 4 2 2 1 | 2 1 1 2 -----------------------+-----+-------------+-----------------------------+-----------------------+------------ . x . . . | 2 | 960 * * | 1 1 1 1 0 0 0 | 1 1 1 1 1 1 0 | 1 1 1 1 . . x . . | 2 | * 480 * | 0 2 0 0 1 1 0 | 1 0 0 2 2 0 1 | 1 1 0 2 . . . x . | 2 | * * 480 | 0 0 2 0 1 0 1 | 0 1 0 2 0 2 1 | 1 0 1 2 -----------------------+-----+-------------+-----------------------------+-----------------------+------------ o3/2x . . . | 3 | 3 0 0 | 320 * * * * * * | 1 1 1 0 0 0 0 | 1 1 1 0 . x3x . . | 6 | 3 3 0 | * 320 * * * * * | 1 0 0 1 1 0 0 | 1 1 0 1 . x . x . | 4 | 2 0 2 | * * 480 * * * * | 0 1 0 1 0 1 0 | 1 0 1 1 . x . . o3*b | 3 | 3 0 0 | * * * 320 * * * | 0 0 1 0 1 1 0 | 0 1 1 1 . . x3x . | 6 | 0 3 3 | * * * * 160 * * | 0 0 0 2 0 0 1 | 1 0 0 2 . . x . o *c3/2*e | 3 | 0 3 0 | * * * * * 160 * | 0 0 0 0 2 0 1 | 0 1 0 2 . . . x3o | 3 | 0 0 3 | * * * * * * 160 | 0 0 0 0 0 2 1 | 0 0 1 2 -----------------------+-----+-------------+-----------------------------+-----------------------+------------ o3/2x3x . . ♦ 12 | 12 6 0 | 4 4 0 0 0 0 0 | 80 * * * * * * | 1 1 0 0 o3/2x . x . ♦ 6 | 6 0 3 | 2 0 3 0 0 0 0 | * 160 * * * * * | 1 0 1 0 o3/2x . . o3*b ♦ 6 | 12 0 0 | 4 0 0 4 0 0 0 | * * 80 * * * * | 0 1 1 0 . x3x3x . ♦ 24 | 12 12 12 | 0 4 6 0 4 0 0 | * * * 80 * * * | 1 0 0 1 . x3x . o3*b *c3/2*e ♦ 12 | 12 12 0 | 0 4 0 4 0 4 0 | * * * * 80 * * | 0 1 0 1 . x . x3o3*b ♦ 12 | 12 0 12 | 0 0 6 4 0 0 4 | * * * * * 80 * | 0 0 1 1 . . x3x3o *c3/2*e ♦ 12 | 0 12 12 | 0 0 0 0 4 4 4 | * * * * * * 40 | 0 0 0 2 -----------------------+-----+-------------+-----------------------------+-----------------------+------------ o3/2x3x3x . ♦ 60 | 60 30 30 | 20 20 30 0 10 0 0 | 5 10 0 5 0 0 0 | 16 * * * o3/2x3x . o3*b *c3/2*e ♦ 30 | 60 30 0 | 20 20 0 20 0 10 0 | 5 0 5 0 5 0 0 | * 16 * * o3/2x . x3o3*b ♦ 30 | 60 0 30 | 20 0 30 20 0 0 10 | 0 10 5 0 0 5 0 | * * 16 * . x3x3x3o3*b *c3/2*e ♦ 96 | 96 96 96 | 0 32 48 32 32 32 32 | 0 0 0 8 8 8 8 | * * * 10
o
3 \ 3/2
x---o
3 \ / \ 3/2
x---x
3 3
o3x3x3x3/2o3/2*b *c3*e . . . . . | 480 | 4 2 2 | 2 4 4 2 2 1 1 | 2 2 1 4 2 2 1 | 2 1 1 2 -----------------------+-----+-------------+-----------------------------+-----------------------+------------ . x . . . | 2 | 960 * * | 1 1 1 1 0 0 0 | 1 1 1 1 1 1 0 | 1 1 1 1 . . x . . | 2 | * 480 * | 0 2 0 0 1 1 0 | 1 0 0 2 2 0 1 | 1 1 0 2 . . . x . | 2 | * * 480 | 0 0 2 0 1 0 1 | 0 1 0 2 0 2 1 | 1 0 1 2 -----------------------+-----+-------------+-----------------------------+-----------------------+------------ o3x . . . | 3 | 3 0 0 | 320 * * * * * * | 1 1 1 0 0 0 0 | 1 1 1 0 . x3x . . | 6 | 3 3 0 | * 320 * * * * * | 1 0 0 1 1 0 0 | 1 1 0 1 . x . x . | 4 | 2 0 2 | * * 480 * * * * | 0 1 0 1 0 1 0 | 1 0 1 1 . x . . o3/2*b | 3 | 3 0 0 | * * * 320 * * * | 0 0 1 0 1 1 0 | 0 1 1 1 . . x3x . | 6 | 0 3 3 | * * * * 160 * * | 0 0 0 2 0 0 1 | 1 0 0 2 . . x . o *c3*e | 3 | 0 3 0 | * * * * * 160 * | 0 0 0 0 2 0 1 | 0 1 0 2 . . . x3/2o | 3 | 0 0 3 | * * * * * * 160 | 0 0 0 0 0 2 1 | 0 0 1 2 -----------------------+-----+-------------+-----------------------------+-----------------------+------------ o3x3x . . ♦ 12 | 12 6 0 | 4 4 0 0 0 0 0 | 80 * * * * * * | 1 1 0 0 o3x . x . ♦ 6 | 6 0 3 | 2 0 3 0 0 0 0 | * 160 * * * * * | 1 0 1 0 o3x . . o3/2*b ♦ 6 | 12 0 0 | 4 0 0 4 0 0 0 | * * 80 * * * * | 0 1 1 0 . x3x3x . ♦ 24 | 12 12 12 | 0 4 6 0 4 0 0 | * * * 80 * * * | 1 0 0 1 . x3x . o3/2*b *c3*e ♦ 12 | 12 12 0 | 0 4 0 4 0 4 0 | * * * * 80 * * | 0 1 0 1 . x . x3/2o3/2*b ♦ 12 | 12 0 12 | 0 0 6 4 0 0 4 | * * * * * 80 * | 0 0 1 1 . . x3x3/2o *c3*e ♦ 12 | 0 12 12 | 0 0 0 0 4 4 4 | * * * * * * 40 | 0 0 0 2 -----------------------+-----+-------------+-----------------------------+-----------------------+------------ o3x3x3x . ♦ 60 | 60 30 30 | 20 20 30 0 10 0 0 | 5 10 0 5 0 0 0 | 16 * * * o3x3x . o3/2*b *c3*e ♦ 30 | 60 30 0 | 20 20 0 20 0 10 0 | 5 0 5 0 5 0 0 | * 16 * * o3x . x3/2o3/2*b ♦ 30 | 60 0 30 | 20 0 30 20 0 0 10 | 0 10 5 0 0 5 0 | * * 16 * . x3x3x3/2o3/2*b *c3*e ♦ 96 | 96 96 96 | 0 32 48 32 32 32 32 | 0 0 0 8 8 8 8 | * * * 10
o
3/2 \ 3/2
x---o
3 \ / \ 3/2
x---x
3 3
o3/2x3x3x3/2o3/2*b *c3*e . . . . . | 480 | 4 2 2 | 2 4 4 2 2 1 1 | 2 2 1 4 2 2 1 | 2 1 1 2 -------------------------+-----+-------------+-----------------------------+-----------------------+------------ . x . . . | 2 | 960 * * | 1 1 1 1 0 0 0 | 1 1 1 1 1 1 0 | 1 1 1 1 . . x . . | 2 | * 480 * | 0 2 0 0 1 1 0 | 1 0 0 2 2 0 1 | 1 1 0 2 . . . x . | 2 | * * 480 | 0 0 2 0 1 0 1 | 0 1 0 2 0 2 1 | 1 0 1 2 -------------------------+-----+-------------+-----------------------------+-----------------------+------------ o3/2x . . . | 3 | 3 0 0 | 320 * * * * * * | 1 1 1 0 0 0 0 | 1 1 1 0 . x3x . . | 6 | 3 3 0 | * 320 * * * * * | 1 0 0 1 1 0 0 | 1 1 0 1 . x . x . | 4 | 2 0 2 | * * 480 * * * * | 0 1 0 1 0 1 0 | 1 0 1 1 . x . . o3/2*b | 3 | 3 0 0 | * * * 320 * * * | 0 0 1 0 1 1 0 | 0 1 1 1 . . x3x . | 6 | 0 3 3 | * * * * 160 * * | 0 0 0 2 0 0 1 | 1 0 0 2 . . x . o *c3*e | 3 | 0 3 0 | * * * * * 160 * | 0 0 0 0 2 0 1 | 0 1 0 2 . . . x3/2o | 3 | 0 0 3 | * * * * * * 160 | 0 0 0 0 0 2 1 | 0 0 1 2 -------------------------+-----+-------------+-----------------------------+-----------------------+------------ o3/2x3x . . ♦ 12 | 12 6 0 | 4 4 0 0 0 0 0 | 80 * * * * * * | 1 1 0 0 o3/2x . x . ♦ 6 | 6 0 3 | 2 0 3 0 0 0 0 | * 160 * * * * * | 1 0 1 0 o3/2x . . o3/2*b ♦ 6 | 12 0 0 | 4 0 0 4 0 0 0 | * * 80 * * * * | 0 1 1 0 . x3x3x . ♦ 24 | 12 12 12 | 0 4 6 0 4 0 0 | * * * 80 * * * | 1 0 0 1 . x3x . o3/2*b *c3*e ♦ 12 | 12 12 0 | 0 4 0 4 0 4 0 | * * * * 80 * * | 0 1 0 1 . x . x3/2o3/2*b ♦ 12 | 12 0 12 | 0 0 6 4 0 0 4 | * * * * * 80 * | 0 0 1 1 . . x3x3/2o *c3*e ♦ 12 | 0 12 12 | 0 0 0 0 4 4 4 | * * * * * * 40 | 0 0 0 2 -------------------------+-----+-------------+-----------------------------+-----------------------+------------ o3/2x3x3x . ♦ 60 | 60 30 30 | 20 20 30 0 10 0 0 | 5 10 0 5 0 0 0 | 16 * * * o3/2x3x . o3/2*b *c3*e ♦ 30 | 60 30 0 | 20 20 0 20 0 10 0 | 5 0 5 0 5 0 0 | * 16 * * o3/2x . x3/2o3/2*b ♦ 30 | 60 0 30 | 20 0 30 20 0 0 10 | 0 10 5 0 0 5 0 | * * 16 * . x3x3x3/2o3/2*b *c3*e ♦ 96 | 96 96 96 | 0 32 48 32 32 32 32 | 0 0 0 8 8 8 8 | * * * 10
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