- general polytopal classes:
- Wythoffian polytera
links
| Acronym | katcabadint (alt.: katacbadint) |
| Name | skewtrigonary cellibiprismatodispenteractitriacontaditeron |
| Circumradius | 3/2 = 1.5 |
| Colonel of regiment | skatbacadint |
| Face vector | 640, 2880, 4000, 2000, 212 |
| Confer |
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External links |
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As abstract polytope katcabadint is automorph, thereby interchanging the roles of sidpith and quidpith.
Incidence matrix according to Dynkin symbol
3/2 3 4
x---o---o---x
3 \ / 3
x
x4o3o3x3x3/2*c . . . . . | 640 | 3 3 3 | 3 6 6 3 3 3 | 1 3 3 3 3 6 1 1 3 | 1 1 3 3 1 ---------------+-----+-------------+-------------------------+------------------------------------+--------------- x . . . . | 2 | 960 * * | 2 2 2 0 0 0 | 1 2 2 1 1 2 0 0 0 | 1 1 2 1 0 . . . x . | 2 | * 960 * | 0 2 0 2 0 1 | 0 1 0 2 0 2 1 0 2 | 1 0 1 2 1 . . . . x | 2 | * * 960 | 0 0 2 0 2 1 | 0 0 1 0 2 2 0 1 2 | 0 1 1 2 1 ---------------+-----+-------------+-------------------------+------------------------------------+--------------- x4o . . . | 4 | 4 0 0 | 480 * * * * * | 1 1 1 0 0 0 0 0 0 | 1 1 1 0 0 x . . x . | 4 | 2 2 0 | * 960 * * * * | 0 1 0 1 0 1 0 0 0 | 1 0 1 1 0 x . . . x | 4 | 2 0 2 | * * 960 * * * | 0 0 1 0 1 1 0 0 0 | 0 1 1 1 0 . . o3x . | 3 | 0 3 0 | * * * 640 * * | 0 0 0 1 0 0 1 0 1 | 1 0 0 1 1 . . o . x3/2*c | 3 | 0 0 3 | * * * * 640 * | 0 0 0 0 1 0 0 1 1 | 0 1 0 1 1 . . . x3x | 6 | 0 3 3 | * * * * * 320 | 0 0 0 0 0 2 0 0 2 | 0 0 1 2 1 ---------------+-----+-------------+-------------------------+------------------------------------+--------------- x4o3o . . ♦ 8 | 12 0 0 | 6 0 0 0 0 0 | 80 * * * * * * * * | 1 1 0 0 0 x4o . x . ♦ 8 | 8 4 0 | 2 4 0 0 0 0 | * 240 * * * * * * * | 1 0 1 0 0 x4o . . x ♦ 8 | 8 0 4 | 2 0 4 0 0 0 | * * 240 * * * * * * | 0 1 1 0 0 x . o3x . ♦ 6 | 3 6 0 | 0 3 0 2 0 0 | * * * 320 * * * * * | 1 0 0 1 0 x . o . x3/2*c ♦ 6 | 3 0 6 | 0 0 3 0 2 0 | * * * * 320 * * * * | 0 1 0 1 0 x . . x3x ♦ 12 | 6 6 6 | 0 3 3 0 0 2 | * * * * * 320 * * * | 0 0 1 1 0 . o3o3x . ♦ 4 | 0 6 0 | 0 0 0 4 0 0 | * * * * * * 160 * * | 1 0 0 0 1 . o3o . x3/2*c ♦ 4 | 0 0 6 | 0 0 0 0 4 0 | * * * * * * * 160 * | 0 1 0 0 1 . . o3x3x3/2*c ♦ 12 | 0 12 12 | 0 0 0 4 4 4 | * * * * * * * * 160 | 0 0 0 1 1 ---------------+-----+-------------+-------------------------+------------------------------------+--------------- x4o3o3x . ♦ 64 | 96 96 0 | 48 96 0 64 0 0 | 8 24 0 32 0 0 16 0 0 | 10 * * * * x4o3o . x3/2*c ♦ 64 | 96 0 96 | 48 0 96 0 64 0 | 8 0 24 0 32 0 0 16 0 | * 10 * * * x4o . x3x ♦ 24 | 24 12 12 | 6 12 12 0 0 4 | 0 3 3 0 0 4 0 0 0 | * * 80 * * x . o3x3x3/2*c ♦ 24 | 12 24 24 | 0 12 12 8 8 8 | 0 0 0 4 4 4 0 0 2 | * * * 80 * . o3o3x3x3/2*c ♦ 20 | 0 30 30 | 0 0 0 20 20 10 | 0 0 0 0 0 0 5 5 5 | * * * * 32
3 3/2 4
x---o---o---x
3 \ / 3/2
x
x4o3/2o3x3x3/2*c . . . . . | 640 | 3 3 3 | 3 6 6 3 3 3 | 1 3 3 3 3 6 1 1 3 | 1 1 3 3 1 -----------------+-----+-------------+-------------------------+------------------------------------+--------------- x . . . . | 2 | 960 * * | 2 2 2 0 0 0 | 1 2 2 1 1 2 0 0 0 | 1 1 2 1 0 . . . x . | 2 | * 960 * | 0 2 0 2 0 1 | 0 1 0 2 0 2 1 0 2 | 1 0 1 2 1 . . . . x | 2 | * * 960 | 0 0 2 0 2 1 | 0 0 1 0 2 2 0 1 2 | 0 1 1 2 1 -----------------+-----+-------------+-------------------------+------------------------------------+--------------- x4o . . . | 4 | 4 0 0 | 480 * * * * * | 1 1 1 0 0 0 0 0 0 | 1 1 1 0 0 x . . x . | 4 | 2 2 0 | * 960 * * * * | 0 1 0 1 0 1 0 0 0 | 1 0 1 1 0 x . . . x | 4 | 2 0 2 | * * 960 * * * | 0 0 1 0 1 1 0 0 0 | 0 1 1 1 0 . . o3x . | 3 | 0 3 0 | * * * 640 * * | 0 0 0 1 0 0 1 0 1 | 1 0 0 1 1 . . o . x3/2*c | 3 | 0 0 3 | * * * * 640 * | 0 0 0 0 1 0 0 1 1 | 0 1 0 1 1 . . . x3x | 6 | 0 3 3 | * * * * * 320 | 0 0 0 0 0 2 0 0 2 | 0 0 1 2 1 -----------------+-----+-------------+-------------------------+------------------------------------+--------------- x4o3/2o . . ♦ 8 | 12 0 0 | 6 0 0 0 0 0 | 80 * * * * * * * * | 1 1 0 0 0 x4o . x . ♦ 8 | 8 4 0 | 2 4 0 0 0 0 | * 240 * * * * * * * | 1 0 1 0 0 x4o . . x ♦ 8 | 8 0 4 | 2 0 4 0 0 0 | * * 240 * * * * * * | 0 1 1 0 0 x . o3x . ♦ 6 | 3 6 0 | 0 3 0 2 0 0 | * * * 320 * * * * * | 1 0 0 1 0 x . o . x3/2*c ♦ 6 | 3 0 6 | 0 0 3 0 2 0 | * * * * 320 * * * * | 0 1 0 1 0 x . . x3x ♦ 12 | 6 6 6 | 0 3 3 0 0 2 | * * * * * 320 * * * | 0 0 1 1 0 . o3/2o3x . ♦ 4 | 0 6 0 | 0 0 0 4 0 0 | * * * * * * 160 * * | 1 0 0 0 1 . o3/2o . x3/2*c ♦ 4 | 0 0 6 | 0 0 0 0 4 0 | * * * * * * * 160 * | 0 1 0 0 1 . . o3x3x3/2*c ♦ 12 | 0 12 12 | 0 0 0 4 4 4 | * * * * * * * * 160 | 0 0 0 1 1 -----------------+-----+-------------+-------------------------+------------------------------------+--------------- x4o3/2o3x . ♦ 64 | 96 96 0 | 48 96 0 64 0 0 | 8 24 0 32 0 0 16 0 0 | 10 * * * * x4o3/2o . x3/2*c ♦ 64 | 96 0 96 | 48 0 96 0 64 0 | 8 0 24 0 32 0 0 16 0 | * 10 * * * x4o . x3x ♦ 24 | 24 12 12 | 6 12 12 0 0 4 | 0 3 3 0 0 4 0 0 0 | * * 80 * * x . o3x3x3/2*c ♦ 24 | 12 24 24 | 0 12 12 8 8 8 | 0 0 0 4 4 4 0 0 2 | * * * 80 * . o3/2o3x3x3/2*c ♦ 20 | 0 30 30 | 0 0 0 20 20 10 | 0 0 0 0 0 0 5 5 5 | * * * * 32
3 3 4/3
x---o---o---x
3 \ / 3/2
x
x4/3o3o3x3x3/2*c . . . . . | 640 | 3 3 3 | 3 6 6 3 3 3 | 1 3 3 3 3 6 1 1 3 | 1 1 3 3 1 -----------------+-----+-------------+-------------------------+------------------------------------+--------------- x . . . . | 2 | 960 * * | 2 2 2 0 0 0 | 1 2 2 1 1 2 0 0 0 | 1 1 2 1 0 . . . x . | 2 | * 960 * | 0 2 0 2 0 1 | 0 1 0 2 0 2 1 0 2 | 1 0 1 2 1 . . . . x | 2 | * * 960 | 0 0 2 0 2 1 | 0 0 1 0 2 2 0 1 2 | 0 1 1 2 1 -----------------+-----+-------------+-------------------------+------------------------------------+--------------- x4/3o . . . | 4 | 4 0 0 | 480 * * * * * | 1 1 1 0 0 0 0 0 0 | 1 1 1 0 0 x . . x . | 4 | 2 2 0 | * 960 * * * * | 0 1 0 1 0 1 0 0 0 | 1 0 1 1 0 x . . . x | 4 | 2 0 2 | * * 960 * * * | 0 0 1 0 1 1 0 0 0 | 0 1 1 1 0 . . o3x . | 3 | 0 3 0 | * * * 640 * * | 0 0 0 1 0 0 1 0 1 | 1 0 0 1 1 . . o . x3/2*c | 3 | 0 0 3 | * * * * 640 * | 0 0 0 0 1 0 0 1 1 | 0 1 0 1 1 . . . x3x | 6 | 0 3 3 | * * * * * 320 | 0 0 0 0 0 2 0 0 2 | 0 0 1 2 1 -----------------+-----+-------------+-------------------------+------------------------------------+--------------- x4/3o3o . . ♦ 8 | 12 0 0 | 6 0 0 0 0 0 | 80 * * * * * * * * | 1 1 0 0 0 x4/3o . x . ♦ 8 | 8 4 0 | 2 4 0 0 0 0 | * 240 * * * * * * * | 1 0 1 0 0 x4/3o . . x ♦ 8 | 8 0 4 | 2 0 4 0 0 0 | * * 240 * * * * * * | 0 1 1 0 0 x . o3x . ♦ 6 | 3 6 0 | 0 3 0 2 0 0 | * * * 320 * * * * * | 1 0 0 1 0 x . o . x3/2*c ♦ 6 | 3 0 6 | 0 0 3 0 2 0 | * * * * 320 * * * * | 0 1 0 1 0 x . . x3x ♦ 12 | 6 6 6 | 0 3 3 0 0 2 | * * * * * 320 * * * | 0 0 1 1 0 . o3o3x . ♦ 4 | 0 6 0 | 0 0 0 4 0 0 | * * * * * * 160 * * | 1 0 0 0 1 . o3o . x3/2*c ♦ 4 | 0 0 6 | 0 0 0 0 4 0 | * * * * * * * 160 * | 0 1 0 0 1 . . o3x3x3/2*c ♦ 12 | 0 12 12 | 0 0 0 4 4 4 | * * * * * * * * 160 | 0 0 0 1 1 -----------------+-----+-------------+-------------------------+------------------------------------+--------------- x4/3o3o3x . ♦ 64 | 96 96 0 | 48 96 0 64 0 0 | 8 24 0 32 0 0 16 0 0 | 10 * * * * x4/3o3o . x3/2*c ♦ 64 | 96 0 96 | 48 0 96 0 64 0 | 8 0 24 0 32 0 0 16 0 | * 10 * * * x4/3o . x3x ♦ 24 | 24 12 12 | 6 12 12 0 0 4 | 0 3 3 0 0 4 0 0 0 | * * 80 * * x . o3x3x3/2*c ♦ 24 | 12 24 24 | 0 12 12 8 8 8 | 0 0 0 4 4 4 0 0 2 | * * * 80 * . o3o3x3x3/2*c ♦ 20 | 0 30 30 | 0 0 0 20 20 10 | 0 0 0 0 0 0 5 5 5 | * * * * 32
3/2 3/2 4/3
x---o---o---x
3 \ / 3
x
x4/3o3/2o3x3x3/2*c . . . . . | 640 | 3 3 3 | 3 6 6 3 3 3 | 1 3 3 3 3 6 1 1 3 | 1 1 3 3 1 -------------------+-----+-------------+-------------------------+------------------------------------+--------------- x . . . . | 2 | 960 * * | 2 2 2 0 0 0 | 1 2 2 1 1 2 0 0 0 | 1 1 2 1 0 . . . x . | 2 | * 960 * | 0 2 0 2 0 1 | 0 1 0 2 0 2 1 0 2 | 1 0 1 2 1 . . . . x | 2 | * * 960 | 0 0 2 0 2 1 | 0 0 1 0 2 2 0 1 2 | 0 1 1 2 1 -------------------+-----+-------------+-------------------------+------------------------------------+--------------- x4/3o . . . | 4 | 4 0 0 | 480 * * * * * | 1 1 1 0 0 0 0 0 0 | 1 1 1 0 0 x . . x . | 4 | 2 2 0 | * 960 * * * * | 0 1 0 1 0 1 0 0 0 | 1 0 1 1 0 x . . . x | 4 | 2 0 2 | * * 960 * * * | 0 0 1 0 1 1 0 0 0 | 0 1 1 1 0 . . o3x . | 3 | 0 3 0 | * * * 640 * * | 0 0 0 1 0 0 1 0 1 | 1 0 0 1 1 . . o . x3/2*c | 3 | 0 0 3 | * * * * 640 * | 0 0 0 0 1 0 0 1 1 | 0 1 0 1 1 . . . x3x | 6 | 0 3 3 | * * * * * 320 | 0 0 0 0 0 2 0 0 2 | 0 0 1 2 1 -------------------+-----+-------------+-------------------------+------------------------------------+--------------- x4/3o3/2o . . ♦ 8 | 12 0 0 | 6 0 0 0 0 0 | 80 * * * * * * * * | 1 1 0 0 0 x4/3o . x . ♦ 8 | 8 4 0 | 2 4 0 0 0 0 | * 240 * * * * * * * | 1 0 1 0 0 x4/3o . . x ♦ 8 | 8 0 4 | 2 0 4 0 0 0 | * * 240 * * * * * * | 0 1 1 0 0 x . o3x . ♦ 6 | 3 6 0 | 0 3 0 2 0 0 | * * * 320 * * * * * | 1 0 0 1 0 x . o . x3/2*c ♦ 6 | 3 0 6 | 0 0 3 0 2 0 | * * * * 320 * * * * | 0 1 0 1 0 x . . x3x ♦ 12 | 6 6 6 | 0 3 3 0 0 2 | * * * * * 320 * * * | 0 0 1 1 0 . o3/2o3x . ♦ 4 | 0 6 0 | 0 0 0 4 0 0 | * * * * * * 160 * * | 1 0 0 0 1 . o3/2o . x3/2*c ♦ 4 | 0 0 6 | 0 0 0 0 4 0 | * * * * * * * 160 * | 0 1 0 0 1 . . o3x3x3/2*c ♦ 12 | 0 12 12 | 0 0 0 4 4 4 | * * * * * * * * 160 | 0 0 0 1 1 -------------------+-----+-------------+-------------------------+------------------------------------+--------------- x4/3o3/2o3x . ♦ 64 | 96 96 0 | 48 96 0 64 0 0 | 8 24 0 32 0 0 16 0 0 | 10 * * * * x4/3o3/2o . x3/2*c ♦ 64 | 96 0 96 | 48 0 96 0 64 0 | 8 0 24 0 32 0 0 16 0 | * 10 * * * x4/3o . x3x ♦ 24 | 24 12 12 | 6 12 12 0 0 4 | 0 3 3 0 0 4 0 0 0 | * * 80 * * x . o3x3x3/2*c ♦ 24 | 12 24 24 | 0 12 12 8 8 8 | 0 0 0 4 4 4 0 0 2 | * * * 80 * . o3/2o3x3x3/2*c ♦ 20 | 0 30 30 | 0 0 0 20 20 10 | 0 0 0 0 0 0 5 5 5 | * * * * 32
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