©
- general polytopal classes:
- Wythoffian polychora
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| Acronym | rawvhitto |
| Name | retrosphenoverted hexadecatesseractioctachoron |
| Cross sections |
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| Circumradius | sqrt(3) = 1.732051 |
| Coordinates | (sqrt(2), 1/sqrt(2), 1/sqrt(2), 0) & all permutations, all changes of sign |
| General of army | rico |
| Colonel of regiment | rico |
| Face vector | 96, 288, 208, 32 |
| Confer |
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External links |
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Incidence matrix according to Dynkin symbol
o4x3x3o3/2*b . . . . | 96 | 4 2 | 2 4 2 1 | 2 1 2 -------------+----+--------+-------------+------- . x . . | 2 | 192 * | 1 1 1 0 | 1 1 1 . . x . | 2 | * 96 | 0 2 0 1 | 1 0 2 -------------+----+--------+-------------+------- o4x . . | 4 | 4 0 | 48 * * * | 1 1 0 . x3x . | 6 | 3 3 | * 64 * * | 1 0 1 . x . o3/2*b | 3 | 3 0 | * * 64 * | 0 1 1 . . x3o | 3 | 0 3 | * * * 32 | 0 0 2 -------------+----+--------+-------------+------- o4x3x . ♦ 24 | 24 12 | 6 8 0 0 | 8 * * o4x . o3/2*b ♦ 12 | 24 0 | 6 0 8 0 | * 8 * . x3x3o3/2*b ♦ 12 | 12 12 | 0 4 4 4 | * * 16
o4x3x3/2o3*b . . . . | 96 | 4 2 | 2 4 2 1 | 2 1 2 -------------+----+--------+-------------+------- . x . . | 2 | 192 * | 1 1 1 0 | 1 1 1 . . x . | 2 | * 96 | 0 2 0 1 | 1 0 2 -------------+----+--------+-------------+------- o4x . . | 4 | 4 0 | 48 * * * | 1 1 0 . x3x . | 6 | 3 3 | * 64 * * | 1 0 1 . x . o3*b | 3 | 3 0 | * * 64 * | 0 1 1 . . x3/2o | 3 | 0 3 | * * * 32 | 0 0 2 -------------+----+--------+-------------+------- o4x3x . ♦ 24 | 24 12 | 6 8 0 0 | 8 * * o4x . o3*b ♦ 12 | 24 0 | 6 0 8 0 | * 8 * . x3x3/2o3*b ♦ 12 | 12 12 | 0 4 4 4 | * * 16
o4/3x3x3o3/2*b . . . . | 96 | 4 2 | 2 4 2 1 | 2 1 2 ---------------+----+--------+-------------+------- . x . . | 2 | 192 * | 1 1 1 0 | 1 1 1 . . x . | 2 | * 96 | 0 2 0 1 | 1 0 2 ---------------+----+--------+-------------+------- o4/3x . . | 4 | 4 0 | 48 * * * | 1 1 0 . x3x . | 6 | 3 3 | * 64 * * | 1 0 1 . x . o3/2*b | 3 | 3 0 | * * 64 * | 0 1 1 . . x3o | 3 | 0 3 | * * * 32 | 0 0 2 ---------------+----+--------+-------------+------- o4/3x3x . ♦ 24 | 24 12 | 6 8 0 0 | 8 * * o4/3x . o3/2*b ♦ 12 | 24 0 | 6 0 8 0 | * 8 * . x3x3o3/2*b ♦ 12 | 12 12 | 0 4 4 4 | * * 16
o4/3x3x3/2o3*b . . . . | 96 | 4 2 | 2 4 2 1 | 2 1 2 ---------------+----+--------+-------------+------- . x . . | 2 | 192 * | 1 1 1 0 | 1 1 1 . . x . | 2 | * 96 | 0 2 0 1 | 1 0 2 ---------------+----+--------+-------------+------- o4/3x . . | 4 | 4 0 | 48 * * * | 1 1 0 . x3x . | 6 | 3 3 | * 64 * * | 1 0 1 . x . o3*b | 3 | 3 0 | * * 64 * | 0 1 1 . . x3/2o | 3 | 0 3 | * * * 32 | 0 0 2 ---------------+----+--------+-------------+------- o4/3x3x . ♦ 24 | 24 12 | 6 8 0 0 | 8 * * o4/3x . o3*b ♦ 12 | 24 0 | 6 0 8 0 | * 8 * . x3x3/2o3*b ♦ 12 | 12 12 | 0 4 4 4 | * * 16
x3x3o3x3*a3/2*c . . . . | 96 | 2 2 2 | 2 1 2 1 2 1 | 1 2 1 1 ----------------+----+----------+-------------------+-------- x . . . | 2 | 96 * * | 1 1 1 0 0 0 | 1 1 1 0 . x . . | 2 | * 96 * | 1 0 0 1 1 0 | 1 1 0 1 . . . x | 2 | * * 96 | 0 0 1 0 1 1 | 0 1 1 1 ----------------+----+----------+-------------------+-------- x3x . . | 6 | 3 3 0 | 32 * * * * * | 1 1 0 0 x . o . *a3/2*c | 3 | 3 0 0 | * 32 * * * * | 1 0 1 0 x . . x3*a | 6 | 3 0 3 | * * 32 * * * | 0 1 1 0 . x3o . | 3 | 0 3 0 | * * * 32 * * | 1 0 0 1 . x . x | 4 | 0 2 2 | * * * * 48 * | 0 1 0 1 . . o3x | 3 | 0 0 3 | * * * * * 32 | 0 0 1 1 ----------------+----+----------+-------------------+-------- x3x3o . *a3/2*c ♦ 12 | 12 12 0 | 4 4 0 4 0 0 | 8 * * * x3x . x3*a ♦ 24 | 12 12 12 | 4 0 4 0 6 0 | * 8 * * x . o3x3*a3/2*c ♦ 12 | 12 0 12 | 0 4 4 0 0 4 | * * 8 * . x3o3x ♦ 12 | 0 12 12 | 0 0 0 4 6 4 | * * * 8
x3x3/2o3/2x3*a3*c . . . . | 96 | 2 2 2 | 2 1 2 1 2 1 | 1 2 1 1 ------------------+----+----------+-------------------+-------- x . . . | 2 | 96 * * | 1 1 1 0 0 0 | 1 1 1 0 . x . . | 2 | * 96 * | 1 0 0 1 1 0 | 1 1 0 1 . . . x | 2 | * * 96 | 0 0 1 0 1 1 | 0 1 1 1 ------------------+----+----------+-------------------+-------- x3x . . | 6 | 3 3 0 | 32 * * * * * | 1 1 0 0 x . o . *a3*c | 3 | 3 0 0 | * 32 * * * * | 1 0 1 0 x . . x3*a | 6 | 3 0 3 | * * 32 * * * | 0 1 1 0 . x3/2o . | 3 | 0 3 0 | * * * 32 * * | 1 0 0 1 . x . x | 4 | 0 2 2 | * * * * 48 * | 0 1 0 1 . . o3/2x | 3 | 0 0 3 | * * * * * 32 | 0 0 1 1 ------------------+----+----------+-------------------+-------- x3x3/2o . *a3*c ♦ 12 | 12 12 0 | 4 4 0 4 0 0 | 8 * * * x3x . x3*a ♦ 24 | 12 12 12 | 4 0 4 0 6 0 | * 8 * * x . o3/2x3*a3*c ♦ 12 | 12 0 12 | 0 4 4 0 0 4 | * * 8 * . x3/2o3/2x ♦ 12 | 0 12 12 | 0 0 0 4 6 4 | * * * 8
β3o3x4o
both( . . . . ) | 96 | 4 2 | 2 2 1 4 | 1 2 2
----------------+----+--------+-------------+-------
both( . . x . ) | 2 | 192 * | 1 1 0 1 | 1 1 1
sefa( β3o . . ) | 2 | * 96 | 0 0 1 2 | 0 2 1
----------------+----+--------+-------------+-------
both( . o3x . ) | 3 | 3 0 | 64 * * * | 1 1 0
both( . . x4o ) | 4 | 4 0 | * 48 * * | 1 0 1
β3o . . ♦ 3 | 0 3 | * * 32 * | 0 2 0
sefa( β3o3x . ) | 6 | 3 3 | * * * 64 | 0 1 1
----------------+----+--------+-------------+-------
both( . o3x4o ) ♦ 12 | 24 0 | 8 6 0 0 | 8 * *
β3o3x . ♦ 12 | 12 12 | 4 0 4 4 | * 16 *
sefa( β3o3x4o ) ♦ 24 | 24 12 | 0 6 0 8 | * * 8
starting figure: x3o3x4o
β3o3x *b3x
both( . . . . ) | 96 | 2 2 2 | 1 1 2 1 2 2 | 1 1 1 2
-------------------+----+----------+-------------------+--------
both( . . x . ) | 2 | 96 * * | 1 0 1 0 1 0 | 1 1 0 1
both( . . . x ) | 2 | * 96 * | 0 1 1 0 0 1 | 1 0 1 1
sefa( β3o . . ) | 2 | * * 96 | 0 0 0 1 1 1 | 0 1 1 1
-------------------+----+----------+-------------------+--------
both( . o3x . ) | 3 | 3 0 0 | 32 * * * * * | 1 1 0 0
both( . o . *b3x ) | 3 | 0 3 0 | * 32 * * * * | 1 0 1 0
both( . . x x ) | 4 | 2 2 0 | * * 48 * * * | 1 0 0 1
β3o . . ♦ 3 | 0 0 3 | * * * 32 * * | 0 1 1 0
sefa( β3o3x . ) | 6 | 3 0 3 | * * * * 32 * | 0 1 0 1
sefa( β3o . *b3x ) | 6 | 0 3 3 | * * * * * 32 | 0 0 1 1
-------------------+----+----------+-------------------+--------
both( . o3x *b3x ) ♦ 12 | 12 12 0 | 4 4 6 0 0 0 | 8 * * *
β3o3x . ♦ 12 | 12 0 12 | 4 0 0 4 4 0 | * 8 * *
β3o . *b3x ♦ 12 | 0 12 12 | 0 4 0 4 0 4 | * * 8 *
sefa( β3o3x *b3x ) ♦ 24 | 12 12 12 | 0 0 6 0 4 4 | * * * 8
starting figure: x3o3x *b3x
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