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| Acronym | octo |
| Name | octeract,
hexadecazetton,
8Dmeasure-polytope (γ8),
geoyott(id) |
| Circumradius | sqrt(2) = 1.414214 |
| Inradius | 1/2 |
| Vertex layers | |
| Coordinates | (1/2, 1/2, 1/2, 1/2, 1/2, 1/2, 1/2, 1/2) & all changes of sign |
| Volume | 1 |
| Surface | 16 |
| Rel. Roundness | π4/6144 = 1.585434 % |
| Dual | ek |
| Dihedral angles | |
| Face vector | 256, 1024, 1792, 1792, 1120, 448, 112, 16 |
| Confer | - general polytopal classes:
- Wythoffian polyzetta hypercube noble polytopes segmentozetta
- analogs:
- regular hypercube Cn
|
External
links |    |
Incidence matrix according toDynkin symbol
o3o3o3o3o3o3o4x. . . . . . . . | 256♦ 8 | 28 | 56 | 70 | 56 | 28 | 8----------------+-----+------+------+------+------+-----+-----+---. . . . . . . x | 2 | 1024♦ 7 | 21 | 35 | 35 | 21 | 7----------------+-----+------+------+------+------+-----+-----+---. . . . . . o4x | 4 | 4 | 1792♦ 6 | 15 | 20 | 15 | 6----------------+-----+------+------+------+------+-----+-----+---. . . . . o3o4x♦ 8 | 12 | 6 | 1792♦ 5 | 10 | 10 | 5----------------+-----+------+------+------+------+-----+-----+---. . . . o3o3o4x♦ 16 | 32 | 24 | 8 | 1120♦ 4 | 6 | 4----------------+-----+------+------+------+------+-----+-----+---. . . o3o3o3o4x♦ 32 | 80 | 80 | 40 | 10 | 448 | 3 | 3----------------+-----+------+------+------+------+-----+-----+---. . o3o3o3o3o4x♦ 64 | 192 | 240 | 160 | 60 | 12 | 112 | 2----------------+-----+------+------+------+------+-----+-----+---. o3o3o3o3o3o4x♦ 128 | 448 | 672 | 560 | 280 | 84 | 14 | 16snubbed forms:o3o3o3o3o3o3o4s
o3o3o3o3o3o3o4/3x. . . . . . . . | 256♦ 8 | 28 | 56 | 70 | 56 | 28 | 8------------------+-----+------+------+------+------+-----+-----+---. . . . . . . x | 2 | 1024♦ 7 | 21 | 35 | 35 | 21 | 7------------------+-----+------+------+------+------+-----+-----+---. . . . . . o4/3x | 4 | 4 | 1792♦ 6 | 15 | 20 | 15 | 6------------------+-----+------+------+------+------+-----+-----+---. . . . . o3o4/3x♦ 8 | 12 | 6 | 1792♦ 5 | 10 | 10 | 5------------------+-----+------+------+------+------+-----+-----+---. . . . o3o3o4/3x♦ 16 | 32 | 24 | 8 | 1120♦ 4 | 6 | 4------------------+-----+------+------+------+------+-----+-----+---. . . o3o3o3o4/3x♦ 32 | 80 | 80 | 40 | 10 | 448 | 3 | 3------------------+-----+------+------+------+------+-----+-----+---. . o3o3o3o3o4/3x♦ 64 | 192 | 240 | 160 | 60 | 12 | 112 | 2------------------+-----+------+------+------+------+-----+-----+---. o3o3o3o3o3o4/3x♦ 128 | 448 | 672 | 560 | 280 | 84 | 14 | 16
o3o3o4x o3o3o4x. . . . . . . . | 256♦ 4 4 | 6 16 6 | 4 24 24 4 | 1 16 36 16 1 | 4 24 24 4 | 6 16 6 | 4 4----------------+-----+---------+--------------+-----------------+-------------------+---------------+----------+----. . . x . . . . | 2 | 512 *♦ 3 4 0 | 3 12 6 0 | 1 12 18 4 0 | 4 18 12 1 | 6 12 3 | 4 3. . . . . . . x | 2 | * 512♦ 0 4 3 | 0 6 12 3 | 0 4 18 12 1 | 1 12 18 4 | 3 12 6 | 3 4----------------+-----+---------+--------------+-----------------+-------------------+---------------+----------+----. . o4x . . . . | 4 | 4 0 | 384 * *♦ 2 4 0 0 | 1 8 6 0 0 | 4 12 4 0 | 6 8 1 | 4 2. . . x . . . x | 4 | 2 2 | * 1024 *♦ 0 3 3 0 | 0 3 9 3 0 | 1 9 9 1 | 3 9 3 | 3 3. . . . . . o4x | 4 | 0 4 | * * 384♦ 0 0 4 2 | 0 0 6 8 1 | 0 4 12 4 | 1 8 6 | 2 4----------------+-----+---------+--------------+-----------------+-------------------+---------------+----------+----. o3o4x . . . .♦ 8 | 12 0 | 6 0 0 | 128 * * *♦ 1 4 0 0 0 | 4 6 0 0 | 6 4 0 | 4 0. . o4x . . . x♦ 8 | 8 4 | 2 4 0 | * 768 * *♦ 0 2 3 0 0 | 1 6 3 0 | 3 6 1 | 3 2. . . x . . o4x♦ 8 | 4 8 | 0 4 2 | * * 768 *♦ 0 0 3 2 0 | 0 3 6 1 | 1 6 3 | 2 3. . . . . o3o4x♦ 8 | 0 12 | 0 0 6 | * * * 128♦ 0 0 0 4 1 | 0 0 6 4 | 0 4 6 | 1 4----------------+-----+---------+--------------+-----------------+-------------------+---------------+----------+----o3o3o4x . . . .♦ 16 | 32 0 | 24 0 0 | 8 0 0 0 | 16 * * * *♦ 4 0 0 0 | 6 0 0 | 4 0. o3o4x . . . x♦ 16 | 24 8 | 12 12 0 | 2 6 0 0 | * 256 * * *♦ 1 3 0 0 | 3 3 0 | 3 1. . o4x . . o4x♦ 16 | 16 16 | 4 16 4 | 0 4 4 0 | * * 576 * *♦ 0 2 2 0 | 1 4 1 | 2 2. . . x . o3o4x♦ 16 | 8 24 | 0 12 12 | 0 0 6 2 | * * * 256 *♦ 0 0 3 1 | 0 3 3 | 1 3. . . . o3o3o4x♦ 16 | 0 32 | 0 0 24 | 0 0 0 8 | * * * * 16♦ 0 0 0 4 | 0 0 6 | 0 4----------------+-----+---------+--------------+-----------------+-------------------+---------------+----------+----o3o3o4x . . . x♦ 32 | 64 16 | 48 32 0 | 16 24 0 0 | 2 8 0 0 0 | 32 * * * | 3 0 0 | 3 0. o3o4x . . o4x♦ 32 | 48 32 | 24 48 8 | 4 24 12 0 | 0 4 6 0 0 | * 192 * * | 1 2 0 | 2 1. . o4x . o3o4x♦ 32 | 32 48 | 8 48 24 | 0 12 24 4 | 0 0 6 4 0 | * * 192 * | 0 2 1 | 1 2. . . x o3o3o4x♦ 32 | 16 64 | 0 32 48 | 0 0 24 16 | 0 0 0 8 2 | * * * 32 | 0 0 3 | 0 3----------------+-----+---------+--------------+-----------------+-------------------+---------------+----------+----o3o3o4x . . o4x♦ 64 | 128 64 | 96 128 16 | 32 96 32 0 | 4 32 24 0 0 | 4 8 0 0 | 24 * * | 2 0. o3o4x . o3o4x♦ 64 | 96 96 | 48 144 48 | 8 72 72 8 | 0 12 36 12 0 | 0 6 6 0 | * 64 * | 1 1. . o4x o3o3o4x♦ 64 | 64 128 | 16 128 96 | 0 32 96 32 | 0 0 24 32 4 | 0 0 8 4 | * * 24 | 0 2----------------+-----+---------+--------------+-----------------+-------------------+---------------+----------+----o3o3o4x . o3o4x♦ 128 | 256 192 | 192 384 96 | 64 288 192 16 | 8 96 144 32 0 | 12 48 24 0 | 6 8 0 | 8 *. o3o4x o3o3o4x♦ 128 | 192 256 | 96 384 192 | 16 192 288 64 | 0 32 144 96 8 | 0 24 48 12 | 0 8 6 | * 8snubbed forms:o3o3o4s o3o3o4x
o3o3o4x o3o3o4/3x. . . . . . . . | 256♦ 4 4 | 6 16 6 | 4 24 24 4 | 1 16 36 16 1 | 4 24 24 4 | 6 16 6 | 4 4------------------+-----+---------+--------------+-----------------+-------------------+---------------+----------+----. . . x . . . . | 2 | 512 *♦ 3 4 0 | 3 12 6 0 | 1 12 18 4 0 | 4 18 12 1 | 6 12 3 | 4 3. . . . . . . x | 2 | * 512♦ 0 4 3 | 0 6 12 3 | 0 4 18 12 1 | 1 12 18 4 | 3 12 6 | 3 4------------------+-----+---------+--------------+-----------------+-------------------+---------------+----------+----. . o4x . . . . | 4 | 4 0 | 384 * *♦ 2 4 0 0 | 1 8 6 0 0 | 4 12 4 0 | 6 8 1 | 4 2. . . x . . . x | 4 | 2 2 | * 1024 *♦ 0 3 3 0 | 0 3 9 3 0 | 1 9 9 1 | 3 9 3 | 3 3. . . . . . o4/3x | 4 | 0 4 | * * 384♦ 0 0 4 2 | 0 0 6 8 1 | 0 4 12 4 | 1 8 6 | 2 4------------------+-----+---------+--------------+-----------------+-------------------+---------------+----------+----. o3o4x . . . .♦ 8 | 12 0 | 6 0 0 | 128 * * *♦ 1 4 0 0 0 | 4 6 0 0 | 6 4 0 | 4 0. . o4x . . . x♦ 8 | 8 4 | 2 4 0 | * 768 * *♦ 0 2 3 0 0 | 1 6 3 0 | 3 6 1 | 3 2. . . x . . o4/3x♦ 8 | 4 8 | 0 4 2 | * * 768 *♦ 0 0 3 2 0 | 0 3 6 1 | 1 6 3 | 2 3. . . . . o3o4/3x♦ 8 | 0 12 | 0 0 6 | * * * 128♦ 0 0 0 4 1 | 0 0 6 4 | 0 4 6 | 1 4------------------+-----+---------+--------------+-----------------+-------------------+---------------+----------+----o3o3o4x . . . .♦ 16 | 32 0 | 24 0 0 | 8 0 0 0 | 16 * * * *♦ 4 0 0 0 | 6 0 0 | 4 0. o3o4x . . . x♦ 16 | 24 8 | 12 12 0 | 2 6 0 0 | * 256 * * *♦ 1 3 0 0 | 3 3 0 | 3 1. . o4x . . o4/3x♦ 16 | 16 16 | 4 16 4 | 0 4 4 0 | * * 576 * *♦ 0 2 2 0 | 1 4 1 | 2 2. . . x . o3o4/3x♦ 16 | 8 24 | 0 12 12 | 0 0 6 2 | * * * 256 *♦ 0 0 3 1 | 0 3 3 | 1 3. . . . o3o3o4/3x♦ 16 | 0 32 | 0 0 24 | 0 0 0 8 | * * * * 16♦ 0 0 0 4 | 0 0 6 | 0 4------------------+-----+---------+--------------+-----------------+-------------------+---------------+----------+----o3o3o4x . . . x♦ 32 | 64 16 | 48 32 0 | 16 24 0 0 | 2 8 0 0 0 | 32 * * * | 3 0 0 | 3 0. o3o4x . . o4/3x♦ 32 | 48 32 | 24 48 8 | 4 24 12 0 | 0 4 6 0 0 | * 192 * * | 1 2 0 | 2 1. . o4x . o3o4/3x♦ 32 | 32 48 | 8 48 24 | 0 12 24 4 | 0 0 6 4 0 | * * 192 * | 0 2 1 | 1 2. . . x o3o3o4/3x♦ 32 | 16 64 | 0 32 48 | 0 0 24 16 | 0 0 0 8 2 | * * * 32 | 0 0 3 | 0 3------------------+-----+---------+--------------+-----------------+-------------------+---------------+----------+----o3o3o4x . . o4/3x♦ 64 | 128 64 | 96 128 16 | 32 96 32 0 | 4 32 24 0 0 | 4 8 0 0 | 24 * * | 2 0. o3o4x . o3o4/3x♦ 64 | 96 96 | 48 144 48 | 8 72 72 8 | 0 12 36 12 0 | 0 6 6 0 | * 64 * | 1 1. . o4x o3o3o4/3x♦ 64 | 64 128 | 16 128 96 | 0 32 96 32 | 0 0 24 32 4 | 0 0 8 4 | * * 24 | 0 2------------------+-----+---------+--------------+-----------------+-------------------+---------------+----------+----o3o3o4x . o3o4/3x♦ 128 | 256 192 | 192 384 96 | 64 288 192 16 | 8 96 144 32 0 | 12 48 24 0 | 6 8 0 | 8 *. o3o4x o3o3o4/3x♦ 128 | 192 256 | 96 384 192 | 16 192 288 64 | 0 32 144 96 8 | 0 24 48 12 | 0 8 6 | * 8
o3o3o4/3x o3o3o4/3x. . . . . . . . | 256♦ 4 4 | 6 16 6 | 4 24 24 4 | 1 16 36 16 1 | 4 24 24 4 | 6 16 6 | 4 4--------------------+-----+---------+--------------+-----------------+-------------------+---------------+----------+----. . . x . . . . | 2 | 512 *♦ 3 4 0 | 3 12 6 0 | 1 12 18 4 0 | 4 18 12 1 | 6 12 3 | 4 3. . . . . . . x | 2 | * 512♦ 0 4 3 | 0 6 12 3 | 0 4 18 12 1 | 1 12 18 4 | 3 12 6 | 3 4--------------------+-----+---------+--------------+-----------------+-------------------+---------------+----------+----. . o4/3x . . . . | 4 | 4 0 | 384 * *♦ 2 4 0 0 | 1 8 6 0 0 | 4 12 4 0 | 6 8 1 | 4 2. . . x . . . x | 4 | 2 2 | * 1024 *♦ 0 3 3 0 | 0 3 9 3 0 | 1 9 9 1 | 3 9 3 | 3 3. . . . . . o4/3x | 4 | 0 4 | * * 384♦ 0 0 4 2 | 0 0 6 8 1 | 0 4 12 4 | 1 8 6 | 2 4--------------------+-----+---------+--------------+-----------------+-------------------+---------------+----------+----. o3o4/3x . . . .♦ 8 | 12 0 | 6 0 0 | 128 * * *♦ 1 4 0 0 0 | 4 6 0 0 | 6 4 0 | 4 0. . o4/3x . . . x♦ 8 | 8 4 | 2 4 0 | * 768 * *♦ 0 2 3 0 0 | 1 6 3 0 | 3 6 1 | 3 2. . . x . . o4/3x♦ 8 | 4 8 | 0 4 2 | * * 768 *♦ 0 0 3 2 0 | 0 3 6 1 | 1 6 3 | 2 3. . . . . o3o4/3x♦ 8 | 0 12 | 0 0 6 | * * * 128♦ 0 0 0 4 1 | 0 0 6 4 | 0 4 6 | 1 4--------------------+-----+---------+--------------+-----------------+-------------------+---------------+----------+----o3o3o4/3x . . . .♦ 16 | 32 0 | 24 0 0 | 8 0 0 0 | 16 * * * *♦ 4 0 0 0 | 6 0 0 | 4 0. o3o4/3x . . . x♦ 16 | 24 8 | 12 12 0 | 2 6 0 0 | * 256 * * *♦ 1 3 0 0 | 3 3 0 | 3 1. . o4/3x . . o4/3x♦ 16 | 16 16 | 4 16 4 | 0 4 4 0 | * * 576 * *♦ 0 2 2 0 | 1 4 1 | 2 2. . . x . o3o4/3x♦ 16 | 8 24 | 0 12 12 | 0 0 6 2 | * * * 256 *♦ 0 0 3 1 | 0 3 3 | 1 3. . . . o3o3o4/3x♦ 16 | 0 32 | 0 0 24 | 0 0 0 8 | * * * * 16♦ 0 0 0 4 | 0 0 6 | 0 4--------------------+-----+---------+--------------+-----------------+-------------------+---------------+----------+----o3o3o4/3x . . . x♦ 32 | 64 16 | 48 32 0 | 16 24 0 0 | 2 8 0 0 0 | 32 * * * | 3 0 0 | 3 0. o3o4/3x . . o4/3x♦ 32 | 48 32 | 24 48 8 | 4 24 12 0 | 0 4 6 0 0 | * 192 * * | 1 2 0 | 2 1. . o4/3x . o3o4/3x♦ 32 | 32 48 | 8 48 24 | 0 12 24 4 | 0 0 6 4 0 | * * 192 * | 0 2 1 | 1 2. . . x o3o3o4/3x♦ 32 | 16 64 | 0 32 48 | 0 0 24 16 | 0 0 0 8 2 | * * * 32 | 0 0 3 | 0 3--------------------+-----+---------+--------------+-----------------+-------------------+---------------+----------+----o3o3o4/3x . . o4/3x♦ 64 | 128 64 | 96 128 16 | 32 96 32 0 | 4 32 24 0 0 | 4 8 0 0 | 24 * * | 2 0. o3o4/3x . o3o4/3x♦ 64 | 96 96 | 48 144 48 | 8 72 72 8 | 0 12 36 12 0 | 0 6 6 0 | * 64 * | 1 1. . o4/3x o3o3o4/3x♦ 64 | 64 128 | 16 128 96 | 0 32 96 32 | 0 0 24 32 4 | 0 0 8 4 | * * 24 | 0 2--------------------+-----+---------+--------------+-----------------+-------------------+---------------+----------+----o3o3o4/3x . o3o4/3x♦ 128 | 256 192 | 192 384 96 | 64 288 192 16 | 8 96 144 32 0 | 12 48 24 0 | 6 8 0 | 8 *. o3o4/3x o3o3o4/3x♦ 128 | 192 256 | 96 384 192 | 16 192 288 64 | 0 32 144 96 8 | 0 24 48 12 | 0 8 6 | * 8
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