birectified hexadecazetton,
Gosset polytopes 05,1,1
wrt. roc
wrt. bersa
- general polytopal classes:
- Wythoffian polyzetta Coxeter-Elte-Gosset polytopes
- analogs:
- birectified hypercube brCn
links
| Acronym | bro |
| Name |
birectified octeract, birectified hexadecazetton, Gosset polytopes 05,1,1 |
| Circumradius | sqrt(3) = 1.732051 |
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Inradius wrt. roc | 3/2 = 1.5 |
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Inradius wrt. bersa | 1/sqrt(2) = 0.707107 |
| Coordinates | (1/sqrt(2), 1/sqrt(2), 1/sqrt(2), 1/sqrt(2), 1/sqrt(2), 1/sqrt(2), 0, 0) & all permutations, all changes of sign |
| Face vector | 1792, 21504, 50176, 55552, 36960, 14784, 3184, 272 |
| Confer |
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External links |
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Incidence matrix according to Dynkin symbol
o3o3o3o3o3x3o4o . . . . . . . . | 1792 ♦ 24 | 60 24 | 80 60 6 | 60 80 15 | 24 60 20 | 4 24 15 | 4 6 ----------------+------+-------+-------------+------------------+------------------+---------------+---------------+------- . . . . . x . . | 2 | 21504 | 5 2 | 10 10 1 | 10 20 5 | 5 20 10 | 1 10 10 | 2 5 ----------------+------+-------+-------------+------------------+------------------+---------------+---------------+------- . . . . o3x . . | 3 | 3 | 35840 * | 4 2 0 | 6 8 1 | 4 12 4 | 1 8 6 | 2 4 . . . . . x3o . | 3 | 3 | * 14336 | 0 5 1 | 0 10 5 | 0 10 10 | 0 5 10 | 1 5 ----------------+------+-------+-------------+------------------+------------------+---------------+---------------+------- . . . o3o3x . . ♦ 4 | 6 | 4 0 | 35840 * * | 3 2 0 | 3 6 1 | 1 6 3 | 2 3 . . . . o3x3o . ♦ 6 | 12 | 4 4 | * 17920 * | 0 4 1 | 0 6 4 | 0 4 6 | 1 4 . . . . . x3o4o ♦ 6 | 12 | 0 8 | * * 1792 ♦ 0 0 5 | 0 0 10 | 0 0 10 | 0 5 ----------------+------+-------+-------------+------------------+------------------+---------------+---------------+------- . . o3o3o3x . . ♦ 5 | 10 | 10 0 | 5 0 0 | 21504 * * | 2 2 0 | 1 4 1 | 2 2 . . . o3o3x3o . ♦ 10 | 30 | 20 10 | 5 5 0 | * 14336 * | 0 3 1 | 0 3 3 | 1 3 . . . . o3x3o4o ♦ 24 | 96 | 32 64 | 0 16 8 | * * 1120 ♦ 0 0 4 | 0 0 6 | 0 4 ----------------+------+-------+-------------+------------------+------------------+---------------+---------------+------- . o3o3o3o3x . . ♦ 6 | 15 | 20 0 | 15 0 0 | 6 0 0 | 7168 * * | 1 2 0 | 2 1 . . o3o3o3x3o . ♦ 15 | 60 | 60 20 | 30 15 0 | 6 6 0 | * 7168 * | 0 2 1 | 1 2 . . . o3o3x3o4o ♦ 80 | 480 | 320 320 | 80 160 40 | 0 32 10 | * * 448 | 0 0 3 | 0 3 ----------------+------+-------+-------------+------------------+------------------+---------------+---------------+------- o3o3o3o3o3x . . ♦ 7 | 21 | 35 0 | 35 0 0 | 21 0 0 | 7 0 0 | 1024 * * | 2 0 . o3o3o3o3x3o . ♦ 21 | 105 | 140 35 | 105 35 0 | 42 21 0 | 7 7 0 | * 2048 * | 1 1 . . o3o3o3x3o4o ♦ 240 | 1920 | 1920 1280 | 960 960 160 | 192 384 60 | 0 64 12 | * * 112 | 0 2 ----------------+------+-------+-------------+------------------+------------------+---------------+---------------+------- o3o3o3o3o3x3o . ♦ 28 | 168 | 280 56 | 280 70 0 | 168 56 0 | 56 28 0 | 8 8 0 | 256 * . o3o3o3o3x3o4o ♦ 672 | 6720 | 8960 4480 | 6720 4480 560 | 2688 2688 280 | 448 896 84 | 0 128 14 | * 16
o3o3o3o3o3x3o4/3o . . . . . . . . | 1792 ♦ 24 | 60 24 | 80 60 6 | 60 80 15 | 24 60 20 | 4 24 15 | 4 6 ------------------+------+-------+-------------+------------------+------------------+---------------+---------------+------- . . . . . x . . | 2 | 21504 | 5 2 | 10 10 1 | 10 20 5 | 5 20 10 | 1 10 10 | 2 5 ------------------+------+-------+-------------+------------------+------------------+---------------+---------------+------- . . . . o3x . . | 3 | 3 | 35840 * | 4 2 0 | 6 8 1 | 4 12 4 | 1 8 6 | 2 4 . . . . . x3o . | 3 | 3 | * 14336 | 0 5 1 | 0 10 5 | 0 10 10 | 0 5 10 | 1 5 ------------------+------+-------+-------------+------------------+------------------+---------------+---------------+------- . . . o3o3x . . ♦ 4 | 6 | 4 0 | 35840 * * | 3 2 0 | 3 6 1 | 1 6 3 | 2 3 . . . . o3x3o . ♦ 6 | 12 | 4 4 | * 17920 * | 0 4 1 | 0 6 4 | 0 4 6 | 1 4 . . . . . x3o4/3o ♦ 6 | 12 | 0 8 | * * 1792 ♦ 0 0 5 | 0 0 10 | 0 0 10 | 0 5 ------------------+------+-------+-------------+------------------+------------------+---------------+---------------+------- . . o3o3o3x . . ♦ 5 | 10 | 10 0 | 5 0 0 | 21504 * * | 2 2 0 | 1 4 1 | 2 2 . . . o3o3x3o . ♦ 10 | 30 | 20 10 | 5 5 0 | * 14336 * | 0 3 1 | 0 3 3 | 1 3 . . . . o3x3o4/3o ♦ 24 | 96 | 32 64 | 0 16 8 | * * 1120 ♦ 0 0 4 | 0 0 6 | 0 4 ------------------+------+-------+-------------+------------------+------------------+---------------+---------------+------- . o3o3o3o3x . . ♦ 6 | 15 | 20 0 | 15 0 0 | 6 0 0 | 7168 * * | 1 2 0 | 2 1 . . o3o3o3x3o . ♦ 15 | 60 | 60 20 | 30 15 0 | 6 6 0 | * 7168 * | 0 2 1 | 1 2 . . . o3o3x3o4/3o ♦ 80 | 480 | 320 320 | 80 160 40 | 0 32 10 | * * 448 | 0 0 3 | 0 3 ------------------+------+-------+-------------+------------------+------------------+---------------+---------------+------- o3o3o3o3o3x . . ♦ 7 | 21 | 35 0 | 35 0 0 | 21 0 0 | 7 0 0 | 1024 * * | 2 0 . o3o3o3o3x3o . ♦ 21 | 105 | 140 35 | 105 35 0 | 42 21 0 | 7 7 0 | * 2048 * | 1 1 . . o3o3o3x3o4/3o ♦ 240 | 1920 | 1920 1280 | 960 960 160 | 192 384 60 | 0 64 12 | * * 112 | 0 2 ------------------+------+-------+-------------+------------------+------------------+---------------+---------------+------- o3o3o3o3o3x3o . ♦ 28 | 168 | 280 56 | 280 70 0 | 168 56 0 | 56 28 0 | 8 8 0 | 256 * . o3o3o3o3x3o4/3o ♦ 672 | 6720 | 8960 4480 | 6720 4480 560 | 2688 2688 280 | 448 896 84 | 0 128 14 | * 16
o3x3o *b3o3o3o3o3o . . . . . . . . | 1792 ♦ 24 | 12 12 60 | 6 30 30 80 | 15 40 40 60 | 20 30 30 24 | 15 12 12 4 | 6 2 2 -------------------+------+-------+-----------------+----------------------+----------------------+--------------------+--------------------+----------- . x . . . . . . | 2 | 21504 | 1 1 5 | 1 5 5 10 | 5 10 10 10 | 10 10 10 5 | 10 5 5 1 | 5 1 1 -------------------+------+-------+-----------------+----------------------+----------------------+--------------------+--------------------+----------- o3x . . . . . . | 3 | 3 | 7168 * * | 1 5 0 0 | 5 10 0 0 | 10 10 0 0 | 10 5 0 0 | 5 1 0 . x3o . . . . . | 3 | 3 | * 7168 * | 1 0 5 0 | 5 0 10 0 | 10 0 10 0 | 10 0 5 0 | 5 0 1 . x . *b3o . . . . | 3 | 3 | * * 35840 | 0 1 1 4 | 1 4 4 6 | 4 6 6 4 | 6 4 4 1 | 4 1 1 -------------------+------+-------+-----------------+----------------------+----------------------+--------------------+--------------------+----------- o3x3o . . . . . ♦ 6 | 12 | 4 4 0 | 1792 * * * ♦ 5 0 0 0 | 10 0 0 0 | 10 0 0 0 | 5 0 0 o3x . *b3o . . . . ♦ 6 | 12 | 4 0 4 | * 8960 * * | 1 4 0 0 | 4 6 0 0 | 6 4 0 0 | 4 1 0 . x3o *b3o . . . . ♦ 6 | 12 | 0 4 4 | * * 8960 * | 1 0 4 0 | 4 0 6 0 | 6 0 4 0 | 4 0 1 . x . *b3o3o . . . ♦ 4 | 6 | 0 0 4 | * * * 35840 | 0 1 1 3 | 1 3 3 3 | 3 3 3 1 | 3 1 1 -------------------+------+-------+-----------------+----------------------+----------------------+--------------------+--------------------+----------- o3x3o *b3o . . . . ♦ 24 | 96 | 32 32 32 | 8 8 8 0 | 1120 * * * ♦ 4 0 0 0 | 6 0 0 0 | 4 0 0 o3x . *b3o3o . . . ♦ 10 | 30 | 10 0 20 | 0 5 0 5 | * 7168 * * | 1 3 0 0 | 3 3 0 0 | 3 1 0 . x3o *b3o3o . . . ♦ 10 | 30 | 0 10 20 | 0 0 5 5 | * * 7168 * | 1 0 3 0 | 3 0 3 0 | 3 0 1 . x . *b3o3o3o . . ♦ 5 | 10 | 0 0 10 | 0 0 0 5 | * * * 21504 | 0 1 1 2 | 1 2 2 1 | 2 1 1 -------------------+------+-------+-----------------+----------------------+----------------------+--------------------+--------------------+----------- o3x3o *b3o3o . . . ♦ 80 | 480 | 160 160 320 | 40 80 80 80 | 10 16 16 0 | 448 * * * | 3 0 0 0 | 3 0 0 o3x . *b3o3o3o . . ♦ 15 | 60 | 20 0 60 | 0 15 0 30 | 0 6 0 6 | * 3584 * * | 1 2 0 0 | 2 1 0 . x3o *b3o3o3o . . ♦ 15 | 60 | 0 20 60 | 0 0 15 30 | 0 0 6 6 | * * 3584 * | 1 0 2 0 | 2 0 1 . x . *b3o3o3o3o . ♦ 6 | 15 | 0 0 20 | 0 0 0 15 | 0 0 0 6 | * * * 7168 | 0 1 1 1 | 1 1 1 -------------------+------+-------+-----------------+----------------------+----------------------+--------------------+--------------------+----------- o3x3o *b3o3o3o . . ♦ 240 | 1920 | 640 640 1920 | 160 480 480 960 | 60 192 192 192 | 12 32 32 0 | 112 * * * | 2 0 0 o3x . *b3o3o3o3o . ♦ 21 | 105 | 35 0 140 | 0 35 0 105 | 0 21 0 42 | 0 7 0 7 | * 1024 * * | 1 1 0 . x3o *b3o3o3o3o . ♦ 21 | 105 | 0 35 140 | 0 0 35 105 | 0 0 21 42 | 0 0 7 7 | * * 1024 * | 1 0 1 . x . *b3o3o3o3o3o ♦ 7 | 21 | 0 0 35 | 0 0 0 35 | 0 0 0 21 | 0 0 0 7 | * * * 1024 | 0 1 1 -------------------+------+-------+-----------------+----------------------+----------------------+--------------------+--------------------+----------- o3x3o *b3o3o3o3o . ♦ 672 | 6720 | 2240 2240 8960 | 560 2240 2240 6720 | 280 1344 1344 2688 | 84 448 448 448 | 14 64 64 0 | 16 * * o3x . *b3o3o3o3o3o ♦ 28 | 168 | 56 0 280 | 0 70 0 280 | 0 56 0 168 | 0 28 0 56 | 0 8 0 8 | * 128 * . x3o *b3o3o3o3o3o ♦ 28 | 168 | 0 56 280 | 0 0 70 280 | 0 0 56 168 | 0 0 28 56 | 0 0 8 8 | * * 128
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