lattice B10 contact polytope (span of its small roots),
lattice D10 contact polytope (span of its roots)
wrt.vee
wrt.reday
- general polytopal classes:
- Wythoffian polyxenna
- analogs:
- rectified orthoplex rOn
links
| Acronym | rake |
| Name | rectified chilliaicositetraxennon, lattice B10 contact polytope (span of its small roots), lattice D10 contact polytope (span of its roots) |
| Circumradius | 1 |
| Inradius wrt.vee | 1/sqrt(2) = 0.707107 |
| Inradius wrt.reday | 1/sqrt(5) = 0.447214 |
| Coordinates | (1/sqrt(2), 1/sqrt(2), 0, 0, 0, 0, 0, 0, 0, 0) & all permutations, all changes of sign |
| Volume | 169/18900 = 0.0089418 |
| Surface | [5 sqrt(2)+502 sqrt(5)]/5760 = 0.199220 |
| Dihedral angles | |
| Face vector | 180, 2880, 14400, 43680, 88704, 120960, 107520, 57600, 15360, 1044 |
| Confer |
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| External links | |
Incidence matrix according toDynkin symbol
o3x3o3o3o3o3o3o3o4o. . . . . . . . . . | 180♦ 32 | 16 224 | 112 896 | 448 2240 | 1120 3584 | 1792 3584 | 1792 2048 | 1024 512 | 256 2--------------------+-----+------+-----------+------------+------------+--------------+-------------+-------------+------------+--------. x . . . . . . . . | 2 | 2880 | 1 14 | 14 84 | 84 280 | 280 560 | 560 672 | 672 448 | 448 128 | 128 1--------------------+-----+------+-----------+------------+------------+--------------+-------------+-------------+------------+--------o3x . . . . . . . . | 3 | 3 | 960 *♦ 14 0 | 84 0 | 280 0 | 560 0 | 672 0 | 448 0 | 128 0. x3o . . . . . . . | 3 | 3 | * 13440 | 1 12 | 12 60 | 60 160 | 160 240 | 240 192 | 192 64 | 64 1--------------------+-----+------+-----------+------------+------------+--------------+-------------+-------------+------------+--------o3x3o . . . . . . .♦ 6 | 12 | 4 4 | 3360 *♦ 12 0 | 60 0 | 160 0 | 240 0 | 192 0 | 64 0. x3o3o . . . . . .♦ 4 | 6 | 0 4 | * 40320 | 1 10 | 10 40 | 40 80 | 80 80 | 80 32 | 32 1--------------------+-----+------+-----------+------------+------------+--------------+-------------+-------------+------------+--------o3x3o3o . . . . . .♦ 10 | 30 | 10 20 | 5 5 | 8064 *♦ 10 0 | 40 0 | 80 0 | 80 0 | 32 0. x3o3o3o . . . . .♦ 5 | 10 | 0 10 | 0 5 | * 80640 | 1 8 | 8 24 | 24 32 | 32 16 | 16 1--------------------+-----+------+-----------+------------+------------+--------------+-------------+-------------+------------+--------o3x3o3o3o . . . . .♦ 15 | 60 | 20 60 | 15 30 | 6 6 | 13440 *♦ 8 0 | 24 0 | 32 0 | 16 0. x3o3o3o3o . . . .♦ 6 | 15 | 0 20 | 0 15 | 0 6 | * 107520 | 1 6 | 6 12 | 12 8 | 8 1--------------------+-----+------+-----------+------------+------------+--------------+-------------+-------------+------------+--------o3x3o3o3o3o . . . .♦ 21 | 105 | 35 140 | 35 105 | 21 42 | 7 7 | 15360 *♦ 6 0 | 12 0 | 8 0. x3o3o3o3o3o . . .♦ 7 | 21 | 0 35 | 0 35 | 0 21 | 0 7 | * 92160 | 1 4 | 4 4 | 4 1--------------------+-----+------+-----------+------------+------------+--------------+-------------+-------------+------------+--------o3x3o3o3o3o3o . . .♦ 28 | 168 | 56 280 | 70 280 | 56 168 | 28 56 | 8 8 | 11520 * | 4 0 | 4 0. x3o3o3o3o3o3o . .♦ 8 | 28 | 0 56 | 0 70 | 0 56 | 0 28 | 0 8 | * 46080 | 1 2 | 2 1--------------------+-----+------+-----------+------------+------------+--------------+-------------+-------------+------------+--------o3x3o3o3o3o3o3o . .♦ 36 | 252 | 84 504 | 126 630 | 126 504 | 84 252 | 36 72 | 9 9 | 5120 * | 2 0. x3o3o3o3o3o3o3o .♦ 9 | 36 | 0 84 | 0 126 | 0 126 | 0 84 | 0 36 | 0 9 | * 10240 | 1 1--------------------+-----+------+-----------+------------+------------+--------------+-------------+-------------+------------+--------o3x3o3o3o3o3o3o3o .♦ 45 | 360 | 120 840 | 210 1260 | 252 1260 | 210 840 | 120 360 | 45 90 | 10 10 | 1024 *. x3o3o3o3o3o3o3o4o♦ 18 | 144 | 0 672 | 0 2016 | 0 4032 | 0 5376 | 0 4608 | 0 2304 | 0 512 | * 20
o3o3o *b3o3o3o3o3o3x3o. . . . . . . . . . | 180♦ 32 | 224 16 | 896 112 | 2240 448 | 3584 1120 | 3584 1792 | 2048 1792 | 256 256 1024 | 2 128 128-----------------------+-----+------+-----------+------------+------------+--------------+-------------+-------------+----------------+-----------. . . . . . . . x . | 2 | 2880 | 14 1 | 84 14 | 280 84 | 560 280 | 672 560 | 448 672 | 64 64 448 | 1 64 64-----------------------+-----+------+-----------+------------+------------+--------------+-------------+-------------+----------------+-----------. . . . . . . o3x . | 3 | 3 | 13440 * | 12 1 | 60 12 | 160 60 | 240 160 | 192 240 | 32 32 192 | 1 32 32. . . . . . . . x3o | 3 | 3 | * 960♦ 0 14 | 0 84 | 0 280 | 0 560 | 0 672 | 0 0 448 | 0 64 64-----------------------+-----+------+-----------+------------+------------+--------------+-------------+-------------+----------------+-----------. . . . . . o3o3x .♦ 4 | 6 | 4 0 | 40320 * | 10 1 | 40 10 | 80 40 | 80 80 | 16 16 80 | 1 16 16. . . . . . . o3x3o♦ 6 | 12 | 4 4 | * 3360♦ 0 12 | 0 60 | 0 160 | 0 240 | 0 0 192 | 0 32 32-----------------------+-----+------+-----------+------------+------------+--------------+-------------+-------------+----------------+-----------. . . . . o3o3o3x .♦ 5 | 10 | 10 0 | 5 0 | 80640 * | 8 1 | 24 8 | 32 24 | 8 8 32 | 1 8 8. . . . . . o3o3x3o♦ 10 | 30 | 20 10 | 5 5 | * 8064♦ 0 10 | 0 40 | 0 80 | 0 0 80 | 0 16 16-----------------------+-----+------+-----------+------------+------------+--------------+-------------+-------------+----------------+-----------. . . . o3o3o3o3x .♦ 6 | 15 | 20 0 | 15 0 | 6 0 | 107520 * | 6 1 | 12 6 | 4 4 12 | 1 4 4. . . . . o3o3o3x3o♦ 15 | 60 | 60 20 | 30 15 | 6 6 | * 13440♦ 0 8 | 0 24 | 0 0 32 | 0 8 8-----------------------+-----+------+-----------+------------+------------+--------------+-------------+-------------+----------------+-----------. . . o3o3o3o3o3x .♦ 7 | 21 | 35 0 | 35 0 | 21 0 | 7 0 | 92160 * | 4 1 | 2 2 4 | 1 2 2. . . . o3o3o3o3x3o♦ 21 | 105 | 140 35 | 105 35 | 42 21 | 7 7 | * 15360♦ 0 6 | 0 0 12 | 0 4 4-----------------------+-----+------+-----------+------------+------------+--------------+-------------+-------------+----------------+-----------. o . *b3o3o3o3o3o3x .♦ 8 | 28 | 56 0 | 70 0 | 56 0 | 28 0 | 8 0 | 46080 * | 1 1 1 | 1 1 1. . . o3o3o3o3o3x3o♦ 28 | 168 | 280 56 | 280 70 | 168 56 | 56 28 | 8 8 | * 11520 | 0 0 4 | 0 2 2-----------------------+-----+------+-----------+------------+------------+--------------+-------------+-------------+----------------+-----------o3o . *b3o3o3o3o3o3x .♦ 9 | 36 | 84 0 | 126 0 | 126 0 | 84 0 | 36 0 | 9 0 | 5120 * * | 1 1 0. o3o *b3o3o3o3o3o3x .♦ 9 | 36 | 84 0 | 126 0 | 126 0 | 84 0 | 36 0 | 9 0 | * 5120 * | 1 0 1. o . *b3o3o3o3o3o3x3o♦ 36 | 252 | 504 84 | 630 126 | 504 126 | 252 84 | 72 36 | 9 9 | * * 5120 | 0 1 1-----------------------+-----+------+-----------+------------+------------+--------------+-------------+-------------+----------------+-----------o3o3o *b3o3o3o3o3o3x .♦ 18 | 144 | 672 0 | 2016 0 | 4032 0 | 5376 0 | 4608 0 | 2304 0 | 256 256 0 | 20 * *o3o . *b3o3o3o3o3o3x3o♦ 45 | 360 | 840 120 | 1260 210 | 1260 252 | 840 210 | 360 120 | 90 45 | 10 0 10 | * 512 *. o3o *b3o3o3o3o3o3x3o♦ 45 | 360 | 840 120 | 1260 210 | 1260 252 | 840 210 | 360 120 | 90 45 | 0 10 10 | * * 512
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