Acronym | soro |
Name |
small rhombated octeract, cantellated octeract |
Circumradius | sqrt[5+3 sqrt(2)] = 3.040171 |
Inradius wrt. hopip | sqrt[(121+84 sqrt(2))/28] = 2.926443 |
Inradius wrt. roc | sqrt[17+12 sqrt(2)]/2 = 2.914214 |
Inradius wrt. sersa | (1+sqrt(2))/2 = 1.207107 |
Dihedral angles
(at margins) | |
Face vector | 7168, 50176, 109312, 127232, 94304, 43456, 11376, 1296 |
Confer |
|
As abstract polytope soro is isomorphic to qro, thereby replacing sirco by querco, srit by qrit, sirn by quarn, srox by qrax, and sersa by quersa.
Incidence matrix according to Dynkin symbol
o3o3o3o3o3x3o4x o3o3o3o3o3o3o4o | 7168 | 12 2 | 30 6 12 1 | 40 15 30 6 | 30 20 40 15 | 12 15 30 20 | 2 6 12 15 | 1 2 6 ----------------+------+------------+------------------------+------------------------+------------------------+----------------------+--------------------+------------ . . . . . x . . | 2 | 43008 * | 5 1 1 0 | 10 5 5 1 | 10 10 10 5 | 5 10 10 10 | 1 5 5 10 | 1 1 5 . . . . . . . x | 2 | * 7168 | 0 0 6 1 | 0 0 15 6 | 0 0 20 15 | 0 0 15 20 | 0 0 6 15 | 0 1 6 ----------------+------+------------+------------------------+------------------------+------------------------+----------------------+--------------------+------------ . . . . o3x . . | 3 | 3 0 | 71680 * * * | 4 1 1 0 | 6 4 4 1 | 4 6 6 4 | 1 4 4 6 | 1 1 4 . . . . . x3o . | 3 | 3 0 | * 14336 * * | 0 5 0 1 | 0 10 0 5 | 0 10 0 10 | 0 5 0 10 | 1 0 5 . . . . . x . x | 4 | 2 2 | * * 21504 * | 0 0 5 1 | 0 0 10 5 | 0 0 10 10 | 0 0 5 10 | 0 1 5 . . . . . . o4x | 4 | 0 4 | * * * 1792 | 0 0 0 6 | 0 0 0 15 | 0 0 0 20 | 0 0 0 15 | 0 0 6 ----------------+------+------------+------------------------+------------------------+------------------------+----------------------+--------------------+------------ . . . o3o3x . . ♦ 4 | 6 0 | 4 0 0 0 | 71680 * * * | 3 1 1 0 | 3 3 3 1 | 1 3 3 3 | 1 1 3 . . . . o3x3o . ♦ 6 | 12 0 | 4 4 0 0 | * 17920 * * | 0 4 0 1 | 0 6 0 4 | 0 4 0 6 | 1 0 4 . . . . o3x . x ♦ 6 | 6 3 | 2 0 3 0 | * * 35840 * | 0 0 4 1 | 0 0 6 4 | 0 0 4 6 | 0 1 4 . . . . . x3o4x ♦ 24 | 24 24 | 0 8 12 6 | * * * 1792 | 0 0 0 5 | 0 0 0 10 | 0 0 0 10 | 0 0 5 ----------------+------+------------+------------------------+------------------------+------------------------+----------------------+--------------------+------------ . . o3o3o3x . . ♦ 5 | 10 0 | 10 0 0 0 | 5 0 0 0 | 43008 * * * | 2 1 1 0 | 1 2 2 1 | 1 1 2 . . . o3o3x3o . ♦ 10 | 30 0 | 20 10 0 0 | 5 5 0 0 | * 14336 * * | 0 3 0 1 | 0 3 0 3 | 1 0 3 . . . o3o3x . x ♦ 8 | 12 4 | 8 0 6 0 | 2 0 4 0 | * * 35840 * | 0 0 3 1 | 0 0 3 3 | 0 1 3 . . . . o3x3o4x ♦ 96 | 192 96 | 64 64 96 24 | 0 16 32 8 | * * * 1120 | 0 0 0 4 | 0 0 0 6 | 0 0 4 ----------------+------+------------+------------------------+------------------------+------------------------+----------------------+--------------------+------------ . o3o3o3o3x . . ♦ 6 | 15 0 | 20 0 0 0 | 15 0 0 0 | 6 0 0 0 | 14336 * * * | 1 1 1 0 | 1 1 1 . . o3o3o3x3o . ♦ 15 | 60 0 | 60 20 0 0 | 30 15 0 0 | 6 6 0 0 | * 7168 * * | 0 2 0 1 | 1 0 2 . . o3o3o3x . x ♦ 10 | 20 5 | 20 0 10 0 | 10 0 10 0 | 2 0 5 0 | * * 21504 * | 0 0 2 1 | 0 1 2 . . . o3o3x3o4x ♦ 320 | 960 320 | 640 320 480 80 | 160 160 320 40 | 0 32 80 10 | * * * 448 | 0 0 0 3 | 0 0 3 ----------------+------+------------+------------------------+------------------------+------------------------+----------------------+--------------------+------------ o3o3o3o3o3x . . ♦ 7 | 21 0 | 35 0 0 0 | 35 0 0 0 | 21 0 0 0 | 7 0 0 0 | 2048 * * * | 1 1 0 . o3o3o3o3x3o . ♦ 21 | 105 0 | 140 35 0 0 | 105 35 0 0 | 42 21 0 0 | 7 7 0 0 | * 2048 * * | 1 0 1 . o3o3o3o3x . x ♦ 12 | 30 6 | 40 0 15 0 | 30 0 20 0 | 12 0 15 0 | 2 0 6 0 | * * 7168 * | 0 1 1 . . o3o3o3x3o4x ♦ 960 | 3840 960 | 3840 1280 1920 240 | 1920 960 1920 160 | 384 384 960 60 | 0 64 192 12 | * * * 112 | 0 0 2 ----------------+------+------------+------------------------+------------------------+------------------------+----------------------+--------------------+------------ o3o3o3o3o3x3o . ♦ 28 | 168 0 | 280 56 0 0 | 280 70 0 0 | 168 56 0 0 | 56 28 0 0 | 8 8 0 0 | 256 * * o3o3o3o3o3x . x ♦ 14 | 42 7 | 70 0 21 0 | 70 0 35 0 | 42 0 35 0 | 14 0 21 0 | 2 0 7 0 | * 1024 * . o3o3o3o3x3o4x ♦ 2688 | 13440 2688 | 17920 4480 6720 672 | 13440 4480 8960 560 | 5376 2688 6720 280 | 896 896 2688 84 | 0 128 448 14 | * * 16
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