| Acronym | gook |
| Name | great octeractiocteractidiacosipentacontahexazetton |
| Circumradius | sqrt[(5-sqrt(2))/2] = 1.338990 |
| Coordinates | ((sqrt(2)-1)/2, 1/2, 1/2, 1/2, 1/2, 1/2, 1/2, 1/2) & all permutations, all changes of sign |
| Face vector | 2048, 14336, 26880, 28672, 19936, 8960, 2384, 288 |
| Confer |
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As abstract polytope gook is isomorphic to sook, thereby replacing octagrams by octagons, resp. gocco by socco, gittith by steth, ginnont by sinnont, goxaxog by soxaxog, and gososaz by sososaz.
Incidence matrix according to Dynkin symbol
o3o3o3o3o3o3x4/3x4*f . . . . . . . . | 2048 | 7 7 | 21 21 7 | 35 35 21 | 35 35 35 | 21 21 35 | 7 7 21 | 1 1 7 ---------------------+------+-----------+------------------+-----------------+-----------------+---------------+--------------+---------- . . . . . . x . | 2 | 7168 * | 6 0 1 | 15 0 6 | 20 0 15 | 15 0 20 | 6 0 15 | 1 0 6 . . . . . . . x | 2 | * 7168 | 0 6 1 | 0 15 6 | 0 20 15 | 0 15 20 | 0 6 15 | 0 1 6 ---------------------+------+-----------+------------------+-----------------+-----------------+---------------+--------------+---------- . . . . . o3x . | 3 | 3 0 | 14336 * * | 5 0 1 | 10 0 5 | 10 0 10 | 5 0 10 | 1 0 5 . . . . . o . x4*f | 4 | 0 4 | * 10752 * | 0 5 1 | 0 10 5 | 0 10 10 | 0 5 10 | 0 1 5 . . . . . . x4/3x | 8 | 4 4 | * * 1792 ♦ 0 0 6 | 0 0 15 | 0 0 20 | 0 0 15 | 0 0 6 ---------------------+------+-----------+------------------+-----------------+-----------------+---------------+--------------+---------- . . . . o3o3x . ♦ 4 | 6 0 | 4 0 0 | 17920 * * | 4 0 1 | 6 0 4 | 4 0 6 | 1 0 4 . . . . o3o . x4*f ♦ 8 | 0 12 | 0 6 0 | * 8960 * | 0 4 1 | 0 6 4 | 0 4 6 | 0 1 4 . . . . . o3x4/3x4*f ♦ 24 | 24 24 | 8 6 6 | * * 1792 ♦ 0 0 5 | 0 0 10 | 0 0 10 | 0 0 5 ---------------------+------+-----------+------------------+-----------------+-----------------+---------------+--------------+---------- . . . o3o3o3x . ♦ 5 | 10 0 | 10 0 0 | 5 0 0 | 14336 * * | 3 0 1 | 3 0 3 | 1 0 3 . . . o3o3o . x4*f ♦ 16 | 0 32 | 0 24 0 | 0 8 0 | * 4480 * | 0 3 1 | 0 3 3 | 0 1 3 . . . . o3o3x4/3x4*f ♦ 64 | 96 96 | 64 48 24 | 16 8 8 | * * 1120 ♦ 0 0 4 | 0 0 6 | 0 0 4 ---------------------+------+-----------+------------------+-----------------+-----------------+---------------+--------------+---------- . . o3o3o3o3x . ♦ 6 | 15 0 | 20 0 0 | 15 0 0 | 6 0 0 | 7168 * * | 2 0 1 | 1 0 2 . . o3o3o3o . x4*f ♦ 32 | 0 80 | 0 80 0 | 0 40 0 | 0 10 0 | * 1344 * | 0 2 1 | 0 1 2 . . . o3o3o3x4/3x4*f ♦ 160 | 320 320 | 320 240 80 | 160 80 40 | 32 10 10 | * * 448 | 0 0 3 | 0 0 3 ---------------------+------+-----------+------------------+-----------------+-----------------+---------------+--------------+---------- . o3o3o3o3o3x . ♦ 7 | 21 0 | 35 0 0 | 35 0 0 | 21 0 0 | 7 0 0 | 2048 * * | 1 0 1 . o3o3o3o3o . x4*f ♦ 64 | 0 192 | 0 240 0 | 0 160 0 | 0 60 0 | 0 12 0 | * 224 * | 0 1 1 . . o3o3o3o3x4/3x4*f ♦ 384 | 960 960 | 1280 960 240 | 960 480 160 | 384 120 60 | 64 12 12 | * * 112 | 0 0 2 ---------------------+------+-----------+------------------+-----------------+-----------------+---------------+--------------+---------- o3o3o3o3o3o3x . ♦ 8 | 28 0 | 56 0 0 | 70 0 0 | 56 0 0 | 28 0 0 | 8 0 0 | 256 * * o3o3o3o3o3o . x4*f ♦ 128 | 0 448 | 0 672 0 | 0 560 0 | 0 280 0 | 0 84 0 | 0 14 0 | * 16 * . o3o3o3o3o3x4/3x4*f ♦ 896 | 2688 2688 | 4480 3360 672 | 4480 2240 560 | 2688 840 280 | 896 168 84 | 128 14 14 | * * 16
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