sososaz

Acronym	sososaz
Name	small hepteractihepteractihecatonicosoctaexon
Circumradius	sqrt[9+2 sqrt(2)]/2 = 1.719624
Inradius wrt. hop	-[7+sqrt(2)]/sqrt(28) = -1.590137
Inradius wrt. ax	(1+sqrt(2))/2 = 1.207107
Inradius wrt. soxaxog	1/2 = 0.5
Coordinates	((1+sqrt(2))/2, 1/2, 1/2, 1/2, 1/2, 1/2, 1/2) & all permutations, all changes of sign
Dihedral angles (at margins)	at pent between ax and soxaxog: 90° at sinnont between soxaxog and soxaxog: 90° at hix between hop and soxaxog: arccos[1/sqrt(7)] = 67.792346°
Face vector	896, 5376, 8512, 7280, 3808, 1148, 156
Confer	general polytopal classes: Wythoffian polyexa analogs: socco series

As abstract polytope sososaz is isomorphic to gososaz, thereby replacing octagons by octagrams, resp. by gocco, resp. steth by gittith, resp. sinnont by ginnont, and soxaxog by goxaxog.

Incidence matrix according to Dynkin symbol

o3o3o3o3o3x4x4/3*e

. . . . . . .      | 896 |    6    6 |   15   15   6 |   20   20  15 |   15  15  20 |   6   6 15 |   1  1  6
-------------------+-----+-----------+---------------+---------------+--------------+------------+----------
. . . . . x .      |   2 | 2688    * |    5    0   1 |   10    0   5 |   10   0  10 |   5   0 10 |   1  0  5
. . . . . . x      |   2 |    * 2688 |    0    5   1 |    0   10   5 |    0  10  10 |   0   5 10 |   0  1  5
-------------------+-----+-----------+---------------+---------------+--------------+------------+----------
. . . . o3x .      |   3 |    3    0 | 4480    *   * |    4    0   1 |    6   0   4 |   4   0  6 |   1  0  4
. . . . o . x4/3*e |   4 |    0    4 |    * 3360   * |    0    4   1 |    0   6   4 |   0   4  6 |   0  1  4
. . . . . x4x      |   8 |    4    4 |    *    * 672 ♦    0    0   5 |    0   0  10 |   0   0 10 |   0  0  5
-------------------+-----+-----------+---------------+---------------+--------------+------------+----------
. . . o3o3x .      ♦   4 |    6    0 |    4    0   0 | 4480    *   * |    3   0   1 |   3   0  3 |   1  0  3
. . . o3o . x4/3*e ♦   8 |    0   12 |    0    6   0 |    * 2240   * |    0   3   1 |   0   3  3 |   0  1  3
. . . . o3x4x4/3*e ♦  24 |   24   24 |    8    6   6 |    *    * 560 ♦    0   0   4 |   0   0  6 |   0  0  4
-------------------+-----+-----------+---------------+---------------+--------------+------------+----------
. . o3o3o3x .      ♦   5 |   10    0 |   10    0   0 |    5    0   0 | 2688   *   * |   2   0  1 |   1  0  2
. . o3o3o . x4/3*e ♦  16 |    0   32 |    0   24   0 |    0    8   0 |    * 840   * |   0   2  1 |   0  1  2
. . . o3o3x4x4/3*e ♦  64 |   96   96 |   64   48  24 |   16    8   8 |    *   * 280 |   0   0  3 |   0  0  3
-------------------+-----+-----------+---------------+---------------+--------------+------------+----------
. o3o3o3o3x .      ♦   6 |   15    0 |   20    0   0 |   15    0   0 |    6   0   0 | 896   *  * |   1  0  1
. o3o3o3o . x4/3*e ♦  32 |    0   80 |    0   80   0 |    0   40   0 |    0  10   0 |   * 168  * |   0  1  1
. . o3o3o3x4x4/3*e ♦ 160 |  320  320 |  320  240  80 |  160   80  40 |   32  10  10 |   *   * 84 |   0  0  2
-------------------+-----+-----------+---------------+---------------+--------------+------------+----------
o3o3o3o3o3x .      ♦   7 |   21    0 |   35    0   0 |   35    0   0 |   21   0   0 |   7   0  0 | 128  *  *
o3o3o3o3o . x4/3*e ♦  64 |    0  192 |    0  240   0 |    0  160   0 |    0  60   0 |   0  12  0 |   * 14  *
. o3o3o3o3x4x4/3*e ♦ 384 |  960  960 | 1280  960 240 |  960  480 160 |  384 120  60 |  64  12 12 |   *  * 14

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