Acronym sososaz
Name small hepteractihepteractihecatonicosoctaexon
Circumradius sqrt[9+2 sqrt(2)]/2 = 1.719624
Coordinates ((1+sqrt(2))/2, 1/2, 1/2, 1/2, 1/2, 1/2, 1/2)   & all permutations, all changes of sign

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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