Acronym gososaz
Name great hepteractihepteractihecatonicosoctaexon
Circumradius sqrt[9-2 sqrt(2)]/2 = 1.242133
Coordinates ((sqrt(2)-1)/2, 1/2, 1/2, 1/2, 1/2, 1/2, 1/2)   & all permutations, all changes of sign

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


Incidence matrix according to Dynkin symbol

o3o3o3o3o3x4/3x4*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*e |   4 |    0    4 |    * 3360   * |    0    4   1 |    0   6   4 |   0   4  6 |   0  1  4
. . . . . x4/3x    |   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*e    8 |    0   12 |    0    6   0 |    * 2240   * |    0   3   1 |   0   3  3 |   0  1  3
. . . . o3x4/3x4*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*e   16 |    0   32 |    0   24   0 |    0    8   0 |    * 840   * |   0   2  1 |   0  1  2
. . . o3o3x4/3x4*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*e   32 |    0   80 |    0   80   0 |    0   40   0 |    0  10   0 |   * 168  * |   0  1  1
. . o3o3o3x4/3x4*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*e   64 |    0  192 |    0  240   0 |    0  160   0 |    0  60   0 |   0  12  0 |   * 14  *
. o3o3o3o3x4/3x4*e  384 |  960  960 | 1280  960 240 |  960  480 160 |  384 120  60 |  64  12 12 |   *  * 14

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