Acronym goxaxog
Name great hexeractihexeractihexacontitetrapeton
Circumradius sqrt[(4-sqrt(2))/2] = 1.137055
Coordinates ((sqrt(2)-1)/2, 1/2, 1/2, 1/2, 1/2, 1/2)   & all permutations, all changes of sign

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


Incidence matrix according to Dynkin symbol

o3o3o3o3x4/3x4*d

. . . . .   .    | 384 |   5   5 |   10  10   5 |  10  10  10 |   5   5 10 |  1  1  5
-----------------+-----+---------+--------------+-------------+------------+---------
. . . . x   .    |   2 | 960   * |    4   0   1 |   6   0   4 |   4   0  6 |  1  0  4
. . . . .   x    |   2 |   * 960 |    0   4   1 |   0   6   4 |   0   4  6 |  0  1  4
-----------------+-----+---------+--------------+-------------+------------+---------
. . . o3x   .    |   3 |   3   0 | 1280   *   * |   3   0   1 |   3   0  3 |  1  0  3
. . . o .   x4*d |   4 |   0   4 |    * 960   * |   0   3   1 |   0   3  3 |  0  1  3
. . . . x4/3x    |   8 |   4   4 |    *   * 240    0   0   4 |   0   0  6 |  0  0  4
-----------------+-----+---------+--------------+-------------+------------+---------
. . o3o3x   .       4 |   6   0 |    4   0   0 | 960   *   * |   2   0  1 |  1  0  2
. . o3o .   x4*d    8 |   0  12 |    0   6   0 |   * 480   * |   0   2  1 |  0  1  2
. . . o3x4/3x4*d   24 |  24  24 |    8   6   6 |   *   * 160 |   0   0  3 |  0  0  3
-----------------+-----+---------+--------------+-------------+------------+---------
. o3o3o3x   .       5 |  10   0 |   10   0   0 |   5   0   0 | 384   *  * |  1  0  1
. o3o3o .   x4*d   16 |   0  32 |    0  24   0 |   0   8   0 |   * 120  * |  0  1  1
. . o3o3x4/3x4*d   64 |  96  96 |   64  48  24 |  16   8   8 |   *   * 60 |  0  0  2
-----------------+-----+---------+--------------+-------------+------------+---------
o3o3o3o3x   .       6 |  15   0 |   20   0   0 |  15   0   0 |   6   0  0 | 64  *  *
o3o3o3o .   x4*d   32 |   0  80 |    0  80   0 |   0  40   0 |   0  10  0 |  * 12  *
. o3o3o3x4/3x4*d  160 | 320 320 |  320 240  80 | 160  80  40 |  32  10 10 |  *  * 12

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