Acronym soxaxog
Name small hexeractihexeractihexacontitetrapeton
Circumradius sqrt[(4+sqrt(2))/2] = 1.645329
Coordinates ((1+sqrt(2))/2, 1/2, 1/2, 1/2, 1/2, 1/2)   & all permutations, all changes of sign

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


Incidence matrix according to Dynkin symbol

o3o3o3o3x4x4/3*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 . x4/3*d |   4 |   0   4 |    * 960   * |   0   3   1 |   0   3  3 |  0  1  3
. . . . x4x      |   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 . x4/3*d    8 |   0  12 |    0   6   0 |   * 480   * |   0   2  1 |  0  1  2
. . . o3x4x4/3*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 . x4/3*d   16 |   0  32 |    0  24   0 |   0   8   0 |   * 120  * |  0  1  1
. . o3o3x4x4/3*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 . x4/3*d   32 |   0  80 |    0  80   0 |   0  40   0 |   0  10  0 |  * 12  *
. o3o3o3x4x4/3*d  160 | 320 320 |  320 240  80 | 160  80  40 |  32  10 10 |  *  * 12

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