Acronym gaqrox
Name great quasirhombihexeract
Circumradius sqrt[(20-9 sqrt(2))/2] = 1.906840
Coordinates ((2 sqrt(2)-1)/2, (2 sqrt(2)-1)/2, (2 sqrt(2)-1)/2, (2 sqrt(2)-1)/2, (sqrt(2)-1)/2, 1/2)   & all permutations, all changes of sign

As abstract polyteron gaqrox is isomorph to grox, thereby replacing octagrams by octagons, resp. quitco by girco, resp. gaqrit by grit, resp. gaqrin by girn.


Incidence matrix according to Dynkin symbol

o3o3o3x3x4/3x

. . . . .   . | 1920 |    4   1   1 |    6    4    4   1 |    4   6    6   4 |   1   4   4  6 |  1   1  4
--------------+------+--------------+--------------------+-------------------+----------------+----------
. . . x .   . |    2 | 3840   *   * |    3    1    1   0 |    3   3    3   1 |   1   3   3  3 |  1   1  3
. . . . x   . |    2 |    * 960   * |    0    4    0   1 |    0   6    0   4 |   0   4   0  6 |  1   0  4
. . . . .   x |    2 |    *   * 960 |    0    0    4   1 |    0   0    6   4 |   0   0   4  6 |  0   1  4
--------------+------+--------------+--------------------+-------------------+----------------+----------
. . o3x .   . |    3 |    3   0   0 | 3840    *    *   * |    2   1    1   0 |   1   2   2  1 |  1   1  2
. . . x3x   . |    6 |    3   3   0 |    * 1280    *   * |    0   3    0   1 |   0   3   0  3 |  1   0  3
. . . x .   x |    4 |    2   0   2 |    *    * 1920   * |    0   0    3   1 |   0   0   3  3 |  0   1  3
. . . . x4/3x |    8 |    0   4   4 |    *    *    * 240     0   0    0   4 |   0   0   0  6 |  0   0  4
--------------+------+--------------+--------------------+-------------------+----------------+----------
. o3o3x .   .     4 |    6   0   0 |    4    0    0   0 | 1920   *    *   * |   1   1   1  0 |  1   1  1
. . o3x3x   .    12 |   12   6   0 |    4    4    0   0 |    * 960    *   * |   0   2   0  1 |  1   0  2
. . o3x .   x     6 |    6   0   3 |    2    0    3   0 |    *   * 1920   * |   0   0   2  1 |  0   1  2
. . . x3x4/3x    48 |   24  24  24 |    0    8   12   6 |    *   *    * 160 |   0   0   0  3 |  0   0  3
--------------+------+--------------+--------------------+-------------------+----------------+----------
o3o3o3x .   .     5 |   10   0   0 |   10    0    0   0 |    5   0    0   0 | 384   *   *  * |  1   1  0
. o3o3x3x   .    20 |   30  10   0 |   20   10    0   0 |    5   5    0   0 |   * 384   *  * |  1   0  1
. o3o3x .   x     8 |   12   0   4 |    8    0    6   0 |    2   0    4   0 |   *   * 960  * |  0   1  1
. . o3x3x4/3x   192 |  192  96  96 |   64   64   96  24 |    0  16   32   8 |   *   *   * 60 |  0   0  2
--------------+------+--------------+--------------------+-------------------+----------------+----------
o3o3o3x3x   .    30 |   60  15   0 |   60   20    0   0 |   30  15    0   0 |   6   6   0  0 | 64   *  *
o3o3o3x .   x    10 |   20   0   5 |   20    0   10   0 |   10   0   10   0 |   2   0   5  0 |  * 192  *
. o3o3x3x4/3x   640 |  960 320 320 |  640  320  480  80 |  160 160  320  40 |   0  32  80 10 |  *   * 12

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