Acronym grox
Name great rhombihexeract,
cantitruncated hexeract
Circumradius sqrt[(20+9 sqrt(2))/2] = 4.045239
Coordinates ((1+2 sqrt(2))/2, (1+2 sqrt(2))/2, (1+2 sqrt(2))/2, (1+2 sqrt(2))/2, (1+sqrt(2))/2, 1/2)   & all permutations, all changes of sign
External
links
wikipedia

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


Incidence matrix according to Dynkin symbol

o3o3o3x3x4x

. . . . . . | 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
. . . . x4x |    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
. . . x3x4x    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
. . o3x3x4x   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  *
. o3o3x3x4x   640 |  960 320 320 |  640  320  480  80 |  160 160  320  40 |   0  32  80 10 |  *   * 12

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