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
Face vector	1920, 5760, 7280, 4960, 1788, 268
Confer	general polytopal classes: Wythoffian polypeta
External links

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