As abstract polytope quoptax is isomorphic to potax, thereby replacing octagrams by octagons, resp. quith by tic and stop by op, resp. quiproh by proh and tistodip by todip, resp quiptin by pattin and stotet by otet.

Incidence matrix according to Dynkin symbol

o3o3x3o3x4/3x

. . . . .   . | 3840 |     6    2    1 |    6    3    3    3    1   2 |    2    3    6    6   3    3    6   1 |   1   2   2   3   3   6  3 |  1   1   2  3
--------------+------+-----------------+------------------------------+---------------------------------------+----------------------------+--------------
. . x . .   . |    2 | 11520    *    * |    2    1    1    1    0   0 |    1    2    2    2   1    1    1   0 |   1   1   1   2   2   2  1 |  1   1   1  2
. . . . x   . |    2 |     * 3840    * |    0    0    3    0    1   1 |    0    0    3    0   3    0    3   1 |   0   1   0   3   0   3  3 |  1   0   1  3
. . . . .   x |    2 |     *    * 1920 |    0    0    0    6    0   2 |    0    0    0    6   0    3    6   1 |   0   0   2   0   3   6  3 |  0   1   2  3
--------------+------+-----------------+------------------------------+---------------------------------------+----------------------------+--------------
. o3x . .   . |    3 |     3    0    0 | 7680    *    *    *    *   * |    1    1    1    1   0    0    0   0 |   1   1   1   1   1   1  0 |  1   1   1  1
. . x3o .   . |    3 |     3    0    0 |    * 3840    *    *    *   * |    0    2    0    0   1    1    0   0 |   1   0   0   2   2   0  1 |  1   1   0  2
. . x . x   . |    4 |     2    2    0 |    *    * 5760    *    *   * |    0    0    2    0   1    0    1   0 |   0   1   0   2   0   2  1 |  1   0   1  2
. . x . .   x |    4 |     2    0    2 |    *    *    * 5760    *   * |    0    0    0    2   0    1    1   0 |   0   0   1   0   2   2  1 |  0   1   1  2
. . . o3x   . |    3 |     0    3    0 |    *    *    *    * 1280   * |    0    0    0    0   3    0    0   1 |   0   0   0   3   0   0  3 |  1   0   0  3
. . . . x4/3x |    8 |     0    4    4 |    *    *    *    *    * 960 |    0    0    0    0   0    0    3   1 |   0   0   0   0   0   3  3 |  0   0   1  3
--------------+------+-----------------+------------------------------+---------------------------------------+----------------------------+--------------
o3o3x . .   . ♦    4 |     6    0    0 |    4    0    0    0    0   0 | 1920    *    *    *   *    *    *   * |   1   1   1   0   0   0  0 |  1   1   1  0
. o3x3o .   . ♦    6 |    12    0    0 |    4    4    0    0    0   0 |    * 1920    *    *   *    *    *   * |   1   0   0   1   1   0  0 |  1   1   0  1
. o3x . x   . ♦    6 |     6    3    0 |    2    0    3    0    0   0 |    *    * 3840    *   *    *    *   * |   0   1   0   1   0   1  0 |  1   0   1  1
. o3x . .   x ♦    6 |     6    0    3 |    2    0    0    3    0   0 |    *    *    * 3840   *    *    *   * |   0   0   1   0   1   1  0 |  0   1   1  1
. . x3o3x   . ♦   12 |    12   12    0 |    0    4    6    0    4   0 |    *    *    *    * 960    *    *   * |   0   0   0   2   0   0  1 |  1   0   0  2
. . x3o .   x ♦    6 |     6    0    3 |    0    2    0    3    0   0 |    *    *    *    *   * 1920    *   * |   0   0   0   0   2   0  1 |  0   1   0  2
. . x . x4/3x ♦   16 |     8    8    8 |    0    0    4    4    0   2 |    *    *    *    *   *    * 1440   * |   0   0   0   0   0   2  1 |  0   0   1  2
. . . o3x4/3x ♦   24 |     0   24   12 |    0    0    0    0    8   6 |    *    *    *    *   *    *    * 160 |   0   0   0   0   0   0  3 |  0   0   0  3
--------------+------+-----------------+------------------------------+---------------------------------------+----------------------------+--------------
o3o3x3o .   . ♦   10 |    30    0    0 |   20   10    0    0    0   0 |    5    5    0    0   0    0    0   0 | 384   *   *   *   *   *  * |  1   1   0  0
o3o3x . x   . ♦    8 |    12    4    0 |    8    0    6    0    0   0 |    2    0    4    0   0    0    0   0 |   * 960   *   *   *   *  * |  1   0   1  0
o3o3x . .   x ♦    8 |    12    0    4 |    8    0    0    6    0   0 |    2    0    0    4   0    0    0   0 |   *   * 960   *   *   *  * |  0   1   1  0
. o3x3o3x   . ♦   30 |    60   30    0 |   20   20   30    0   10   0 |    0    5   10    0   5    0    0   0 |   *   *   * 384   *   *  * |  1   0   0  1
. o3x3o .   x ♦   12 |    24    0    6 |    8    8    0   12    0   0 |    0    2    0    4   0    4    0   0 |   *   *   *   * 960   *  * |  0   1   0  1
. o3x . x4/3x ♦   24 |    24   12   12 |    8    0   12   12    0   3 |    0    0    4    4   0    0    3   0 |   *   *   *   *   * 960  * |  0   0   1  1
. . x3o3x4/3x ♦  192 |   192  192   96 |    0   64   96   96   64  48 |    0    0    0    0  16   32   24   8 |   *   *   *   *   *   * 60 |  0   0   0  2
--------------+------+-----------------+------------------------------+---------------------------------------+----------------------------+--------------
o3o3x3o3x   . ♦   60 |   180   60    0 |  120   60   90    0   20   0 |   30   30   60    0  15    0    0   0 |   6  15   0   6   0   0  0 | 64   *   *  *
o3o3x3o .   x ♦   20 |    60    0   10 |   40   20    0   30    0   0 |   10   10    0   20   0   10    0   0 |   2   0   5   0   5   0  0 |  * 192   *  *
o3o3x . x4/3x ♦   32 |    48   16   16 |   32    0   24   24    0   4 |    8    0   16   16   0    0    6   0 |   0   4   4   0   0   4  0 |  *   * 240  *
. o3x3o3x4/3x ♦  960 |  1920  960  480 |  640  640  960  960  320 240 |    0  160  320  320 160  320  240  40 |   0   0   0  32  80  80 10 |  *   *   * 12