As abstract polytope quapox is isomorphic to spox, thereby replacing quidpith by sidpith and quappin by span.

Incidence matrix according to Dynkin symbol

o3o3x3o3o4/3x

. . . . .   . | 1280 |    9    3 |    9    9   18   3 |   3    9   18   3    9    9   1 |   3   6   3   9   9  3 |  1   3   3  3
--------------+------+-----------+--------------------+---------------------------------+------------------------+--------------
. . x . .   . |    2 | 5760    * |    2    2    2   0 |   1    4    4   1    2    1   0 |   2   2   2   4   2  1 |  1   1   1  2
. . . . .   x |    2 |    * 1920 |    0    0    6   2 |   0    0    6   0    3    6   1 |   0   2   0   3   6  3 |  0   1   2  3
--------------+------+-----------+--------------------+---------------------------------+------------------------+--------------
. o3x . .   . |    3 |    3    0 | 3840    *    *   * |   1    2    2   0    0    0   0 |   2   2   1   2   1  0 |  1   2   1  1
. . x3o .   . |    3 |    3    0 |    * 3840    *   * |   0    2    0   1    1    0   0 |   1   0   2   2   0  1 |  1   1   0  2
. . x . .   x |    4 |    2    2 |    *    * 5760   * |   0    0    2   0    1    1   0 |   0   1   0   2   2  1 |  0   1   1  2
. . . . o4/3x |    4 |    0    4 |    *    *    * 960 |   0    0    0   0    0    3   1 |   0   0   0   0   3  3 |  0   0   1  3
--------------+------+-----------+--------------------+---------------------------------+------------------------+--------------
o3o3x . .   . ♦    4 |    6    0 |    4    0    0   0 | 960    *    *   *    *    *   * |   2   2   0   0   0  0 |  1   2   1  0
. o3x3o .   . ♦    6 |   12    0 |    4    4    0   0 |   * 1920    *   *    *    *   * |   1   0   1   1   0  0 |  1   1   0  1
. o3x . .   x ♦    6 |    6    3 |    2    0    3   0 |   *    * 3840   *    *    *   * |   0   1   0   1   1  0 |  0   1   1  1
. . x3o3o   . ♦    4 |    6    0 |    0    4    0   0 |   *    *    * 960    *    *   * |   0   0   2   0   0  1 |  1   0   0  2
. . x3o .   x ♦    6 |    6    3 |    0    2    3   0 |   *    *    *   * 1920    *   * |   0   0   0   2   0  1 |  0   1   0  2
. . x . o4/3x ♦    8 |    4    8 |    0    0    4   2 |   *    *    *   *    * 1440   * |   0   0   0   0   2  1 |  0   0   1  2
. . . o3o4/3x ♦    8 |    0   12 |    0    0    0   6 |   *    *    *   *    *    * 160 |   0   0   0   0   0  3 |  0   0   0  3
--------------+------+-----------+--------------------+---------------------------------+------------------------+--------------
o3o3x3o .   . ♦   10 |   30    0 |   20   10    0   0 |   5    5    0   0    0    0   0 | 384   *   *   *   *  * |  1   1   0  0
o3o3x . .   x ♦    8 |   12    4 |    8    0    6   0 |   2    0    4   0    0    0   0 |   * 960   *   *   *  * |  0   1   1  0
. o3x3o3o   . ♦   10 |   30    0 |   10   20    0   0 |   0    5    0   5    0    0   0 |   *   * 384   *   *  * |  1   0   0  1
. o3x3o .   x ♦   12 |   24    6 |    8    8   12   0 |   0    2    4   0    4    0   0 |   *   *   * 960   *  * |  0   1   0  1
. o3x . o4/3x ♦   12 |   12   12 |    4    0   12   3 |   0    0    4   0    0    3   0 |   *   *   *   * 960  * |  0   0   1  1
. . x3o3o4/3x ♦   64 |   96   96 |    0   64   96  48 |   0    0    0  16   32   24   8 |   *   *   *   *   * 60 |  0   0   0  2
--------------+------+-----------+--------------------+---------------------------------+------------------------+--------------
o3o3x3o3o   . ♦   20 |   90    0 |   60   60    0   0 |  15   30    0  15    0    0   0 |   6   0   6   0   0  0 | 64   *   *  *
o3o3x3o .   x ♦   20 |   60   10 |   40   20   30   0 |  10   10   20   0   10    0   0 |   2   5   0   5   0  0 |  * 192   *  *
o3o3x . o4/3x ♦   16 |   24   16 |   16    0   24   4 |   4    0   16   0    0    6   0 |   0   4   0   0   4  0 |  *   * 240  *
. o3x3o3o4/3x ♦  320 |  960  480 |  320  640  960 240 |   0  160  320 160  320  240  40 |   0   0  32  80  80 10 |  *   *   * 12