As abstract polytope quotacog is isomorphic to tacog, thereby replacing octagrams by octagons, resp. stop by op and quith by tic, resp. tistodip by todip, quithip by ticcup, and quitit by tat, resp. stotet by otet, traquith by tratic, quititip by tattip, and quittin by tan.

Incidence matrix according to Dynkin symbol

x3o3o3o3x4/3x

. . . . .   . | 1920 |    4    4   1 |    6   12    4    6   4 |    4   12    6   12   12    4   6 |   1   4   4    6  12   4  12   1   4 |  1   1   4   6  4  1
--------------+------+---------------+-------------------------+-----------------------------------+--------------------------------------+---------------------
x . . . .   . |    2 | 3840    *   * |    3    3    1    0   0 |    3    6    3    3    3    0   0 |   1   3   3    3   6   1   3   0   0 |  1   1   3   3  1  0
. . . . x   . |    2 |    * 3840   * |    0    3    0    3   1 |    0    3    0    6    3    3   3 |   0   1   0    3   3   3   6   1   3 |  1   0   1   3  3  1
. . . . .   x |    2 |    *    * 960 |    0    0    4    0   4 |    0    0    6    0   12    0   6 |   0   0   4    0  12   0  12   0   4 |  0   1   4   6  4  1
--------------+------+---------------+-------------------------+-----------------------------------+--------------------------------------+---------------------
x3o . . .   . |    3 |    3    0   0 | 3840    *    *    *   * |    2    2    1    0    0    0   0 |   1   2   2    1   2   0   0   0   0 |  1   1   2   1  0  0
x . . . x   . |    4 |    2    2   0 |    * 5760    *    *   * |    0    2    0    2    1    0   0 |   0   1   0    2   2   1   2   0   0 |  1   0   1   2  1  0
x . . . .   x |    4 |    2    0   2 |    *    * 1920    *   * |    0    0    3    0    3    0   0 |   0   0   3    0   6   0   3   0   0 |  0   1   3   3  1  0
. . . o3x   . |    3 |    0    3   0 |    *    *    * 3840   * |    0    0    0    2    0    2   1 |   0   0   0    1   0   2   2   1   2 |  1   0   0   1  2  1
. . . . x4/3x |    8 |    0    4   4 |    *    *    *    * 960 |    0    0    0    0    3    0   3 |   0   0   0    0   3   0   6   0   3 |  0   0   1   3  3  1
--------------+------+---------------+-------------------------+-----------------------------------+--------------------------------------+---------------------
x3o3o . .   . ♦    4 |    6    0   0 |    4    0    0    0   0 | 1920    *    *    *    *    *   * |   1   1   1    0   0   0   0   0   0 |  1   1   1   0  0  0
x3o . . x   . ♦    6 |    6    3   0 |    2    3    0    0   0 |    * 3840    *    *    *    *   * |   0   1   0    1   1   0   0   0   0 |  1   0   1   1  0  0
x3o . . .   x ♦    6 |    6    0   3 |    2    0    3    0   0 |    *    * 1920    *    *    *   * |   0   0   2    0   2   0   0   0   0 |  0   1   2   1  0  0
x . . o3x   . ♦    6 |    3    6   0 |    0    3    0    2   0 |    *    *    * 3840    *    *   * |   0   0   0    1   0   1   1   0   0 |  1   0   0   1  1  0
x . . . x4/3x ♦   16 |    8    8   8 |    0    4    4    0   2 |    *    *    *    * 1440    *   * |   0   0   0    0   2   0   2   0   0 |  0   0   1   2  1  0
. . o3o3x   . ♦    4 |    0    6   0 |    0    0    0    4   0 |    *    *    *    *    * 1920   * |   0   0   0    0   0   1   0   1   1 |  1   0   0   0  1  1
. . . o3x4/3x ♦   24 |    0   24  12 |    0    0    0    8   6 |    *    *    *    *    *    * 480 |   0   0   0    0   0   0   2   0   2 |  0   0   0   1  2  1
--------------+------+---------------+-------------------------+-----------------------------------+--------------------------------------+---------------------
x3o3o3o .   . ♦    5 |   10    0   0 |   10    0    0    0   0 |    5    0    0    0    0    0   0 | 384   *   *    *   *   *   *   *   * |  1   1   0   0  0  0
x3o3o . x   . ♦    8 |   12    4   0 |    8    6    0    0   0 |    2    4    0    0    0    0   0 |   * 960   *    *   *   *   *   *   * |  1   0   1   0  0  0
x3o3o . .   x ♦    8 |   12    0   4 |    8    0    6    0   0 |    2    0    4    0    0    0   0 |   *   * 960    *   *   *   *   *   * |  0   1   1   0  0  0
x3o . o3x   . ♦    9 |    9    9   0 |    3    9    0    3   0 |    0    3    0    3    0    0   0 |   *   *   * 1280   *   *   *   *   * |  1   0   0   1  0  0
x3o . . x4/3x ♦   24 |   24   12  12 |    8   12   12    0   3 |    0    4    4    0    3    0   0 |   *   *   *    * 960   *   *   *   * |  0   0   1   1  0  0
x . o3o3x   . ♦    8 |    4   12   0 |    0    6    0    8   0 |    0    0    0    4    0    2   0 |   *   *   *    *   * 960   *   *   * |  1   0   0   0  1  0
x . . o3x4/3x ♦   48 |   24   48  24 |    0   24   12   16  12 |    0    0    0    8    6    0   2 |   *   *   *    *   *   * 480   *   * |  0   0   0   1  1  0
. o3o3o3x   . ♦    5 |    0   10   0 |    0    0    0   10   0 |    0    0    0    0    0    5   0 |   *   *   *    *   *   *   * 384   * |  1   0   0   0  0  1
. . o3o3x4/3x ♦   64 |    0   96  32 |    0    0    0   64  24 |    0    0    0    0    0   16   8 |   *   *   *    *   *   *   *   * 120 |  0   0   0   0  1  1
--------------+------+---------------+-------------------------+-----------------------------------+--------------------------------------+---------------------
x3o3o3o3x   . ♦   30 |   60   60   0 |   60   90    0   60   0 |   30   60    0   60    0   30   0 |   6  15   0   20   0  15   0   6   0 | 64   *   *   *  *  *
x3o3o3o .   x ♦   10 |   20    0   5 |   20    0   10    0   0 |   10    0   10    0    0    0   0 |   2   0   5    0   0   0   0   0   0 |  * 192   *   *  *  *
x3o3o . x4/3x ♦   32 |   48   16  16 |   32   24   24    0   4 |    8   16   16    0    6    0   0 |   0   4   4    0   4   0   0   0   0 |  *   * 240   *  *  *
x3o . o3x4/3x ♦   72 |   72   72  36 |   24   72   36   24  18 |    0   24   12   24   18    0   3 |   0   0   0    8   6   0   3   0   0 |  *   *   * 160  *  *
x . o3o3x4/3x ♦  128 |   64  192  64 |    0   96   32  128  48 |    0    0    0   64   24   32  16 |   0   0   0    0   0  16   8   0   2 |  *   *   *   * 60  *
. o3o3o3x4/3x ♦  160 |    0  320  80 |    0    0    0  320  80 |    0    0    0    0    0  160  40 |   0   0   0    0   0   0   0  32  10 |  *   *   *   *  * 12