As abstract polytope tocto is isomorphic to queto, thereby replacing the octagons by octagrams, resp. tic by quith, resp. tat by quitit, resp. tan by quittin, resp. tox by quotox, resp. tasa by quitasa.

Incidence matrix according to Dynkin symbol

o3o3o3o3o3o3x4x

. . . . . . . . | 2048 |    7    1 |    21    7 |    35   21 |    35   35 |   21  35 |    7  21 |   1  7
----------------+------+-----------+------------+------------+------------+----------+----------+-------
. . . . . . x . |    2 | 7168    * |     6    1 |    15    6 |    20   15 |   15  20 |    6  15 |   1  6
. . . . . . . x |    2 |    * 1024 ♦     0    7 |     0   21 |     0   35 |    0  35 |    0  21 |   0  7
----------------+------+-----------+------------+------------+------------+----------+----------+-------
. . . . . o3x . |    3 |    3    0 | 14336    * |     5    1 |    10    5 |   10  10 |    5  10 |   1  5
. . . . . . x4x |    8 |    4    4 |     * 1792 ♦     0    6 |     0   15 |    0  20 |    0  15 |   0  6
----------------+------+-----------+------------+------------+------------+----------+----------+-------
. . . . o3o3x . ♦    4 |    6    0 |     4    0 | 17920    * |     4    1 |    6   4 |    4   6 |   1  4
. . . . . o3x4x ♦   24 |   24   12 |     8    6 |     * 1792 ♦     0    5 |    0  10 |    0  10 |   0  5
----------------+------+-----------+------------+------------+------------+----------+----------+-------
. . . o3o3o3x . ♦    5 |   10    0 |    10    0 |     5    0 | 14336    * |    3   1 |    3   3 |   1  3
. . . . o3o3x4x ♦   64 |   96   32 |    64   24 |    16    8 |     * 1120 ♦    0   4 |    0   6 |   0  4
----------------+------+-----------+------------+------------+------------+----------+----------+-------
. . o3o3o3o3x . ♦    6 |   15    0 |    20    0 |    15    0 |     6    0 | 7168   * |    2   1 |   1  2
. . . o3o3o3x4x ♦  160 |  320   80 |   320   80 |   160   40 |    32   10 |    * 448 |    0   3 |   0  3
----------------+------+-----------+------------+------------+------------+----------+----------+-------
. o3o3o3o3o3x . ♦    7 |   21    0 |    35    0 |    35    0 |    21    0 |    7   0 | 2048   * |   1  1
. . o3o3o3o3x4x ♦  384 |  960  192 |  1280  240 |   960  160 |   384   60 |   64  12 |    * 112 |   0  2
----------------+------+-----------+------------+------------+------------+----------+----------+-------
o3o3o3o3o3o3x . ♦    8 |   28    0 |    56    0 |    70    0 |    56    0 |   28   0 |    8   0 | 256  *
. o3o3o3o3o3x4x ♦  896 | 2688  448 |  4480  672 |  4480  560 |  2688  280 |  896  84 |  128  14 |   * 16