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

Note that the tets, pens, hixes, hops, and ocas become retrograde here.

Incidence matrix according to Dynkin symbol

o3o3o3o3o3o3x4/3x

. . . . . . .   . | 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
. . . . . . x4/3x |    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
. . . . . o3x4/3x ♦   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
. . . . o3o3x4/3x ♦   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
. . . o3o3o3x4/3x ♦  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
. . o3o3o3o3x4/3x ♦  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  *
. o3o3o3o3o3x4/3x ♦  896 | 2688  448 |  4480  672 |  4480  560 |  2688  280 |  896  84 |  128  14 |   * 16