As abstract polytope quititip is isomorphic to tattip, thereby replacing the octagrams by octagons, resp. quith by tic and stop by op, resp. quithip by ticcup and quitit by tat.

Incidence matrix according to Dynkin symbol

x o3o3x4/3x

. . . .   . | 128 |  1   3  1 |  3  1   3  3 |  3  3  1  3 |  1 3 1
------------+-----+-----------+--------------+-------------+-------
x . . .   . |   2 | 64   *  * |  3  1   0  0 |  3  3  0  0 |  1 3 0
. . . x   . |   2 |  * 192  * |  1  0   2  1 |  2  1  1  2 |  1 2 1
. . . .   x |   2 |  *   * 64 |  0  1   0  3 |  0  3  0  3 |  0 3 1
------------+-----+-----------+--------------+-------------+-------
x . . x   . |   4 |  2   2  0 | 96  *   *  * |  2  1  0  0 |  1 2 0
x . . .   x |   4 |  2   0  2 |  * 32   *  * |  0  3  0  0 |  0 3 0
. . o3x   . |   3 |  0   3  0 |  *  * 128  * |  1  0  1  1 |  1 1 1
. . . x4/3x |   8 |  0   4  4 |  *  *   * 48 |  0  1  0  2 |  0 2 1
------------+-----+-----------+--------------+-------------+-------
x . o3x   . ♦   6 |  3   6  0 |  3  0   2  0 | 64  *  *  * |  1 1 0
x . . x4/3x ♦  16 |  8   8  8 |  4  4   0  2 |  * 24  *  * |  0 2 0
. o3o3x   . ♦   4 |  0   6  0 |  0  0   4  0 |  *  * 32  * |  1 0 1
. . o3x4/3x ♦  24 |  0  24 12 |  0  0   8  6 |  *  *  * 16 |  0 1 1
------------+-----+-----------+--------------+-------------+-------
x o3o3x   . ♦   8 |  4  12  0 |  6  0   8  0 |  4  0  2  0 | 16 * *
x . o3x4/3x ♦  48 | 24  48 24 | 24 12  16 12 |  8  6  0  2 |  * 8 *
. o3o3x4/3x ♦  64 |  0  96 32 |  0  0  64 24 |  0  0 16  8 |  * * 2

oo3oo3xx4/3xx&#x   → height = 1
(quitit || quitit)

o.3o.3o.4/3o.    | 64  * |  3  1  1  0  0 |  3  3  3  1  0  0 |  1 3  3  3  0 0 | 1  1 3 0
.o3.o3.o4/3.o    |  * 64 |  0  0  1  3  1 |  0  0  3  1  3  3 |  0 0  3  3  1 3 | 0  1 3 1
-----------------+-------+----------------+-------------------+-----------------+---------
.. .. x.   ..    |  2  0 | 96  *  *  *  * |  2  1  1  0  0  0 |  1 2  2  1  0 0 | 1  1 2 0
.. .. ..   x.    |  2  0 |  * 32  *  *  * |  0  3  0  1  0  0 |  0 3  0  3  0 0 | 1  0 3 0
oo3oo3oo4/3oo&#x |  1  1 |  *  * 64  *  * |  0  0  3  1  0  0 |  0 0  3  3  0 0 | 0  1 3 0
.. .. .x   ..    |  0  2 |  *  *  * 96  * |  0  0  1  0  2  1 |  0 0  2  1  1 2 | 0  1 2 1
.. .. ..   .x    |  0  2 |  *  *  *  * 32 |  0  0  0  1  0  3 |  0 0  0  3  0 3 | 0  0 3 1
-----------------+-------+----------------+-------------------+-----------------+---------
.. o.3x.   ..    |  3  0 |  3  0  0  0  0 | 64  *  *  *  *  * |  1 1  1  0  0 0 | 1  1 1 0
.. .. x.4/3x.    |  8  0 |  4  4  0  0  0 |  * 24  *  *  *  * |  0 2  0  1  0 0 | 1  0 2 0
.. .. xx   ..&#x |  2  2 |  1  0  2  1  0 |  *  * 96  *  *  * |  0 0  2  1  0 0 | 0  1 2 0
.. .. ..   xx&#x |  2  2 |  0  1  2  0  1 |  *  *  * 32  *  * |  0 0  0  3  0 0 | 0  0 3 0
.. .o3.x   ..    |  0  3 |  0  0  0  3  0 |  *  *  *  * 64  * |  0 0  1  0  1 1 | 0  1 1 1
.. .. .x4/3.x    |  0  8 |  0  0  0  4  4 |  *  *  *  *  * 24 |  0 0  0  1  0 2 | 0  0 2 1
-----------------+-------+----------------+-------------------+-----------------+---------
o.3o.3x.   ..    ♦  4  0 |  6  0  0  0  0 |  4  0  0  0  0  0 | 16 *  *  *  * * | 1  1 0 0
.. o.3x.4/3x.    ♦ 24  0 | 24 12  0  0  0 |  8  6  0  0  0  0 |  * 8  *  *  * * | 1  0 1 0
.. oo3xx   ..&#x ♦  3  3 |  3  0  3  3  0 |  1  0  3  0  1  0 |  * * 64  *  * * | 0  1 1 0
.. .. xx4/3xx&#x ♦  8  8 |  4  4  8  4  4 |  0  1  4  4  0  1 |  * *  * 24  * * | 0  0 2 0
.o3.o3.x   ..    ♦  0  4 |  0  0  0  6  0 |  0  0  0  0  4  0 |  * *  *  * 16 * | 0  1 0 1
.. .o3.x4/3.x    ♦  0 24 |  0  0  0 24 12 |  0  0  0  0  8  6 |  * *  *  *  * 8 | 0  0 1 1
-----------------+-------+----------------+-------------------+-----------------+---------
o.3o.3x.4/3x.    ♦ 64  0 | 96 32  0  0  0 | 64 24  0  0  0  0 | 16 8  0  0  0 0 | 1  * * *
oo3oo3xx   ..&#x ♦  4  4 |  6  0  4  6  0 |  4  0  6  0  4  0 |  1 0  4  0  1 0 | * 16 * *
.. oo3xx4/3xx&#x ♦ 24 24 | 24 12 24 24 12 |  8  6 24 12  8  6 |  0 1  8  6  0 1 | *  * 8 *
.o3.o3.x4/3.x    ♦  0 64 |  0  0  0 96 32 |  0  0  0  0 64 24 |  0 0  0  0 16 8 | *  * * 1