x4o o4q o4q x4o
               
o4q         o4q
               
x4o o4q o4q x4o

The non-regular hexagons {(h,H,H)²} are diagonally elongated squares. Its vertex angles are h = 90° resp. H = 135°.

Incidence matrix according to Dynkin symbol

oooo3xoox4oqqo&#xt   → outer heights = 1/sqrt(2) = 0.707107
                       inner height = 1
(co || pseudo q-cube || pseudo q-cube || co)

o...3o...4o...     | 12 * *  * ♦  4  2 0  0  0 | 2 2  4  1  0 0 0 | 1 2 2 0 0
.o..3.o..4.o..     |  * 8 *  * |  0  3 1  0  0 | 0 0  3  3  0 0 0 | 0 1 3 0 0
..o.3..o.4..o.     |  * * 8  * |  0  0 1  3  0 | 0 0  0  3  3 0 0 | 0 0 3 1 0
...o3...o4...o     |  * * * 12 ♦  0  0 0  2  4 | 0 0  0  1  4 2 2 | 0 0 2 2 1
-------------------+-----------+---------------+------------------+----------
.... x... ....     |  2 0 0  0 | 24  * *  *  * | 1 1  1  0  0 0 0 | 1 1 1 0 0
oo..3oo..4oo..&#x  |  1 1 0  0 |  * 24 *  *  * | 0 0  2  1  0 0 0 | 0 1 2 0 0
.oo.3.oo.4.oo.&#x  |  0 1 1  0 |  *  * 8  *  * | 0 0  0  3  0 0 0 | 0 0 3 0 0
..oo3..oo4..oo&#x  |  0 0 1  1 |  *  * * 24  * | 0 0  0  1  2 0 0 | 0 0 2 1 0
.... ...x ....     |  0 0 0  2 |  *  * *  * 24 | 0 0  0  0  1 1 1 | 0 0 1 1 1
-------------------+-----------+---------------+------------------+----------
o...3x... ....     |  3 0 0  0 |  3  0 0  0  0 | 8 *  *  *  * * * | 1 1 0 0 0
.... x...4o...     |  4 0 0  0 |  4  0 0  0  0 | * 6  *  *  * * * | 1 0 1 0 0
.... xo.. ....&#x  |  2 1 0  0 |  1  2 0  0  0 | * * 24  *  * * * | 0 1 1 0 0
.... .... oqqo&#xt |  1 2 2  1 |  0  2 2  2  0 | * *  * 12  * * * | 0 0 2 0 0  {(h,H,H)2}
.... ..ox ....&#x  |  0 0 1  2 |  0  0 0  2  1 | * *  *  * 24 * * | 0 0 1 1 0
...o3...x ....     |  0 0 0  3 |  0  0 0  0  3 | * *  *  *  * 8 * | 0 0 0 1 1
.... ...x4...o     |  0 0 0  4 |  0  0 0  0  4 | * *  *  *  * * 6 | 0 0 1 0 1
-------------------+-----------+---------------+------------------+----------
o...3x...4o...     ♦ 12 0 0  0 | 24  0 0  0  0 | 8 6  0  0  0 0 0 | 1 * * * *
oo..3xo.. ....&#x  ♦  3 1 0  0 |  3  3 0  0  0 | 1 0  3  0  0 0 0 | * 8 * * *
.... xoox4oqqo&#xt ♦  4 4 4  4 |  4  8 4  8  4 | 0 1  4  4  4 0 1 | * * 6 * *
..oo3..ox ....&#x  ♦  0 0 1  3 |  0  0 0  3  3 | 0 0  0  0  3 1 0 | * * * 8 *
...o3...x4...o     ♦  0 0 0 12 |  0  0 0  0 24 | 0 0  0  0  0 8 6 | * * * * 1

or
o...3o...4o...     & | 24  * ♦  4  2 0 |  2  2  4  1 | 1  2 2
.o..3.o..4.o..     & |  * 16 |  0  3 1 |  0  0  3  3 | 0  1 3
---------------------+-------+---------+-------------+-------
.... x... ....     & |  2  0 | 48  * * |  1  1  1  0 | 1  1 1
oo..3oo..4oo..&#x  & |  1  1 |  * 48 * |  0  0  2  1 | 0  1 2
.oo.3.oo.4.oo.&#x    |  0  2 |  *  * 8 |  0  0  0  3 | 0  0 3
---------------------+-------+---------+-------------+-------
o...3x... ....     & |  3  0 |  3  0 0 | 16  *  *  * | 1  1 0
.... x...4o...     & |  4  0 |  4  0 0 |  * 12  *  * | 1  0 1
.... xo.. ....&#x  & |  2  1 |  1  2 0 |  *  * 48  * | 0  1 1
.... .... oqqo&#xt   |  2  4 |  0  4 2 |  *  *  * 12 | 0  0 2  {(h,H,H)2}
---------------------+-------+---------+-------------+-------
o...3x...4o...     & ♦ 12  0 | 24  0 0 |  8  6  0  0 | 2  * *
oo..3xo.. ....&#x  & ♦  3  1 |  3  3 0 |  1  0  3  0 | * 16 *
.... xoox4oqqo&#xt   ♦  8  8 |  8 16 4 |  0  2  8  4 | *  * 6

oo3xo4oq wx&#zx   → height = 0
(tegum sum of (x,w)-cope and (q,x)-cube-prism (=tes))

o.3o.4o. o.     | 24  * ♦  4  2 0 |  2  2  4  1 | 1  2 2
.o3.o4.o .o     |  * 16 |  0  3 1 |  0  0  3  3 | 0  1 3
----------------+-------+---------+-------------+-------
.. x. .. ..     |  2  0 | 48  * * |  1  1  1  0 | 1  1 1
oo3oo4oo oo&#x  |  1  1 |  * 48 * |  0  0  2  1 | 0  1 2
.. .. .. .x     |  0  2 |  *  * 8 |  0  0  0  3 | 0  0 3
----------------+-------+---------+-------------+-------
o.3x. .. ..     |  3  0 |  3  0 0 | 16  *  *  * | 1  1 0
.. x.4o. ..     |  4  0 |  4  0 0 |  * 12  *  * | 1  0 1
.. xo .. ..&#x  |  2  1 |  1  2 0 |  *  * 48  * | 0  1 1
.. .. oq wx&#zx |  2  4 |  0  4 2 |  *  *  * 12 | 0  0 2  {(h,H,H)2}
----------------+-------+---------+-------------+-------
o.3x.4o. ..     ♦ 12  0 | 24  0 0 |  8  6  0  0 | 2  * *
oo3xo .. ..&#x  ♦  3  1 |  3  3 0 |  1  0  3  0 | * 16 *
.. xo4oq wx&#zx ♦  8  8 |  8 16 4 |  0  2  8  4 | *  * 6