x4x o4w o4w x4x
               
o4w         o4w
               
x4x o4w o4w x4x

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

ooo3xox4xwx&#xt   → both heights = 1/sqrt(2) = 0.707107
(tic || pseudo w-cube || tic)

o..3o..4o..     | 24 *  * |  2  1  1  0  0  0 | 1 2  2  1  0 0 0 | 1 1 2 0 0
.o.3.o.4.o.     |  * 8  * ♦  0  0  3  3  0  0 | 0 0  3  3  3 0 0 | 0 1 3 1 0
..o3..o4..o     |  * * 24 |  0  0  0  1  2  1 | 0 0  0  1  2 1 2 | 0 0 2 1 1
----------------+---------+-------------------+------------------+----------
... x.. ...     |  2 0  0 | 24  *  *  *  *  * | 1 1  1  0  0 0 0 | 1 1 1 0 0
... ... x..     |  2 0  0 |  * 12  *  *  *  * | 0 2  0  1  0 0 0 | 1 0 2 0 0
oo.3oo.4oo.&#x  |  1 1  0 |  *  * 24  *  *  * | 0 0  2  1  0 0 0 | 0 1 2 0 0
.oo3.oo4.oo&#x  |  0 1  1 |  *  *  * 24  *  * | 0 0  0  1  2 0 0 | 0 0 2 1 0
... ..x ...     |  0 0  2 |  *  *  *  * 24  * | 0 0  0  0  1 1 1 | 0 0 1 1 1
... ... ..x     |  0 0  2 |  *  *  *  *  * 12 | 0 0  0  1  0 0 2 | 0 0 2 0 1
----------------+---------+-------------------+------------------+----------
o..3x.. ...     |  3 0  0 |  3  0  0  0  0  0 | 8 *  *  *  * * * | 1 1 0 0 0
... x..4x..     |  8 0  0 |  4  4  0  0  0  0 | * 6  *  *  * * * | 1 0 1 0 0
... xo. ...&#x  |  2 1  0 |  1  0  2  0  0  0 | * * 24  *  * * * | 0 1 1 0 0
... ... xwx&#xt |  2 2  2 |  0  1  2  2  0  1 | * *  * 12  * * * | 0 0 2 0 0  {(h,H,H)2}
... .ox ...&#x  |  0 1  2 |  0  0  0  2  1  0 | * *  *  * 24 * * | 0 0 1 1 0
..o3..x ...     |  0 0  3 |  0  0  0  0  3  0 | * *  *  *  * 8 * | 0 0 0 1 1
... ..x4..x     |  0 0  8 |  0  0  0  0  4  4 | * *  *  *  * * 6 | 0 0 1 0 1
----------------+---------+-------------------+------------------+----------
o..3x..4x..     ♦ 24 0  0 | 24 12  0  0  0  0 | 8 6  0  0  0 0 0 | 1 * * * *
oo.3xo. ...&#x  ♦  3 1  0 |  3  0  3  0  0  0 | 1 0  3  0  0 0 0 | * 8 * * *
... xox4xwx&#xt ♦  8 4  8 |  4  4  8  8  4  4 | 0 1  4  4  4 0 1 | * * 6 * *
.oo3.ox ...&#x  ♦  0 1  3 |  0  0  0  3  3  0 | 0 0  0  0  3 1 0 | * * * 8 *
..o3..x4..x     ♦  0 0 24 |  0  0  0  0 24 12 | 0 0  0  0  0 8 6 | * * * * 1

or
o..3o..4o..     & | 48 * |  2  1  1 |  1  2  2  1 | 1  1 2
.o.3.o.4.o.       |  * 8 ♦  0  0  6 |  0  0  6  3 | 0  2 3
------------------+------+----------+-------------+-------
... x.. ...     & |  2 0 | 48  *  * |  1  1  1  0 | 1  1 1
... ... x..     & |  2 0 |  * 24  * |  0  2  0  1 | 1  0 2
oo.3oo.4oo.&#x  & |  1 1 |  *  * 48 |  0  0  2  1 | 0  1 2
------------------+------+----------+-------------+-------
o..3x.. ...     & |  3 0 |  3  0  0 | 16  *  *  * | 1  1 0
... x..4x..     & |  8 0 |  4  4  0 |  * 12  *  * | 1  0 1
... xo. ...&#x  & |  2 1 |  1  0  2 |  *  * 48  * | 0  1 1
... ... xwx&#xt   |  4 2 |  0  2  4 |  *  *  * 12 | 0  0 2  {(h,H,H)2}
------------------+------+----------+-------------+-------
o..3x..4x..     & ♦ 24 0 | 24 12  0 |  8  6  0  0 | 2  * *
oo.3xo. ...&#x  & ♦  3 1 |  3  0  3 |  1  0  3  0 | * 16 *
... xox4xwx&#xt   ♦ 16 4 |  8  8 16 |  0  1  8  4 | *  * 6

oo3xo4xw qo&#zx   → height = 0
(tegum sum of (x,x,q)-ticcup and w-cube)

o.3o.4o. o.     | 48 * |  2  1  1 |  1  2  2  1 | 1  1 2
.o3.o4.o .o     |  * 8 ♦  0  0  6 |  0  0  6  3 | 0  2 3
----------------+------+----------+-------------+-------
.. x. .. ..     |  2 0 | 48  *  * |  1  1  1  0 | 1  1 1
.. .. x. ..     |  2 0 |  * 24  * |  0  2  0  1 | 1  0 2
oo3oo4oo oo&#x  |  1 1 |  *  * 48 |  0  0  2  1 | 0  1 2
----------------+------+----------+-------------+-------
o.3x. .. ..     |  3 0 |  3  0  0 | 16  *  *  * | 1  1 0
.. x.4x. ..     |  8 0 |  4  4  0 |  * 12  *  * | 1  0 1
.. xo .. ..&#x  |  2 1 |  1  0  2 |  *  * 48  * | 0  1 1
.. .. xw qo&#zx |  4 2 |  0  2  4 |  *  *  * 12 | 0  0 2  {(h,H,H)2}
----------------+------+----------+-------------+-------
o.3x.4x. ..     ♦ 24 0 | 24 12  0 |  8  6  0  0 | 2  * *
oo3xo .. ..&#x  ♦  3 1 |  3  0  3 |  1  0  3  0 | * 16 *
.. xo4xw qo&#zx ♦ 16 4 |  8  8 16 |  0  1  8  4 | *  * 6