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

qo xw4xo&#zx   → height = 0
(tegum sum of (q,x,x)-op and w-{4})

o. o.4o.     | 16 * | 1 1  1 | 1 1 1  [3,8,H]
.o .o4.o     |  * 4 | 0 0  4 | 0 2 2  [(3,h)2]
-------------+------+--------+------
.. x. ..     |  2 0 | 8 *  * | 1 1 0
.. .. x.     |  2 0 | * 8  * | 1 0 1
oo oo4oo&#x  |  1 1 | * * 16 | 0 1 1
-------------+------+--------+------
.. x.4x.     |  8 0 | 4 4  0 | 2 * *
qo xw ..&#zx |  4 2 | 2 0  4 | * 4 *  {(h,H,H)2}
.. .. xo&#x  |  2 1 | 0 1  2 | * * 8

wxw wwx oqq&#zx   → height = 0

o.. o.. o..       | 4  * |  4 0 0 | 2 2 0  [(3,h)2]
.o. .o. .o      & | * 16 |  1 1 1 | 1 1 1  [3,8,H]
------------------+------+--------+------
oo. oo. oo.&#x  & | 1  1 | 16 * * | 1 1 0
.x. ... ...     & | 0  2 |  * 8 * | 1 0 1
.oo .oo .oo&#x    | 0  2 |  * * 8 | 0 1 1
------------------+------+--------+------
wz. ... oq.&#zx & | 2  4 |  4 2 0 | 4 * *  {(h,H,H)2}
ooo ooo ooo&#x    | 1  2 |  2 0 1 | * 8 *
.wx .xw ...&#zx   | 0  8 |  0 4 4 | * * 2  {8}

xox4xwx&#xt   → both heights = 1/sqrt(2) = 0.707107
({8} || pseudo w-{4} || {8})

o..4o..     | 8 * * | 1 1 1 0 0 0 | 1 1 1 0 0  [3,8,H]
.o.4.o.     | * 4 * | 0 0 2 2 0 0 | 0 1 2 1 0  [(3,h)2]
..o4..o     | * * 8 | 0 0 0 1 1 1 | 0 0 1 1 1  [3,8,H]
------------+-------+-------------+----------
x.. ...     | 2 0 0 | 4 * * * * * | 1 1 0 0 0
... x..     | 2 0 0 | * 4 * * * * | 1 0 1 0 0
oo.4oo.&#x  | 1 1 0 | * * 8 * * * | 0 1 1 0 0
.oo4.oo&#x  | 0 1 1 | * * * 8 * * | 0 0 1 1 0
..x ...     | 0 0 2 | * * * * 4 * | 0 0 0 1 1
... ..x     | 0 0 2 | * * * * * 4 | 0 0 1 0 1
------------+-------+-------------+----------
x..4x..     | 8 0 0 | 4 4 0 0 0 0 | 1 * * * *
xo. ...&#x  | 2 1 0 | 1 0 2 0 0 0 | * 4 * * *
... xwx&#xt | 2 2 2 | 0 1 2 2 0 1 | * * 4 * *  {(h,H,H)2}
.ox ...&#x  | 0 1 2 | 0 0 0 2 1 0 | * * * 4 *
..x4..x     | 0 0 8 | 0 0 0 0 4 4 | * * * * 1