The non-regular hexagons {(h,H,H)²} are diagonally elongated squares. Their vertex angles are h = 90° resp. H = 135°. The rhombs {(r,R)²} are just a coplanar pair of regular triangles. Their vertex angles are r = 60° resp. R = 120°.

Note that the layer-wise x distances, used below in the descriptions, all qualify as false edges. Rather those are just the RR diagonals of the rhombs. – Those would become real ones only within its decomposition into squippy + pexco + squippy.

Incidence matrix according to Dynkin symbol

Awx ooq4oxo&#zx   → height = 0, A = 1+2 sqrt(2) = 3.828427
(tegum sum of A-line, (w,x,x)-cube, and gyro (x,q,q)-cube)

o.. o..4o..     | 2 * * | 4  0 0 | 4 0  [r4]
.o. .o.4.o.     | * 8 * | 1  2 0 | 2 1  [R,R,h]
..o ..o4..o     | * * 8 | 0  2 1 | 1 2  [r,H,H]
----------------+-------+--------+----
oo. oo.4oo.&#x  | 1 1 0 | 8  * * | 2 0
.oo .oo4.oo&#x  | 0 1 1 | * 16 * | 1 1
..x ... ...     | 0 0 2 | *  * 4 | 0 2
----------------+-------+--------+----
... ... oxo&#xt | 1 2 1 | 2  2 0 | 8 *  {(r,R)2}
.wx .oq ...&#zx | 0 2 4 | 0  4 2 | * 4  {(h,H,H)2}

ooqqoo4oxooxo&#xt   → height(1,2) = height(2,3) = height(4,5) = height(5,6) = 1/sqrt(2) = 0.707107
                      height(3,4) = 1
(pt || pseudo {4} || pseudo dual q-{4} || pseudo dual q-{4} || pseudo {4} || pt)

o.....4o.....     | 1 * * * * * | 4 0 0 0 0 | 4 0 0  [r4]
.o....4.o....     | * 4 * * * * | 1 2 0 0 0 | 2 1 0  [R,R,h]
..o...4..o...     | * * 4 * * * | 0 2 1 0 0 | 1 2 1  [r,H,H]
...o..4...o..     | * * * 4 * * | 0 0 1 2 0 | 1 2 1  [r,H,H]
....o.4....o.     | * * * * 4 * | 0 0 0 2 1 | 0 1 2  [R,R,h]
.....o4.....o     | * * * * * 1 | 0 0 0 0 4 | 0 0 4  [r4]
------------------+-------------+-----------+------
oo....4oo....&#x  | 1 1 0 0 0 0 | 4 * * * * | 2 0 0
.oo...4.oo...&#x  | 0 1 1 0 0 0 | * 8 * * * | 1 1 0
..oo..4..oo..&#x  | 0 0 1 1 0 0 | * * 4 * * | 0 2 0
...oo.4...oo.&#x  | 0 0 0 1 1 0 | * * * 8 * | 0 1 1
....oo4....oo&#x  | 0 0 0 0 1 1 | * * * * 4 | 0 0 2
------------------+-------------+-----------+------
...... oxo...&#xt | 1 2 1 0 0 0 | 2 2 0 0 0 | 4 * *  {(r,R)2}
.oqqo. ......&#xt | 0 1 2 2 1 0 | 0 2 2 2 0 | * 4 *  {(h,H,H)2}
...... ...oxo&#xt | 0 0 0 1 2 1 | 0 0 0 2 2 | * * 4  {(r,R)2}