x4x w4o   w4o x4x    
                         
x4x x4u w4x   w4x x4u x4x
                         
w4o w4x           w4x w4o
                         
x4x x4u w4x   w4x x4u x4x
                         
    x4x w4o   w4o 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

oxxxo3xxoxx4xxwxx&#xt   → all heights = 1/sqrt(2) = 0.707107
(tic || pseudo girco || pseudo (x,w)-sirco || pseudo girco || tic)

o....3o....4o....     & | 48  *  * |  2  1  2  0  0  0  0  0 |  1  2  1  2  2  0  0  0  0  0 0 | 1  1  1  2  0 0
.o...3.o...4.o...     & |  * 96  * |  0  0  1  1  1  1  1  0 |  0  0  1  1  1  1  1  1  1  1 0 | 0  1  1  1  1 1
..o..3..o..4..o..       |  *  * 24 |  0  0  0  0  0  0  4  2 |  0  0  0  0  0  0  0  4  2  2 1 | 0  2  0  0  2 1
------------------------+----------+-------------------------+---------------------------------+----------------
..... x.... .....     & |  2  0  0 | 48  *  *  *  *  *  *  * |  1  1  0  1  0  0  0  0  0  0 0 | 1  1  0  1  0 0
..... ..... x....     & |  2  0  0 |  * 24  *  *  *  *  *  * |  0  2  0  0  2  0  0  0  0  0 0 | 1  0  1  2  0 0
oo...3oo...4oo...&#x  & |  1  1  0 |  *  * 96  *  *  *  *  * |  0  0  1  1  1  0  0  0  0  0 0 | 0  1  1  1  0 0
.x... ..... .....     & |  0  2  0 |  *  *  * 48  *  *  *  * |  0  0  1  0  0  1  0  1  0  0 0 | 0  1  1  0  1 0
..... .x... .....     & |  0  2  0 |  *  *  *  * 48  *  *  * |  0  0  0  1  0  0  1  0  1  0 0 | 0  1  0  1  0 1
..... ..... .x...     & |  0  2  0 |  *  *  *  *  * 48  *  * |  0  0  0  0  1  1  1  0  0  1 0 | 0  0  1  1  1 1
.oo..3.oo..4.oo..&#x  & |  0  1  1 |  *  *  *  *  *  * 96  * |  0  0  0  0  0  0  0  1  1  1 0 | 0  1  0  0  1 1
..x.. ..... .....       |  0  0  2 |  *  *  *  *  *  *  * 24 |  0  0  0  0  0  0  0  2  0  0 1 | 0  2  0  0  1 0
------------------------+----------+-------------------------+---------------------------------+----------------
o....3x.... .....     & |  3  0  0 |  3  0  0  0  0  0  0  0 | 16  *  *  *  *  *  *  *  *  * * | 1  1  0  0  0 0
..... x....4x....     & |  8  0  0 |  4  4  0  0  0  0  0  0 |  * 12  *  *  *  *  *  *  *  * * | 1  0  0  1  0 0
ox... ..... .....&#x  & |  1  2  0 |  0  0  2  1  0  0  0  0 |  *  * 48  *  *  *  *  *  *  * * | 0  1  1  0  0 0
..... xx... .....&#x  & |  2  2  0 |  1  0  2  0  1  0  0  0 |  *  *  * 48  *  *  *  *  *  * * | 0  1  0  1  0 0
..... ..... xx...&#x  & |  2  2  0 |  0  1  2  0  0  1  0  0 |  *  *  *  * 48  *  *  *  *  * * | 0  0  1  1  0 0
.x... ..... .x...     & |  0  4  0 |  0  0  0  2  0  2  0  0 |  *  *  *  *  * 24  *  *  *  * * | 0  0  1  0  1 0
..... .x...4.x...     & |  0  8  0 |  0  0  0  0  4  4  0  0 |  *  *  *  *  *  * 12  *  *  * * | 0  0  0  1  0 1
.xx.. ..... .....&#x  & |  0  2  2 |  0  0  0  1  0  0  2  1 |  *  *  *  *  *  *  * 48  *  * * | 0  1  0  0  1 0
..... .xo.. .....&#x  & |  0  2  1 |  0  0  0  0  1  0  2  0 |  *  *  *  *  *  *  *  * 48  * * | 0  1  0  0  0 1
..... ..... .xwx.&#xt   |  0  4  2 |  0  0  0  0  0  2  4  0 |  *  *  *  *  *  *  *  *  * 24 * | 0  0  0  0  1 1  {(h,H,H)2}
..x..3..o.. .....       |  0  0  3 |  0  0  0  0  0  0  0  3 |  *  *  *  *  *  *  *  *  *  * 8 | 0  2  0  0  0 0
------------------------+----------+-------------------------+---------------------------------+----------------
o....3x....4x....     & ♦ 24  0  0 | 24 12  0  0  0  0  0  0 |  8  6  0  0  0  0  0  0  0  0 0 | 2  *  *  *  * *
oxx..3xxo.. .....&#xt & ♦  3  6  3 |  3  0  6  3  3  0  6  3 |  1  0  3  3  0  0  0  3  3  0 1 | * 16  *  *  * *
ox... ..... xx...&#x  & ♦  2  4  0 |  0  1  4  2  0  2  0  0 |  0  0  2  0  2  1  0  0  0  0 0 | *  * 24  *  * *
..... xx...4xx...&#x  & ♦  8  8  0 |  4  4  8  0  4  4  0  0 |  0  1  0  4  4  0  1  0  0  0 0 | *  *  * 12  * *
.xxx. ..... .xwx.&#xt   ♦  0  8  4 |  0  0  0  4  0  4  8  2 |  0  0  0  0  0  2  0  4  0  2 0 | *  *  *  * 12 *
..... .xox.4.xwx.&#xt   ♦  0 16  4 |  0  0  0  0  8  8 16  0 |  0  0  0  0  0  0  2  0  8  4 0 | *  *  *  *  * 6

oxx3xxo4xxw Qqo&#zxt   → height = 0, Q=2q = 2.828427
(tegum sum of (x,x,Q)-ticcup, (x,x,x,q)-gircope, and (x,w)-sirco)

o..3o..4o.. o..     | 48  *  * |  2  1  2  0  0  0  0  0 |  1  2  1  2  2  0  0  0  0  0 0 | 1  1  1  2  0 0
.o.3.o.4.o. .o.     |  * 96  * |  0  0  1  1  1  1  1  0 |  0  0  1  1  1  1  1  1  1  1 0 | 0  1  1  1  1 1
..o3..o4..o ..o     |  *  * 24 |  0  0  0  0  0  0  4  2 |  0  0  0  0  0  0  0  4  2  2 1 | 0  2  0  0  2 1
--------------------+----------+-------------------------+---------------------------------+----------------
... x.. ... ...     |  2  0  0 | 48  *  *  *  *  *  *  * |  1  1  0  1  0  0  0  0  0  0 0 | 1  1  0  1  0 0
... ... x.. ...     |  2  0  0 |  * 24  *  *  *  *  *  * |  0  2  0  0  2  0  0  0  0  0 0 | 1  0  1  2  0 0
oo.3oo.4oo. oo.&#x  |  1  1  0 |  *  * 96  *  *  *  *  * |  0  0  1  1  1  0  0  0  0  0 0 | 0  1  1  1  0 0
.x. ... ... ...     |  0  2  0 |  *  *  * 48  *  *  *  * |  0  0  1  0  0  1  0  1  0  0 0 | 0  1  1  0  1 0
... .x. ... ...     |  0  2  0 |  *  *  *  * 48  *  *  * |  0  0  0  1  0  0  1  0  1  0 0 | 0  1  0  1  0 1
... ... .x. ...     |  0  2  0 |  *  *  *  *  * 48  *  * |  0  0  0  0  1  1  1  0  0  1 0 | 0  0  1  1  1 1
.oo3.oo4.oo .oo&#x  |  0  1  1 |  *  *  *  *  *  * 96  * |  0  0  0  0  0  0  0  1  1  1 0 | 0  1  0  0  1 1
..x ... ... ...     |  0  0  2 |  *  *  *  *  *  *  * 24 |  0  0  0  0  0  0  0  2  0  0 1 | 0  2  0  0  1 0
--------------------+----------+-------------------------+---------------------------------+----------------
o..3x.. ... ...     |  3  0  0 |  3  0  0  0  0  0  0  0 | 16  *  *  *  *  *  *  *  *  * * | 1  1  0  0  0 0
... x..4x.. ...     |  8  0  0 |  4  4  0  0  0  0  0  0 |  * 12  *  *  *  *  *  *  *  * * | 1  0  0  1  0 0
ox. ... ... ...&#x  |  1  2  0 |  0  0  2  1  0  0  0  0 |  *  * 48  *  *  *  *  *  *  * * | 0  1  1  0  0 0
... xx. ... ...&#x  |  2  2  0 |  1  0  2  0  1  0  0  0 |  *  *  * 48  *  *  *  *  *  * * | 0  1  0  1  0 0
... ... xx. ...&#x  |  2  2  0 |  0  1  2  0  0  1  0  0 |  *  *  *  * 48  *  *  *  *  * * | 0  0  1  1  0 0
.x. ... .x. ...     |  0  4  0 |  0  0  0  2  0  2  0  0 |  *  *  *  *  * 24  *  *  *  * * | 0  0  1  0  1 0
... .x.4.x. ...     |  0  8  0 |  0  0  0  0  4  4  0  0 |  *  *  *  *  *  * 12  *  *  * * | 0  0  0  1  0 1
.xx ... ... ...&#x  |  0  2  2 |  0  0  0  1  0  0  2  1 |  *  *  *  *  *  *  * 48  *  * * | 0  1  0  0  1 0
... .xo ... ...&#x  |  0  2  1 |  0  0  0  0  1  0  2  0 |  *  *  *  *  *  *  *  * 48  * * | 0  1  0  0  0 1
... ... .xw .qo&#zx |  0  4  2 |  0  0  0  0  0  2  4  0 |  *  *  *  *  *  *  *  *  * 24 * | 0  0  0  0  1 1  {(h,H,H)2}
..x3..o ... ...     |  0  0  3 |  0  0  0  0  0  0  0  3 |  *  *  *  *  *  *  *  *  *  * 8 | 0  2  0  0  0 0
--------------------+----------+-------------------------+---------------------------------+----------------
o..3x..4x.. ...     ♦ 24  0  0 | 24 12  0  0  0  0  0  0 |  8  6  0  0  0  0  0  0  0  0 0 | 2  *  *  *  * *
oxx3xxo ... ...&#xt ♦  3  6  3 |  3  0  6  3  3  0  6  3 |  1  0  3  3  0  0  0  3  3  0 1 | * 16  *  *  * *
ox. ... xx. ...&#x  ♦  2  4  0 |  0  1  4  2  0  2  0  0 |  0  0  2  0  2  1  0  0  0  0 0 | *  * 24  *  * *
... xx.4xx. ...&#x  ♦  8  8  0 |  4  4  8  0  4  4  0  0 |  0  1  0  4  4  0  1  0  0  0 0 | *  *  * 12  * *
.xx ... .xw .qo&#zx ♦  0  8  4 |  0  0  0  4  0  4  8  2 |  0  0  0  0  0  2  0  4  0  2 0 | *  *  *  * 12 *
... .xo4.xw .qo&#zx ♦  0 16  4 |  0  0  0  0  8  8 16  0 |  0  0  0  0  0  0  2  0  8  4 0 | *  *  *  *  * 6