Acronym ...
Name uBxx3xoAo3xooA3*a&#zx
 
Vertex figure [36], [34,6], [(3,6)2]
Confer
uniform relative:
trat   that   hexat  
related CRF tilings:
uBxx3uxBx3xooA3*a&#zx  
related rhomb tiling:
rhombic uBxx3xoAo3xooA3*a&#zx  

Trat could be considered as a vertex overlay of hexat plus 3 shifted copies of trats with edge size 3 (see there). This decomposition allows for a 3-step transformation running then through this tiling and uBxx3uxBx3xooA3*a&#zx towards a pure hexat (A = 3x, B = 4x). – So this transformation sequence is not a true partial Stott expansion one because pairs of triangles become transformed into single hexagons. But this could be recovered by combining these pairs into rhombs. The corresponding sequence member here then would be rhomb-uBxx3xoAo3xooA3*a&#zx.


Incidence matrix according to Dynkin symbol

uBxx3xoAo3xooA3*a&#zx   (N → ∞, A = 3x, B = 4x)

o...3o...3o...3*a     | 6N *  *  * |  1  1  1  1  1  0  0 |  1  1  1  1  1 0 0  [34,6]
.o..3.o..3.o..3*a     |  * N  *  * |  0  0  6  0  0  0  0 |  3  3  0  0  0 0 0  [36]
..o.3..o.3..o.3*a     |  * * 3N  * |  0  0  0  2  0  2  0 |  0  0  1  0  2 1 0  [(3,6)2]
...o3...o3...o3*a     |  * *  * 3N |  0  0  0  0  2  0  2 |  0  0  0  1  2 0 1  [(3,6)2]
----------------------+------------+----------------------+-------------------
.... x... ....        |  2 0  0  0 | 3N  *  *  *  *  *  * |  1  0  0  1  0 0 0
.... .... x...        |  2 0  0  0 |  * 3N  *  *  *  *  * |  0  1  1  0  0 0 0
oo..3oo..3oo..3*a     |  1 1  0  0 |  *  * 6N  *  *  *  * |  1  1  0  0  0 0 0
o.o.3o.o.3o.o.3*a     |  1 0  1  0 |  *  *  * 6N  *  *  * |  0  0  1  0  1 0 0
o..o3o..o3o..o3*a     |  1 0  0  1 |  *  *  *  * 6N  *  * |  0  0  0  1  1 0 0
..x. .... ....        |  0 0  2  0 |  *  *  *  *  * 3N  * |  0  0  0  0  1 1 0
...x .... ....        |  0 0  0  2 |  *  *  *  *  *  * 3N |  0  0  0  0  1 0 1
----------------------+------------+----------------------+-------------------
.... xo.. ....   &#x  |  2 1  0  0 |  1  0  2  0  0  0  0 | 3N  *  *  *  * * *
.... .... xo..   &#x  |  2 1  0  0 |  0  1  2  0  0  0  0 |  * 3N  *  *  * * *
.... .... x.o.   &#x  |  2 0  1  0 |  0  1  0  2  0  0  0 |  *  * 3N  *  * * *
.... x..o ....   &#x  |  2 0  0  1 |  1  0  0  0  2  0  0 |  *  *  * 3N  * * *
u.xx .... ....   &#xt |  2 0  2  2 |  0  0  0  2  2  1  1 |  *  *  *  * 3N * *
..x. .... ..o.3*a     |  0 0  3  0 |  0  0  0  0  0  3  0 |  *  *  *  *  * N *
...x3...o ....        |  0 0  0  3 |  0  0  0  0  0  0  3 |  *  *  *  *  * * N
or
o...3o...3o...3*a       | 6N *  * |  2  1   2  0 |  2  2  1  0  [34,6]
.o..3.o..3.o..3*a       |  * N  * |  0  6   0  0 |  6  0  0  0  [36]
..o.3..o.3..o.3*a     & |  * * 6N |  0  0   2  2 |  0  1  2  1  [(3,6)2]
------------------------+---------+--------------+------------
.... x... ....        & |  2 0  0 | 6N  *   *  * |  1  1  0  0
oo..3oo..3oo..3*a       |  1 1  0 |  * 6N   *  * |  2  0  0  0
o.o.3o.o.3o.o.3*a     & |  1 0  1 |  *  * 12N  * |  0  1  1  0
..x. .... ....        & |  0 0  2 |  *  *   * 6N |  0  0  1  1
------------------------+---------+--------------+------------
.... xo.. ....   &#x  & |  2 1  0 |  1  2   0  0 | 6N  *  *  *
.... .... x.o.   &#x  & |  2 0  1 |  1  0   2  0 |  * 6N  *  *
u.xx .... ....   &#xt   |  2 0  4 |  0  0   4  2 |  *  * 3N  *
..x. .... ..o.3*a     & |  0 0  3 |  0  0   0  3 |  *  *  * 2N

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