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