Acronym	...
Name	partially expanded tri-hexagonal rhombic tiling, rhombic uBxx3xoAo3xooA3*a&#zx
Vertex figure	[r6], [R2,6], [3,6,r,6]
Confer	uniform relative: trat   that   hexat   related CRF tilings: uBxx3xoAo3xooA3*a&#zx   related rhomb tiling: rhombic uBxx3uxBx3xooA3*a&#zx   general polytopal classes: partial Stott expansions

Both, trat and the tri-hexagonal rhombic tiling (derived from the former by combining 2 triangles each) 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 partial Stott expansion of the latter running then through this tiling and rhombic uBxx3uxBx3xooA3*a&#zx towards a pure hexat (A = 3x, B = 4x).

Incidence matrix according to Dynkin symbol

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

o...3o...3o...3*a     | 6N *  *  * |  1  1  1  0  0 |  1  1  1 0 0  [R2,6]
.o..3.o..3.o..3*a     |  * N  *  * |  6  0  0  0  0 |  3  3  0 0 0  [r6]
..o.3..o.3..o.3*a     |  * * 3N  * |  0  2  0  2  0 |  0  1  2 1 0  [3,6,r,6]
...o3...o3...o3*a     |  * *  * 3N |  0  0  2  0  2 |  1  0  2 0 1  [3,6,r,6]
----------------------+------------+----------------+-------------
oo..3oo..3oo..3*a     |  1 1  0  0 | 6N  *  *  *  * |  1  1  0 0 0
o.o.3o.o.3o.o.3*a     |  1 0  1  0 |  * 6N  *  *  * |  0  1  1 0 0
o..o3o..o3o..o3*a     |  1 0  0  1 |  *  * 6N  *  * |  1  0  1 0 0
..x. .... ....        |  0 0  2  0 |  *  *  * 3N  * |  0  0  1 1 0
...x .... ....        |  0 0  0  2 |  *  *  *  * 3N |  0  0  1 0 1
----------------------+------------+----------------+-------------
.... xo.o ....   &#xt |  2 1  0  1 |  2  0  2  0  0 | 3N  *  * * *
.... .... xoo.   &#xt |  2 1  1  0 |  2  2  0  0  0 |  * 3N  * * *
u.xx .... ....   &#xt |  2 0  2  2 |  0  2  2  1  1 |  *  * 3N * *
..x. .... ..o.3*a     |  0 0  3  0 |  0  0  0  3  0 |  *  *  * N *
...x3...o ....        |  0 0  0  3 |  0  0  0  0  3 |  *  *  * * N

or
o...3o...3o...3*a       | 6N *  * |  1   2  0 |  2  1  0  [R2,6]
.o..3.o..3.o..3*a       |  * N  * |  6   0  0 |  6  0  0  [r6]
..o.3..o.3..o.3*a     & |  * * 6N |  0   2  2 |  1  2  1  [3,6,r,6]
------------------------+---------+-----------+---------
oo..3oo..3oo..3*a       |  1 1  0 | 6N   *  * |  2  0  0
o.o.3o.o.3o.o.3*a     & |  1 0  1 |  * 12N  * |  1  1  0
..x. .... ....        & |  0 0  2 |  *   * 6N |  0  1  1
------------------------+---------+-----------+---------
.... xo.o ....   &#xt & |  2 1  1 |  2   2  0 | 6N  *  *
u.xx .... ....   &#xt   |  2 0  4 |  0   4  2 |  * 3N  *
..x. .... ..o.3*a     & |  0 0  3 |  0   0  3 |  *  * 2N