Acronym	...
Name	partially contracted hexagonal tiling, rhombic uBxx3uxBx3xooA3*a&#zx
Vertex figure	[63], [62,R], [3,6,r,6]
Confer	uniform relative: trat   that   hexat   related CRF tilings: uBxx3uxBx3xooA3*a&#zx   related rhomb tiling: rhombic uBxx3xoAo3xooA3*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 rhombic uBxx3xoAo3xooA3*a&#zx and this tiling towards a pure hexat (A = 3x, B = 4x).

Incidence matrix according to Dynkin symbol

(rhombic)
uBxx3uxBx3xooA3*a&#zx   (N → ∞, A = 3x, B = 4x)

o...3o...3o...3*a     | 6N  *  *  * |  1  1  1  0  0  0  0 |  1  1  1 0 0 0  [62,R]
.o..3.o..3.o..3*a     |  * 3N  *  * |  2  0  0  2  0  0  0 |  1  2  0 1 0 0  [3,6,r,6]
..o.3..o.3..o.3*a     |  *  * 3N  * |  0  2  0  0  2  0  0 |  1  0  2 0 1 0  [3,6,r,6]
...o3...o3...o3*a     |  *  *  * 6N |  0  0  1  0  0  1  1 |  0  1  1 0 0 1  [63]
----------------------+-------------+----------------------+---------------
oo..3oo..3oo..3*a     |  1  1  0  0 | 6N  *  *  *  *  *  * |  1  1  0 0 0 0
o.o.3o.o.3o.o.3*a     |  1  0  1  0 |  * 6N  *  *  *  *  * |  1  0  1 0 0 0
o..o3o..o3o..o3*a     |  1  0  0  1 |  *  * 6N  *  *  *  * |  0  1  1 0 0 0
.... .x.. ....        |  0  2  0  0 |  *  *  * 3N  *  *  * |  0  1  0 1 0 0
..x. .... ....        |  0  0  2  0 |  *  *  *  * 3N  *  * |  0  0  1 0 1 0
...x .... ....        |  0  0  0  2 |  *  *  *  *  * 3N  * |  0  0  1 0 0 1
.... ...x ....        |  0  0  0  2 |  *  *  *  *  *  * 3N |  0  1  0 0 0 1
----------------------+-------------+----------------------+---------------
.... .... xoo.   &#xt |  2  1  1  0 |  2  2  0  0  0  0  0 | 3N  *  * * * *
.... ux.x ....   &#xt |  2  2  0  2 |  2  0  2  1  0  0  1 |  * 3N  * * * *
u.xx .... ....   &#xt |  2  0  2  2 |  0  2  2  0  1  1  0 |  *  * 3N * * *
.... .x..3.o..        |  0  3  0  0 |  0  0  0  3  0  0  0 |  *  *  * N * *
..x. .... ..o.3*a     |  0  0  3  0 |  0  0  0  0  3  0  0 |  *  *  * * N *
...x3...x ....        |  0  0  0  6 |  0  0  0  0  0  3  3 |  *  *  * * * N

or
o...3o...3o...3*a       | 6N  *  * |   2  1  0  0 |  1  2  0 0  [62,R]
.o..3.o..3.o..3*a     & |  * 6N  * |   2  0  2  0 |  1  2  1 0  [3,6,r,6]
...o3...o3...o3*a       |  *  * 6N |   0  1  0  2 |  0  2  0 1  [63]
------------------------+----------+--------------+-----------
oo..3oo..3oo..3*a     & |  1  1  0 | 12N  *  *  * |  1  1  0 0
o..o3o..o3o..o3*a       |  1  0  1 |   * 6N  *  * |  0  2  0 0
.... .x.. ....        & |  0  2  0 |   *  * 6N  * |  0  1  1 0
...x .... ....        & |  0  0  2 |   *  *  * 6N |  0  1  0 1
------------------------+----------+--------------+-----------
.... .... xoo.   &#xt   |  2  2  0 |   4  0  0  0 | 3N  *  * *
u.xx .... ....   &#xt   |  2  2  2 |   2  2  1  1 |  * 6N  * *
.... .x..3.o..        & |  0  3  0 |   0  0  3  0 |  *  * 2N *
...x3...x ....          |  0  0  6 |   0  0  0  6 |  *  *  * N