Acronym ... Name tri-hexagonal rhombic tiling Vertex figure [r6], [R3] Dual that Confer uniform relative: trat   hexat   related rhomb tiling: rhomb-uBxx3xoAo3xooA3*a&#zx   rhomb-uBxx3uxBx3xooA3*a&#zx   general polytopal classes: partial Stott expansions Externallinks

The rhombs can easily decomposed into pairs of regular triangles (therefore r=60°, R=120°). Then this tiling becomes just trat. – It also can be seen as the dual of that.

This tiling further could be considered as a vertex overlay of hexat plus 3 shifted copies of trats with edge size 3. Then this decomposition allows for a further 3-step partial Stott expansion running through rhomb-uBxx3xoAo3xooA3*a&#zx and rhomb-uBxx3uxBx3xooA3*a&#zx towards a pure hexat (A = 3x, B = 4x).

Incidence matrix according to Dynkin symbol

```(rhombic)
xAoo3xoAo3xooA3*a&#zx   (N → ∞, A = 3x)

o...3o...3o...3*a     | 6N * * * |  1  1  1 |  1  1  1  [R3]
.o..3.o..3.o..3*a     |  * N * * |  6  0  0 |  0  3  3  [r6]
..o.3..o.3..o.3*a     |  * * N * |  0  6  0 |  3  0  3  [r6]
...o3...o3...o3*a     |  * * * N |  0  0  6 |  3  3  0  [r6]
----------------------+----------+----------+---------
oo..3oo..3oo..3*a&#x  |  1 1 0 0 | 6N  *  * |  0  1  1
o.o.3o.o.3o.o.3*a&#x  |  1 0 1 0 |  * 6N  * |  1  0  1
o..o3o..o3o..o3*a&#x  |  1 0 0 1 |  *  * 6N |  1  1  0
----------------------+----------+----------+---------
x.oo .... ....   &#xt |  2 0 1 1 |  0  2  2 | 3N  *  *
.... xo.o ....   &#xt |  2 1 0 1 |  2  0  2 |  * 3N  *
.... .... xoo.   &#xt |  2 1 1 0 |  2  2  0 |  *  * 3N
```
```or
o...3o...3o...3*a       | 2N * |  3 |  3  [R3]
.o..3.o..3.o..3*a     & |  * N |  6 |  6  [r6]
------------------------+------+----+---
oo..3oo..3oo..3*a&#x  & |  1 1 | 6N |  2
------------------------+------+----+---
x.oo .... ....   &#xt & |  2 2 |  4 | 3N
```