This tiling could be obtained by a partial Stott contraction from o3o4x3*a: first color the triangles of that tiling in 4 colors, say yellow, brown, black, and green. Then apply a tripesic contraction, which would contract all yellow triangles into just vertices.

Incidence matrix

pac-o3o4x3*a (y-triangle → pt)   (N → ∞)

2N  * | 1  1  1 1  1  1 1  1  1 |  2  2  2 1 1 1  y   [(3^2,4)^3]
 * 2N | 0  1  1 0  1  1 0  1  1 |  1  1  1 1 1 1  bsg [(3,4)^3]
------+-------------------------+---------------
 2  0 | N  *  * *  *  * *  *  * |  2  0  0 0 0 0  b:y:sg
 1  1 | * 2N  * *  *  * *  *  * |  1  0  0 1 0 0  b:s:yg
 1  1 | *  * 2N *  *  * *  *  * |  1  0  0 0 1 0  b:g:ys
 2  0 | *  *  * N  *  * *  *  * |  0  2  0 0 0 0  s:y:bg
 1  1 | *  *  * * 2N  * *  *  * |  0  1  0 1 0 0  s:b:yg
 1  1 | *  *  * *  * 2N *  *  * |  0  1  0 0 0 1  s:g:yb
 2  0 | *  *  * *  *  * N  *  * |  0  0  2 0 0 0  g:y:bs
 1  1 | *  *  * *  *  * * 2N  * |  0  0  1 0 1 0  g:b:ys
 1  1 | *  *  * *  *  * *  * 2N |  0  0  1 0 0 1  g:s:yb
------+-------------------------+---------------
 2  1 | 1  1  1 0  0  0 0  0  0 | 2N  *  * * * *  b  {3}
 2  1 | 0  0  0 1  1  1 0  0  0 |  * 2N  * * * *  s  {3}
 2  1 | 0  0  0 0  0  0 1  1  1 |  *  * 2N * * *  g  {3}
 2  2 | 0  2  0 0  2  0 0  0  0 |  *  *  * N * *  bs {4}
 2  2 | 0  0  2 0  0  0 0  2  0 |  *  *  * * N *  bg {4}
 2  2 | 0  0  0 0  0  2 0  0  2 |  *  *  * * * N  sg {4}