Acronym ...
Name hyperbolic [(33,4)4] tiling
 
Vertex figure [(33,4)4]
Confer
related hyperbolic polytopes:
pex-o3o4o3*a   pac-o3o4x3*a   o3o4x3*a  
general polytopal classes:
partial Stott expansions  

Even so this tiling is uniform, it neither has a triangular fundamental domain, nor directly relates to those tilings with Coxeter domains.

This tiling could be obtained by a 2 step 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: this would result in pac-o3o4x3*a. Then apply a second such contraction onto that, reducing the brown triangles into points too. This would be the tiling under consideration. – One even could apply this again with respect to the black triangles. Then only the green triangles would be left, providing pex-o3o4o3*a. (A fourth application then clearly would reduce the complete tiling into a single point.)



Incidence matrix

(N → ∞)

N |  4  4  4  4 |  6  6 4  [((3^3),4)^4]
--+-------------+--------
2 | 2N  *  *  * |  2  0 0  s:s
2 |  * 2N  *  * |  0  2 0  g:g
2 |  *  * 2N  * |  1  0 1  s:r
2 |  *  *  * 2N |  0  1 1  g:r
--+-------------+--------
3 |  2  0  1  0 | 2N  * *  s {3}
3 |  0  2  0  1 |  * 2N *  g {3}
4 |  0  0  2  2 |  *  * N  r {4}

pabex-o3o4o3*a (y-triangle → pt  &  b-triangle → pt)   (N → ∞)

N | 2 2 2 2  4  4 |  6  6 4  [((3^3),4)^4]
--+---------------+--------
2 | N * * *  *  * |  2  0 0  s:y
2 | * N * *  *  * |  2  0 0  s:b
2 | * * N *  *  * |  0  2 0  g:y
2 | * * * N  *  * |  0  2 0  g:b
2 | * * * * 2N  * |  1  0 1  s:r
2 | * * * *  * 2N |  0  1 1  g:r
--+---------------+--------
3 | 1 1 0 0  1  0 | 2N  * *  s {3}
3 | 0 0 1 1  0  1 |  * 2N *  g {3}
4 | 0 0 0 0  2  2 |  *  * N  r {4}

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