Acronym | ... |
Name | hyperbolic [(33,4)4] tiling |
Vertex figure | [(33,4)4] |
Confer |
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Although 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.)
(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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