Truncated tetrapentagonal tiling

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Truncated tetrapentagonal tiling
Truncated tetrapentagonal tiling
Poincaré disk model of the hyperbolic plane
Type Hyperbolic uniform tiling
Vertex configuration 4.8.10
Schläfli symbol tr{5,4} or
Wythoff symbol 2 5 4 |
Coxeter diagram CDel node 1.pngCDel 5.pngCDel node 1.pngCDel 4.pngCDel node 1.png or CDel node 1.pngCDel split1-54.pngCDel nodes 11.png
Symmetry group [5,4], (*542)
Dual Order-4-5 kisrhombille tiling
Properties Vertex-transitive

In geometry, the truncated tetrapentagonal tiling is a uniform tiling of the hyperbolic plane. It has Schläfli symbol of t0,1,2{4,5} or tr{4,5}.


Truncated tetrapentagonal tiling with mirror lines. CDel node c1.pngCDel 5.pngCDel node c1.pngCDel 4.pngCDel node c2.png

There are four small index subgroup constructed from [5,4] by mirror removal and alternation. In these images fundamental domains are alternately colored black and white, and mirrors exist on the boundaries between colors.

A radical subgroup is constructed [5*,4], index 10, as [5+,4], (5*2) with gyration points removed, becoming orbifold (*22222), and its direct subgroup [5*,4]+, index 20, becomes orbifold (22222).

Related polyhedra and tiling[edit]

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