Truncated tetrapentagonal tiling

Truncated tetrapentagonal tiling

Poincaré disk model of the hyperbolic plane
TypeHyperbolic uniform tiling
Vertex configuration4.8.10
Schläfli symboltr{5,4} or t\begin{Bmatrix} 5 \\ 4 \end{Bmatrix}
Wythoff symbol2 5 4 |
Coxeter diagram or
Symmetry group[5,4], (*542)
DualOrder-4-5 kisrhombille tiling
PropertiesVertex-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}.

Symmetry

Truncated tetrapentagonal tiling with mirror lines.

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

See also

Wikimedia Commons has media related to Uniform tiling 4-8-10.

References

External links

This article is issued from Wikipedia - version of the Sunday, April 03, 2016. The text is available under the Creative Commons Attribution/Share Alike but additional terms may apply for the media files.