Tetrapentagonal tiling

Tetrapentagonal tiling

Poincaré disk model of the hyperbolic plane
TypeHyperbolic uniform tiling
Vertex configuration(4.5)2
Schläfli symbolr{5,4} or
rr{5,5} or
Wythoff symbol2 | 5 4
5 5 | 2
Coxeter diagram or
Symmetry group[5,4], (*542)
[5,5], (*552)
DualOrder-5-4 rhombille tiling
PropertiesVertex-transitive edge-transitive

In geometry, the tetrapentagonal tiling is a uniform tiling of the hyperbolic plane. It has Schläfli symbol of t1{4,5} or r{4,5}.


A half symmetry [1+,4,5] = [5,5] construction exists, which can be seen as two colors of pentagons. This coloring can be called a rhombipentapentagonal tiling.

Dual tiling

The dual tiling is made of rhombic faces and has a face configuration V4.5.4.5:

See also

Wikimedia Commons has media related to Uniform tiling 4-5-4-5.


This article is issued from Wikipedia - version of the 10/26/2014. The text is available under the Creative Commons Attribution/Share Alike but additional terms may apply for the media files.