Tetrapentagonal tiling

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Tetrapentagonal tiling
Tetrapentagonal tiling
Poincaré disk model of the hyperbolic plane
Type Hyperbolic uniform tiling
Vertex configuration (4.5)2
Schläfli symbol r{5,4}
rr{5,5}
Wythoff symbol 2 | 5 4
5 5 | 2
Coxeter diagram CDel node.pngCDel 5.pngCDel node 1.pngCDel 4.pngCDel node.png
CDel node 1.pngCDel 5.pngCDel node.pngCDel 5.pngCDel node 1.png
Symmetry group [5,4], (*542)
[5,5], (*552)
Dual Order-5-4 rhombille tiling
Properties Vertex-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}.

Symmetry

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.

Uniform tiling 552-t02.png

Dual tiling

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

Order-5-4 quasiregular rhombic tiling.png

Related polyhedra and tiling

See also

References

  • John H. Conway, Heidi Burgiel, Chaim Goodman-Strass, The Symmetries of Things 2008, ISBN 978-1-56881-220-5 (Chapter 19, The Hyperbolic Archimedean Tessellations)
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External links

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