Tetrapentagonal tiling

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}.

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 symbol5 4
5 5 | 2
Coxeter diagram or
or
Symmetry group[5,4], (*542)
[5,5], (*552)
DualOrder-5-4 rhombille tiling
PropertiesVertex-transitive edge-transitive

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.

Dual tiling

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

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)
  • "Chapter 10: Regular honeycombs in hyperbolic space". The Beauty of Geometry: Twelve Essays. Dover Publications. 1999. ISBN 0-486-40919-8. LCCN 99035678.
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