# Truncated order-4 pentagonal tiling

In geometry, the truncated order-4 pentagonal tiling is a uniform tiling of the hyperbolic plane. It has Schläfli symbol of t0,1{5,4}.

Truncated pentagonal tiling

Poincaré disk model of the hyperbolic plane
Type Hyperbolic uniform tiling
Vertex configuration 4.10.10
Schläfli symbol t{5,4}
Wythoff symbol 2 4 | 5
2 5 5 |
Coxeter diagram
or
Symmetry group [5,4], (*542)
[5,5], (*552)
Dual Order-5 tetrakis square tiling
Properties Vertex-transitive

## Uniform colorings

A half symmetry [1+,4,5] = [5,5] coloring can be constructed with two colors of decagons. This coloring is called a truncated pentapentagonal tiling.

## Symmetry

There is only one subgroup of [5,5], [5,5]+, removing all the mirrors. This symmetry can be doubled to 542 symmetry by adding a bisecting mirror.

Small index subgroups of [5,5]
Type Reflective domains Rotational symmetry
Index 1 2
Diagram
Coxeter
(orbifold)
[5,5] = =
(*552)
[5,5]+ = =
(552)

## 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.