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 t_0,1{5,4}.

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-Strauss, 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. 

See also

• Uniform tilings in hyperbolic plane
• List of regular polytopes

External links

• Weisstein, Eric W.. "Hyperbolic tiling". http://mathworld.wolfram.com/HyperbolicTiling.html. 
• Weisstein, Eric W.. "Poincaré hyperbolic disk". http://mathworld.wolfram.com/PoincareHyperbolicDisk.html. 
• Hyperbolic and Spherical Tiling Gallery
• KaleidoTile 3: Educational software to create spherical, planar and hyperbolic tilings
• Hyperbolic Planar Tessellations, Don Hatch