Truncated order-5 pentagonal tiling

Truncated order-5 pentagonal tiling
Poincaré disk model of the hyperbolic plane
Type	Hyperbolic uniform tiling
Vertex configuration	5.10.10
Schläfli symbol	t{5,5}
Wythoff symbol	2 5 | 5
Coxeter diagram
Symmetry group	[5,5], (*552)
Dual	Order-5 pentakis pentagonal tiling
Properties	Vertex-transitive

In geometry, the truncated order-5 pentagonal tiling is a regular tiling of the hyperbolic plane. It has Schläfli symbol of t_0,1{5,5}, constructed from one pentagons and two decagons around every vertex.

Related tilings

Uniform pentapentagonal tilings
Symmetry: [5,5], (*552)							[5,5]+, (552)
=	=	=	=	=	=	=	=
Order-5 pentagonal tiling {5,5}	Truncated order-5 pentagonal tiling t{5,5}	Order-4 pentagonal tiling r{5,5}	Truncated order-5 pentagonal tiling 2t{5,5} = t{5,5}	Order-5 pentagonal tiling 2r{5,5} = {5,5}	Tetrapentagonal tiling rr{5,5}	Truncated order-4 pentagonal tiling tr{5,5}	Snub pentapentagonal tiling sr{5,5}
Uniform duals
Order-5 pentagonal tiling V5.5.5.5.5	V5.10.10	Order-5 square tiling V5.5.5.5	V5.10.10	Order-5 pentagonal tiling V5.5.5.5.5	V4.5.4.5	V4.10.10	V3.3.5.3.5

See also

• Square tiling
• Uniform tilings in hyperbolic plane
• List of regular polytopes

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. LCCN 99035678.

External links

• Weisstein, Eric W. "Hyperbolic tiling". MathWorld.
• Weisstein, Eric W. "Poincaré hyperbolic disk". MathWorld.
• Hyperbolic and Spherical Tiling Gallery
• KaleidoTile 3: Educational software to create spherical, planar and hyperbolic tilings
• Hyperbolic Planar Tessellations, Don Hatch