Truncated order-5 square tiling

In geometry, the truncated order-5 square tiling is a uniform tiling of the hyperbolic plane. It has Schläfli symbol of t_0,1{4,5}.

Truncated order-5 square tiling
Poincaré disk model of the hyperbolic plane
Type	Hyperbolic uniform tiling
Vertex configuration	8.8.5
Schläfli symbol	t{4,5}
Wythoff symbol	2 5 \| 4
Coxeter diagram
Symmetry group	[5,4], (*542)
Dual	Order-4 pentakis pentagonal tiling
Properties	Vertex-transitive

More information Symmetry: [5,4], (*542), [5,4]+, (542) ...

Uniform pentagonal/square tilings v t e
Symmetry: [5,4], (*542)							[5,4]⁺, (542)	[5⁺,4], (5*2)	[5,4,1⁺], (*552)


{5,4}	t{5,4}	r{5,4}	2t{5,4}=t{4,5}	2r{5,4}={4,5}	rr{5,4}	tr{5,4}	sr{5,4}	s{5,4}	h{4,5}
Uniform duals


V5⁴	V4.10.10	V4.5.4.5	V5.8.8	V4⁵	V4.4.5.4	V4.8.10	V3.3.4.3.5	V3.3.5.3.5	V5⁵

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More information Symmetry*n42 [n,4], Spherical ...

*n42 symmetry mutation of truncated tilings: n.8.8 v t e
Symmetry *n42 [n,4]	Spherical		Euclidean	Compact hyperbolic				Paracompact
Symmetry *n42 [n,4]	*242 [2,4]	*342 [3,4]	*442 [4,4]	*542 [5,4]	*642 [6,4]	*742 [7,4]	*842 [8,4]...	*∞42 [∞,4]
Truncated figures
Config.	2.8.8	3.8.8	4.8.8	5.8.8	6.8.8	7.8.8	8.8.8	∞.8.8
n-kis figures
Config.	V2.8.8	V3.8.8	V4.8.8	V5.8.8	V6.8.8	V7.8.8	V8.8.8	V∞.8.8

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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.

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Related polyhedra and tiling