Order-5 pentagonal tiling

Order-5 pentagonal tiling
Poincaré disk model of the hyperbolic plane
Type	Hyperbolic regular tiling
Vertex configuration	5⁵
Schläfli symbol	{5,5}
Wythoff symbol	5 \| 5 2
Coxeter diagram
Symmetry group	[5,5], (*552)
Dual	self dual
Properties	Vertex-transitive, edge-transitive, face-transitive

In geometry, the order-5 pentagonal tiling is a regular tiling of the hyperbolic plane. It has Schläfli symbol of {5,5}, constructed from five pentagons around every vertex. As such, it is self-dual.

Related tilings

Spherical		Hyperbolic tilings
{2,5}	{3,5}	{4,5}		{6,5}	{7,5}	{8,5}	...	{∞,5}

This tiling is topologically related as a part of sequence of regular polyhedra and tilings with vertex figure (5ⁿ).

Finite	Compact hyperbolic					Paracompact
{5,3}	{5,4}		{5,6}	{5,7}	{5,8}...	{5,∞}

Uniform pentapentagonal tilings
Symmetry: $[5,5], (*552)$							$[5,5] +, (552)$
=	=	=	=	=	=	=	=

${5,5}$	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


$V5.5.5.5.5$	$V5.10.10$	Order-5 square tiling $V5.5.5.5$	$V5.10.10$	$V5.5.5.5.5$	$V4.5.4.5$	$V4.10.10$	$V3.3.5.3.5$

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.