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
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 v
{2,5}	{3,5}	{4,5}	{5,5}	{6,5}			...	{∞,5}

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

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

Uniform pentapentagonal tilings v
Symmetry: [5,5], (*552)							[5,5]+, (552)
=	=	=	=	=	=	=	=
{5,5}	t{5,5}	r{5,5}	2t{5,5}=t{5,5}	2r{5,5}={5,5}	rr{5,5}	tr{5,5}	sr{5,5}
Uniform duals
V5.5.5.5.5	V5.10.10	V5.5.5.5	V5.10.10	V5.5.5.5.5	V4.5.4.5	V4.10.10	V3.3.5.3.5

See also[]

Wikimedia Commons has media related to Order-5 pentagonal tiling.

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

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.

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

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