Infinite-order pentagonal tiling

Infinite-order pentagonal tiling
Poincaré disk model of the hyperbolic plane
Type	Hyperbolic regular tiling
Vertex configuration	5∞
Schläfli symbol	{5,∞}
Wythoff symbol	∞ | 5 2
Coxeter diagram
Symmetry group	[∞,5], (*∞52)
Dual	Order-5 apeirogonal tiling
Properties	face-transitive

In 2-dimensional

Symmetry

There is a half symmetry form, , seen with alternating colors:

Related polyhedra and tiling

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

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

Paracompact uniform apeirogonal/pentagonal tilings v t e
Symmetry: [∞,5], (*∞52)							[∞,5]+ (∞52)	[1+,∞,5] (*∞55)		[∞,5+] (5*∞)
{∞,5}	t{∞,5}	r{∞,5}	2t{∞,5}=t{5,∞}	2r{∞,5}={5,∞}	rr{∞,5}	tr{∞,5}	sr{∞,5}	h{∞,5}	h2{∞,5}	s{5,∞}
Uniform duals
V∞5	V5.∞.∞	V5.∞.5.∞	V∞.10.10	V5∞	V4.5.4.∞	V4.10.∞	V3.3.5.3.∞		V(∞.5)5	V3.5.3.5.3.∞

See also

Wikimedia Commons has media related to Infinite-order pentagonal tiling.

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

References

• ISBN 978-1-56881-220-5
  .
• LCCN 99035678
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• Weisstein, Eric W. "Hyperbolic tiling". MathWorld.
• Weisstein, Eric W. "Poincaré hyperbolic disk". MathWorld.
• Hyperbolic and Spherical Tiling Gallery