Pentaapeirogonal tiling

pentaapeirogonal tiling
Poincaré disk model of the hyperbolic plane
Type	Hyperbolic uniform tiling
Vertex configuration	(5.∞)2
Schläfli symbol	r{∞,5}
Wythoff symbol	2 | ∞ 5
Coxeter diagram
Symmetry group	[∞,5], (*∞52)
Dual	Order-5-infinite rhombille tiling
Properties	Vertex-transitive edge-transitive

In geometry, the pentaapeirogonal tiling is a uniform tiling of the hyperbolic plane with a Schläfli symbol of r{∞,5}.

Related polyhedra and tiling

*5n2 symmetry mutations of quasiregular tilings: (5.n)2
Symmetry *5n2 [n,5]	Spherical	Hyperbolic					Paracompact	Noncompact
	*352 [3,5]	*452 [4,5]	*552 [5,5]	*652 [6,5]	*752 [7,5]	*852 [8,5]...	*∞52 [∞,5]	[ni,5]
Figures
Config.	(5.3)2	(5.4)2	(5.5)2	(5.6)2	(5.7)2	(5.8)2	(5.∞)2	(5.ni)2
Rhombic figures
Config.	V(5.3)2	V(5.4)2	V(5.5)2	V(5.6)2	V(5.7)2	V(5.8)2	V(5.∞)2	V(5.∞)2

See also

• List of uniform planar tilings
• Tilings of regular polygons
• Uniform tilings in hyperbolic plane

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)

External links

• Weisstein, Eric W., "Hyperbolic tiling", MathWorld.
• Weisstein, Eric W., "Poincaré hyperbolic disk", MathWorld.