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
Error creating thumbnail: {2,5} File:CDel 2.png	File:Uniform tiling 532-t2.svg {3,5} File:CDel 3.png	File:H2-5-4-primal.svg {4,5} File:CDel 4.png	Error creating thumbnail: {5,5}	File:H2 tiling 256-1.png {6,5} File:CDel 6.png	File:H2 tiling 257-1.png {7,5} File:CDel 7.png	File:H2 tiling 258-1.png {8,5} File:CDel 8.png	...	File:H2 tiling 25i-1.png {∞,5} File:CDel infin.png

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

Finite	Compact hyperbolic					Paracompact
File:Uniform polyhedron-53-t0.svg {5,3} File:CDel 3.png	File:H2-5-4-dual.svg {5,4} File:CDel 4.png	File:Uniform tiling 55-t0.png {5,5}	File:Uniform tiling 56-t0.png {5,6} File:CDel 6.png	File:Uniform tiling 57-t0.png {5,7} File:CDel 7.png	File:Uniform tiling 58-t0.png {5,8}... File:CDel 8.png	File:H2 tiling 25i-4.png {5,∞} File:CDel infin.png

See also

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

References

• John H. Conway, Heidi Burgiel, Chaim Goodman-Strauss, The Symmetries of Things 2008, (Chapter 19, The Hyperbolic Archimedean Tessellations)

External links

• Hyperbolic and Spherical Tiling Gallery
• KaleidoTile 3: Educational software to create spherical, planar and hyperbolic tilings
• Hyperbolic Planar Tessellations, Don Hatch