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	File:CDel infin.pngFile:CDel 5.pngFile:CDel node 1.png File:CDel node 1.pngFile:CDel split1-55.pngFile:CDel branch.pngFile:CDel labelinfin.png
Symmetry group	[∞,5], (*∞52)
Dual	Order-5 apeirogonal tiling
Properties	Vertex-transitive, edge-transitive, face-transitive

In 2-dimensional hyperbolic geometry, the infinite-order pentagonal tiling is a regular tiling. It has Schläfli symbol of {5,∞}. All vertices are ideal, located at "infinity", seen on the boundary of the Poincaré hyperbolic disk projection.

Symmetry

There is a half symmetry form, File:CDel node 1.pngFile:CDel split1-55.pngFile:CDel branch.pngFile:CDel labelinfin.png, seen with alternating colors:

File:H2 tiling 55i-4.png

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					Paracompact
File:Uniform polyhedron-53-t0.svg {5,3} File:CDel node 1.pngFile:CDel 5.pngFile:CDel 3.png	File:H2-5-4-dual.svg {5,4} File:CDel node 1.pngFile:CDel 5.pngFile:CDel 4.png	File:Uniform tiling 55-t0.png {5,5} File:CDel node 1.pngFile:CDel 5.pngFile:CDel 5.png	File:Uniform tiling 56-t0.png {5,6} File:CDel node 1.pngFile:CDel 5.pngFile:CDel 6.png	File:Uniform tiling 57-t0.png {5,7} File:CDel node 1.pngFile:CDel 5.pngFile:CDel 7.png	File:Uniform tiling 58-t0.png {5,8}... File:CDel node 1.pngFile:CDel 5.pngFile:CDel 8.png	Error creating thumbnail: {5,∞} File:CDel node 1.pngFile:CDel 5.pngFile:CDel infin.png

See also

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

External links

• Hyperbolic and Spherical Tiling Gallery Archived 2013-03-24 at the Wayback Machine