Infinite-order hexagonal tiling

Infinite-order hexagonal tiling
Infinite-order hexagonal tiling Poincaré disk model of the hyperbolic plane
Type	Hyperbolic regular tiling
Vertex configuration	6^∞
Schläfli symbol	{6,∞}
Wythoff symbol	∞ \| 6 2
Coxeter diagram	File:CDel node.pngFile:CDel infin.pngFile:CDel node.pngFile:CDel 6.pngFile:CDel node 1.png File:CDel node 1.pngFile:CDel split1-66.pngFile:CDel branch.pngFile:CDel labelinfin.png
Symmetry group	[∞,6], (*∞62)
Dual	Order-6 apeirogonal tiling
Properties	Vertex-transitive, edge-transitive, face-transitive

In 2-dimensional hyperbolic geometry, the infinite-order hexagonal tiling is a regular tiling. It has Schläfli symbol of {6,∞}. All vertices are ideal, located at "infinity", seen on the boundary of the Poincaré hyperbolic disk projection.

Symmetry

This tiling is topologically related as a part of sequence of regular polyhedra and tilings with vertex figure (6ⁿ).

*n62 symmetry mutation of regular tilings: {6,n} v t e
Spherical	Euclidean	Hyperbolic tilings
File:Hexagonal dihedron.svg {6,2}	File:Uniform tiling 63-t0.svg {6,3}	File:H2 tiling 246-1.png {6,4}	File:H2 tiling 256-1.png {6,5}	File:H2 tiling 266-4.png {6,6}	File:H2 tiling 267-4.png {6,7}	File:H2 tiling 268-4.png {6,8}	...	File:H2 tiling 26i-4.png {6,∞}

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