Order-4 pentagonal tiling

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Order-4 pentagonal tiling
Type	Regular tiling
Vertex figure	5.5.5.5
Schläfli symbol(s)	{5,4}
Wythoff symbol(s)	4 | 5 2
Coxeter-Dynkin(s)
Symmetry	[5,4]
Dual	Order-5 square tiling
Properties	Vertex-transitive, edge-transitive, face-transitive
Image:Order-4 pentagonal tiling vertfig.png 5.5.5.5
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In geometry, the order-4 pentagonal tiling is a regular tiling of the hyperbolic plane. It has Schläfli symbol of {5,4}.

The image shows a Poincaré disk model projection of the hyperbolic plane.

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

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[edit] References

• Grünbaum, Branko; Shephard, G. C. (1987). Tilings and Patterns. New York: W. H. Freeman and Company. ISBN 0-7167-1193-1. 

[edit] See also

• Square tiling
• Tilings of regular polygons
• List of uniform planar tilings
• List of regular polytopes

[edit] External links

• Eric W. Weisstein, Hyperbolic tiling at MathWorld.
• Eric W. Weisstein, Poincaré hyperbolic disk at MathWorld.
• Hyperbolic and Spherical Tiling Gallery
• KaleidoTile 3: Educational software to create spherical, planar and hyperbolic tilings
• Hyperbolic Planar Tessellations, Don Hatch