Order-5 square tiling
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| Order-5 square tiling | |
|---|---|
| Order-5 square tiling Poincaré disk model of the hyperbolic plane | |
| Type | Hyperbolic regular tiling |
| Vertex configuration | 45 |
| Schläfli symbol | {4,5} |
| Wythoff symbol | 4 2 |
| Coxeter diagram | Template:CDD |
| Symmetry group | [5,4], (*542) |
| Dual | Order-4 pentagonal tiling |
| Properties | Vertex-transitive, edge-transitive, face-transitive |
In geometry, the order-5 square tiling is a regular tiling of the hyperbolic plane. It has Schläfli symbol of {4,5}.
Related polyhedra and tiling
Template:Order-5 regular tilings
This tiling is topologically related as a part of sequence of regular polyhedra and tilings with vertex figure (4n). Template:Regular square tiling table
Template:Order 5-4 tiling table
This hyperbolic tiling is related to a semiregular infinite skew polyhedron with the same vertex figure in Euclidean 3-space.
References
- John H. Conway, Heidi Burgiel, Chaim Goodman-Strauss, The Symmetries of Things 2008, Template:Isbn (Chapter 19, The Hyperbolic Archimedean Tessellations)
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See also
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- Square tiling
- Uniform tilings in hyperbolic plane
- List of regular polytopes
- Medial rhombic triacontahedron
External links
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- Hyperbolic and Spherical Tiling Gallery
- KaleidoTile 3: Educational software to create spherical, planar and hyperbolic tilings
- Hyperbolic Planar Tessellations, Don Hatch