Tetraheptagonal tiling
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| Tetraheptagonal tiling | |
|---|---|
 Poincaré disk model of the hyperbolic plane | |
| Type | Hyperbolic uniform tiling |
| Vertex configuration | (4.7)2 |
| Schläfli symbol | r{7,4} or rr{7,7} |
| Wythoff symbol | 2 | 7 4 7 7 | 2 |
| Coxeter diagram |    
|
| Symmetry group | [7,4], (*742) [7,7], (*772) |
| Dual | Order-7-4 rhombille tiling |
| Properties | Vertex-transitive edge-transitive |
In geometry, the tetraheptagonal tiling is a uniform tiling of the hyperbolic plane. It has Schläfli symbol of r{4,7}.
Symmetry
 A half symmetry [1+,4,7] = [7,7] construction exists, which can be seen as two colors of heptagons. This coloring can be called a rhombiheptaheptagonal tiling. |
 The dual tiling is made of rhombic faces and has a face configuration V4.7.4.7. |
Related polyhedra and tiling
Template:Order 7-4 tiling table Template:Order 7-7 tiling table
See also
 |
Wikimedia Commons has media related to Uniform tiling 4-7-4-7. |
References
- John H. Conway, Heidi Burgiel, Chaim Goodman-Strauss, The Symmetries of Things 2008, ISBN 978-1-56881-220-5 Search this book on
. (Chapter 19, The Hyperbolic Archimedean Tessellations) - "Chapter 10: Regular honeycombs in hyperbolic space". The Beauty of Geometry: Twelve Essays. Dover Publications. 1999. ISBN 0-486-40919-8. LCCN 99035678. Search this book on
External links
- Weisstein, Eric W. "Hyperbolic tiling". MathWorld.
- Weisstein, Eric W. "Poincaré hyperbolic disk". MathWorld.
- Hyperbolic and Spherical Tiling Gallery
- KaleidoTile 3: Educational software to create spherical, planar and hyperbolic tilings
- Hyperbolic Planar Tessellations, Don Hatch
Template:Hyperbolic-geometry-stub
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