| Order-8 pentagonal tiling | |
|---|---|
 Poincaré disk model of the hyperbolic plane | |
| Type | Hyperbolic regular tiling |
| Vertex configuration | 58 |
| Schläfli symbol | {5,8} |
| Wythoff symbol | 8 h 5 2 |
| Coxeter diagram |    
|
| Symmetry group | [8,5], (*852) |
| Dual | Order-5 octagonal tiling |
| Properties | Vertex-transitive, edge-transitive, face-transitive |
In geometry, the order-8 pentagonal tiling is a regular tiling of the hyperbolic plane. It has Schläfli symbol of {5,8}.
Related tilings
edit| Regular tilings: {n,8} | |||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|
| Spherical | Hyperbolic tilings | ||||||||||
 {2,8} 
|
 {3,8} 
|
 {4,8} 
|
{5,8}
|
 {6,8} 
|
 {7,8} 
|
 {8,8}
|
... |  {∞,8} 
| |||
This tiling is topologically related as a part of sequence of regular polyhedra and tilings with vertex figure (5n).
| Finite | Compact hyperbolic | Paracompact | ||||
|---|---|---|---|---|---|---|
 {5,3}
|
 {5,4}
|
 {5,5}
|
 {5,6}
|
 {5,7}
|
 {5,8}...
|
 {5,∞}
|
See also
edit
Wikimedia Commons has media related to Order-8 pentagonal tiling.
References
edit- John H. Conway, Heidi Burgiel, Chaim Goodman-Strauss, The Symmetries of Things 2008, ISBN 978-1-56881-220-5 (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.
External links
edit- 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
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