French
DeutschOrder-8 pentagonal tiling
| 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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