Order-7 heptagonal tiling
| Order-7 heptagonal tiling | |
|---|---|
 Poincaré disk model of the hyperbolic plane | |
| Type | Hyperbolic regular tiling |
| Vertex figure | 77 |
| Schläfli symbol | {7,7} |
| Wythoff symbol | 7 | 7 2 |
| Coxeter diagram |    |
| Symmetry group | [7,7], (*772) |
| Dual | self dual |
| Properties | Vertex-transitive, edge-transitive, face-transitive |
In geometry, the order-7 heptagonal tiling is a regular tiling of the hyperbolic plane. It has Schläfli symbol of {7,7}, constructed from seven heptagons around every vertex. As such, it is self-dual.
Related tilings
| Symmetry: [7,7], (*772) | [7,7]+, (772) | ||||||
|---|---|---|---|---|---|---|---|
=   =   |
= = |
=  =  |
=  = |
= = |
=  = |
= = |
 = = |
 |
 |
 |
 |
 |
 |
 |
 |
| {7,7} | t{7,7} |
r{7,7} | 2t{7,7}=t{7,7} | 2r{7,7}={7,7} | rr{7,7} | tr{7,7} | sr{7,7} |
| Uniform duals | |||||||
 |
|
|
|
|
|
|
 |
|
 |
 |
|
|
 |
 |
|
| V77 | V7.14.14 | V7.7.7.7 | V7.14.14 | V77 | V4.7.4.7 | V4.14.14 | V3.3.7.3.7 |
See also
 |
Wikimedia Commons has media related to Order-7 heptagonal tiling. |
References
- John H. Conway, Heidi Burgiel, Chaim Goodman-Strass, 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
- 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
| ||||||||||||||||||||||||||||||||||||||
This article is issued from Wikipedia - version of the Monday, November 03, 2014. The text is available under the Creative Commons Attribution/Share Alike but additional terms may apply for the media files.