KNOWPIA
WELCOME TO KNOWPIA
Order-7 heptagonal tiling 
Summary
| Order-7 heptagonal tiling | |
|---|---|
 Poincaré disk model of the hyperbolic plane | |
| Type | Hyperbolic regular tiling |
| Vertex configuration | 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 edit
| Uniform heptaheptagonal 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 | ||||
This tiling is a part of regular series {n,7}:
| Tiles of the form {n,7} | ||||||||
|---|---|---|---|---|---|---|---|---|
| Spherical | Hyperbolic tilings | |||||||
 {2,7} 
|
 {3,7} 
|
 {4,7}
|
 {5,7} 
|
 {6,7} 
|
 {7,7}  {8,7} 
|
... |  {∞,7} 
| |
See also edit
Wikimedia Commons has media related to Order-7 heptagonal 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