Order-7 heptagonal tiling
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Order-7 heptagonal tiling | |
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![]() 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 | |||||||||||
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Symmetry: [7,7], (*772) | [7,7]+, (772) | ||||||||||
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{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 | |||||||||||
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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} | ||||||||
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Spherical | Hyperbolic tilings | |||||||
![]() {2,7} ![]() ![]() ![]() ![]() ![]() |
![]() {3,7} ![]() ![]() ![]() ![]() ![]() |
![]() {4,7} ![]() ![]() ![]() ![]() ![]() |
![]() {5,7} ![]() ![]() ![]() ![]() ![]() |
![]() {6,7} ![]() ![]() ![]() ![]() ![]() |
![]() {7,7} ![]() ![]() ![]() ![]() ![]() |
![]() {8,7} ![]() ![]() ![]() ![]() ![]() |
... | ![]() {∞,7} ![]() ![]() ![]() ![]() ![]() |
See also
[edit]![](http://upload.wikimedia.org/wikipedia/en/thumb/4/4a/Commons-logo.svg/30px-Commons-logo.svg.png)
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