Infinite-order hexagonal tiling
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| Infinite-order hexagonal tiling | |
|---|---|
 Poincaré disk model of the hyperbolic plane | |
| Type | Hyperbolic regular tiling |
| Vertex configuration | 6∞ |
| Schläfli symbol | {6,∞} |
| Wythoff symbol | ∞ | 6 2 |
| Coxeter diagram |       
|
| Symmetry group | [∞,6], (*∞62) |
| Dual | Order-6 apeirogonal tiling |
| Properties | Vertex-transitive, edge-transitive, face-transitive |
In 2-dimensional hyperbolic geometry, the infinite-order hexagonal tiling is a regular tiling. It has Schläfli symbol of {6,∞}. All vertices are ideal, located at "infinity", seen on the boundary of the Poincaré hyperbolic disk projection.
Symmetry
There is a half symmetry form, , seen with alternating colors:
- 200px
Related polyhedra and tiling
This tiling is topologically related as a part of sequence of regular polyhedra and tilings with vertex figure (6n).
| *n62 symmetry mutation of regular tilings: {6,n} | ||||||||
|---|---|---|---|---|---|---|---|---|
| Spherical | Euclidean | Hyperbolic tilings | ||||||
 {6,2} |
 {6,3} |
 {6,4} |
 {6,5} |
 {6,6} |
 {6,7} |
 {6,8} |
... | {6,∞} |
See also
- Hexagonal tiling
- Uniform tilings in hyperbolic plane
- List of regular polytopes
References
- John H. Conway; Heidi Burgiel; Chaim Goodman-Strauss (2008). "Chapter 19, The Hyperbolic Archimedean Tessellations". The Symmetries of Things. ISBN 978-1-56881-220-5.
- H. S. M. Coxeter (1999). "Chapter 10: Regular honeycombs in hyperbolic space". The Beauty of Geometry: Twelve Essays. Dover Publications. ISBN 0-486-40919-8.
External links
- Weisstein, Eric W.. "Hyperbolic tiling". http://mathworld.wolfram.com/HyperbolicTiling.html.
- Weisstein, Eric W.. "Poincaré hyperbolic disk". http://mathworld.wolfram.com/PoincareHyperbolicDisk.html.
- Hyperbolic and Spherical Tiling Gallery
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