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.
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Transcription
Symmetry
There is a half symmetry form, , seen with alternating colors:
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
![](http://upload.wikimedia.org/wikipedia/en/thumb/4/4a/Commons-logo.svg/30px-Commons-logo.svg.png)
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. LCCN 99035678.
External links
- Weisstein, Eric W. "Hyperbolic tiling". MathWorld.
- Weisstein, Eric W. "Poincaré hyperbolic disk". MathWorld.
- Hyperbolic and Spherical Tiling Gallery
![](/s/i/modif.png)