Top Qs
Timeline
Chat
Perspective
Truncated tetrapentagonal tiling
A uniform tiling of the hyperbolic plane From Wikipedia, the free encyclopedia
Remove ads
Remove ads
In geometry, the truncated tetrapentagonal tiling is a uniform tiling of the hyperbolic plane. It has Schläfli symbol of t0,1,2{4,5} or tr{4,5}.
Truncated tetrapentagonal tiling | |
---|---|
![]() Poincaré disk model of the hyperbolic plane | |
Type | Hyperbolic uniform tiling |
Vertex configuration | 4.8.10 |
Schläfli symbol | tr{5,4} or |
Wythoff symbol | 2 5 4 | |
Coxeter diagram | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
Symmetry group | [5,4], (*542) |
Dual | Order-4-5 kisrhombille tiling |
Properties | Vertex-transitive |
Remove ads
Symmetry






There are four small index subgroup constructed from [5,4] by mirror removal and alternation. In these images fundamental domains are alternately colored black and white, and mirrors exist on the boundaries between colors.
A radical subgroup is constructed [5*,4], index 10, as [5+,4], (5*2) with gyration points removed, becoming orbifold (*22222), and its direct subgroup [5*,4]+, index 20, becomes orbifold (22222).
Remove ads
Related polyhedra and tiling
Remove ads
See also
Wikimedia Commons has media related to Uniform tiling 4-8-10.
References
- 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)
- Coxeter, H. S. M. (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
- KaleidoTile 3: Educational software to create spherical, planar and hyperbolic tilings
- Hyperbolic Planar Tessellations, Don Hatch
Wikiwand - on
Seamless Wikipedia browsing. On steroids.
Remove ads