Pentaapeirogonal tiling
pentaapeirogonal tiling | |
---|---|
![]() Poincaré disk model of the hyperbolic plane | |
Type | Hyperbolic uniform tiling |
Vertex figure | 5.∞.5.∞ |
Schläfli symbol | r{∞,5} |
Wythoff symbol | 2 | ∞ 5 |
Coxeter diagram | ![]() ![]() ![]() ![]() ![]() |
Symmetry group | [∞,5], (*∞52) |
Dual | Order-5-infinite rhombille tiling |
Properties | Vertex-transitive edge-transitive |
In geometry, the pentaapeirogonal tiling is a uniform tiling of the hyperbolic plane with a Schläfli symbol of r{∞,5}.
Related polyhedra and tiling
Symmetry *5n2 [n,5] |
Spherical | Hyperbolic... | Paracompact | Noncompact | ||||
---|---|---|---|---|---|---|---|---|
*352 [3,5] |
*452 [4,5] |
*552 [5,5] |
*652 [6,5] |
*752 [7,5] |
*852 [8,5]... |
*∞52 [∞,5] |
[iπ/λ,5] | |
Coxeter | ![]() ![]() ![]() ![]() ![]() |
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Quasiregular figures configuration |
![]() 5.3.5.3 |
![]() 5.4.5.4 |
![]() 5.5.5.5 |
![]() 5.6.5.6 |
![]() 5.7.5.7 |
![]() 5.8.5.8 |
![]() 5.∞.5.∞ |
5.∞.5.∞ |
Dual figures | ||||||||
Coxeter | ![]() ![]() ![]() ![]() ![]() |
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Dual (rhombic) figures configuration |
![]() V5.3.5.3 |
![]() V5.4.5.4 |
![]() V5.5.5.5 |
![]() V5.6.5.6 |
V5.7.5.7 |
V5.8.5.8 |
V5.∞.5.∞ |
V5.∞.5.∞ |
See also
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Wikimedia Commons has media related to Uniform tiling 5-i-5-i. |
- List of uniform planar tilings
- Tilings of regular polygons
- Uniform tilings in hyperbolic plane
References
- John H. Conway, Heidi Burgiel, Chaim Goodman-Strass, 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
- Weisstein, Eric W., "Hyperbolic tiling", MathWorld.
- Weisstein, Eric W., "Poincaré hyperbolic disk", MathWorld.
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