Truncated order-5 square tiling
Truncated order-5 square tiling | |
---|---|
Poincaré disk model of the hyperbolic plane | |
Type | Hyperbolic uniform tiling |
Vertex figure | 8.8.5 |
Schläfli symbol | t{4,5} |
Wythoff symbol | 2 5 | 4 |
Coxeter diagram | |
Symmetry group | [5,4], (*542) |
Dual | Order-4 pentakis pentagonal tiling |
Properties | Vertex-transitive |
In geometry, the truncated order-5 square tiling is a uniform tiling of the hyperbolic plane. It has Schläfli symbol of t0,1{4,5}.
Related polyhedra and tiling
Symmetry: [5,4], (*542) | [5,4]+, (542) | [5+,4], (5*2) | [5,4,1+], (*552) | |||||||
---|---|---|---|---|---|---|---|---|---|---|
{5,4} | t{5,4} | r{5,4} | 2t{5,4}=t{4,5} | 2r{5,4}={4,5} | rr{5,4} | tr{5,4} | sr{5,4} | s{5,4} | h{4,5} | |
Uniform duals | ||||||||||
V54 | V4.10.10 | V4.5.4.5 | V5.8.8 | V45 | V4.4.5.4 | V4.8.10 | V3.3.4.3.5 | V3.3.5.3.5 | V55 |
Symmetry *n42 [n,4] |
Spherical | Euclidean | Compact hyperbolic | Paracompact | ||||
---|---|---|---|---|---|---|---|---|
*242 [2,4] D4h |
*342 [3,4] Oh |
*442 [4,4] P4m |
*542 [5,4] |
*642 [6,4] |
*742 [7,4] |
*842 [8,4]... |
*∞42 [∞,4] | |
Truncated figures |
2.8.8 | 3.8.8 |
4.8.8 |
5.8.8 |
6.8.8 |
7.8.8 |
8.8.8 |
∞.8.8 |
Coxeter Schläfli |
t{4,2} |
t{4,3} |
t{4,4} |
t{4,5} |
t{4,6} |
t{4,7} |
t{4,8} |
t{4,∞} |
Uniform dual figures | ||||||||
n-kis figures |
V2.8.8 |
V3.8.8 |
V4.8.8 |
V5.8.8 |
V6.8.8 |
V7.8.8 |
V8.8.8 |
V∞.8.8 |
Coxeter |
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.
See also
- Uniform tilings in hyperbolic plane
- List of regular polytopes
External links
Wikimedia Commons has media related to Uniform tiling 5-8-8. |
- 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
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