| Snub order-8 triangular tiling | |
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 Poincaré disk model of the hyperbolic plane | |
| Type | Hyperbolic uniform tiling |
| Vertex configuration | 3.3.3.3.3.4 |
| Schläfli symbol | s{3,8} s(4,3,3) |
| Wythoff symbol | | 4 3 3 |
| Coxeter diagram |       
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| Symmetry group | , (3*4) , (433) |
| Dual | Order-4-3-3 snub dual tiling |
| Properties | Vertex-transitive |
In geometry, the snub tritetratrigonal tiling or snub order-8 triangular tiling is a uniform tiling of the hyperbolic plane. It has Schläfli symbols of s{(3,4,3)} and s{3,8}.
Images
Drawn in chiral pairs:
Symmetry
The alternated construction from the truncated order-8 triangular tiling has 2 colors of triangles and achiral symmetry. It has Schläfli symbol of s{3,8}.
Related polyhedra and tiling
| Symmetry: , (*433) | , (433) | |||||||||
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| h{8,3} t0(4,3,3) |
r{3,8}/2 t0,1(4,3,3) |
h{8,3} t1(4,3,3) |
h2{8,3} t1,2(4,3,3) |
{3,8}/2 t2(4,3,3) |
h2{8,3} t0,2(4,3,3) |
t{3,8}/2 t0,1,2(4,3,3) |
s{3,8}/2 s(4,3,3) | |||
| Uniform duals | ||||||||||
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| V(3.4) | V3.8.3.8 | V(3.4) | V3.6.4.6 | V(3.3) | V3.6.4.6 | V6.6.8 | V3.3.3.3.3.4 | |||
| Uniform octagonal/triangular tilings | |||||||||||||
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| Symmetry: , (*832) | (832) |
(*443) |
(3*4) | ||||||||||
| {8,3} | t{8,3} | r{8,3} | t{3,8} | {3,8} | rr{8,3} s2{3,8} |
tr{8,3} | sr{8,3} | h{8,3} | h2{8,3} | s{3,8} | |||
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| V8 | V3.16.16 | V3.8.3.8 | V6.6.8 | V3 | V3.4.8.4 | V4.6.16 | V3.8 | V(3.4) | V8.6.6 | V3.4 | |||
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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)
- "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
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
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