| Snub order-8 triangular tiling | |
|---|---|
| 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 | |
| Symmetry group | [8,3+], (3*4)[(4,3,3)]+, (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}.
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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
Uniform (4,3,3) tilings- v
- t
- e
| Symmetry: [(4,3,3)], (*433) | [(4,3,3)]+, (433) | |||||||||
|---|---|---|---|---|---|---|---|---|---|---|
| h{8,3}t0(4,3,3) | r{3,8}1/2t0,1(4,3,3) | h{8,3}t1(4,3,3) | h2{8,3}t1,2(4,3,3) | {3,8}1/2t2(4,3,3) | h2{8,3}t0,2(4,3,3) | t{3,8}1/2t0,1,2(4,3,3) | s{3,8}1/2s(4,3,3) | |||
| Uniform duals | ||||||||||
| V(3.4)3 | V3.8.3.8 | V(3.4)3 | V3.6.4.6 | V(3.3)4 | V3.6.4.6 | V6.6.8 | V3.3.3.3.3.4 | |||
Uniform octagonal/triangular tilings
| |||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Symmetry: [8,3], (*832) | [8,3]+(832) | [1+,8,3](*443) | [8,3+](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} | |||
| or | or | ||||||||||||
| Uniform duals | |||||||||||||
| V83 | V3.16.16 | V3.8.3.8 | V6.6.8 | V38 | V3.4.8.4 | V4.6.16 | V34.8 | V(3.4)3 | V8.6.6 | V35.4 | |||
- 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.