Snub order-8 triangular tiling
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}.
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: [(4,3,3)], (*433) | [(4,3,3)]+, (433) | |||||||||
---|---|---|---|---|---|---|---|---|---|---|
![]() ![]() ![]() ![]() | ![]() ![]() ![]() ![]() | ![]() ![]() ![]() ![]() | ![]() ![]() ![]() ![]() | ![]() ![]() ![]() ![]() | ![]() ![]() ![]() ![]() | ![]() ![]() ![]() ![]() | ![]() ![]() ![]() ![]() | |||
![]() ![]() ![]() ![]() ![]() | ![]() ![]() ![]() ![]() ![]() | ![]() ![]() ![]() ![]() ![]() | ![]() ![]() ![]() ![]() ![]() | ![]() ![]() ![]() ![]() ![]() | ![]() ![]() ![]() ![]() ![]() | ![]() ![]() ![]() ![]() ![]() | ![]() ![]() ![]() ![]() ![]() | |||
![]() | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() | |||
h{8,3} t0(4,3,3) | r{3,8}1/2 t0,1(4,3,3) | h{8,3} t1(4,3,3) | h2{8,3} t1,2(4,3,3) | {3,8}1/2 t2(4,3,3) | h2{8,3} t0,2(4,3,3) | t{3,8}1/2 t0,1,2(4,3,3) | s{3,8}1/2 s(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} | |||
![]() ![]() ![]() ![]() ![]() | ![]() ![]() ![]() ![]() ![]() | ![]() ![]() ![]() ![]() ![]() | ![]() ![]() ![]() ![]() ![]() | ![]() ![]() ![]() ![]() ![]() | ![]() ![]() ![]() ![]() ![]() | ![]() ![]() ![]() ![]() ![]() | ![]() ![]() ![]() ![]() ![]() | ![]() ![]() ![]() ![]() ![]() | |||||
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | ![]() ![]() ![]() ![]() ![]() | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |||||||
![]() | ![]() | ![]() ![]() | ![]() ![]() | ![]() ![]() | ![]() | ![]() | ![]() | ![]() ![]() | ![]() ![]() | ![]() ![]() | |||
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 | |||
![]() ![]() ![]() ![]() ![]() | ![]() ![]() ![]() ![]() ![]() | ![]() ![]() ![]() ![]() ![]() | ![]() ![]() ![]() ![]() ![]() | ![]() ![]() ![]() ![]() ![]() | ![]() ![]() ![]() ![]() ![]() | ![]() ![]() ![]() ![]() ![]() | ![]() ![]() ![]() ![]() ![]() | ![]() ![]() ![]() ![]() ![]() | ![]() ![]() ![]() ![]() ![]() | ![]() ![]() ![]() ![]() ![]() | |||
![]() | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() |
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
![](http://upload.wikimedia.org/wikipedia/en/thumb/4/4a/Commons-logo.svg/30px-Commons-logo.svg.png)
Wikimedia Commons has media related to Uniform tiling 3-3-3-3-3-4.
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