Cantic order-4 hexagonal tiling
| Tritetratetragonal tiling | |
|---|---|
 Poincaré disk model of the hyperbolic plane | |
| Type | Hyperbolic uniform tiling |
| Vertex configuration | 3.8.4.8 |
| Schläfli symbol | t0,1{(4,4,3)} |
| Wythoff symbol | 4 4 | 3 |
| Coxeter diagram |    |
| Symmetry group | [(4,4,3)], (*443) |
| Dual | Order-4-4-3 t01 dual tiling |
| Properties | Vertex-transitive |
In geometry, the tritetratrigonal tiling or cantic order-4 hexagonal tiling is a uniform tiling of the hyperbolic plane. It has Schläfli symbol of t0,1{(4,4,3)} or h2{6,4}.
Related polyhedra and tiling
| Symmetry: [(4,4,3)] (*443) | [(4,4,3)]+ (443) |
[(4,4,3+)] (3*22) |
[(4,1+,4,3)] (*3232) | |||||||
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| h{6,4} t0{(4,4,3)} {(4,4,3)} |
h2{6,4} t0,1{(4,4,3)} r{(3,4,4)} |
{4,6} t1{(4,4,3)} {(4,3,4)} |
h2{6,4} t1,2{(4,4,3)} r{(4,4,3)} |
h{6,4} t2{(4,4,3)} {(3,4,4)} |
r{6,4} t0,2{(4,4,3)} r{(4,3,4)} |
t{4,6} t0,1,2{(4,4,3)} t{(4,3,4)} |
s{4,6} s{(4,4,3)} |
hr{6,4} hr{(4,3,4)} |
h{4,6} h{(4,3,4)} |
q{4,6} h2{(4,3,4)} |
| Uniform duals | ||||||||||
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| V(3.4)4 | V3.8.4.8 | V(4.4)3 | V3.8.4.8 | V(3.4)4 | V4.6.4.6 | V6.8.8 | V3.3.3.4.3.4 | V(4.4.3)2 | V66 | V4.3.4.6.6 |
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
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Wikimedia Commons has media related to Uniform tiling 3-8-4-8. |
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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