Cantic octagonal tiling
In geometry, the tritetratrigonal tiling or shieldotritetragonal tiling is a uniform tiling of the hyperbolic plane. It has Schläfli symbol of t1,2(4,3,3). It can also be named as a cantic octagonal tiling, h2{8,3}.
| Cantic octagonal tiling | |
|---|---|
 Poincaré disk model of the hyperbolic plane | |
| Type | Hyperbolic uniform tiling |
| Vertex configuration | 3.6.4.6 |
| Schläfli symbol | h2{8,3} |
| Wythoff symbol | 4 3 | 3 |
| Coxeter diagram |     =     |
| Symmetry group | [(4,3,3)], (*433) |
| Dual | Order-4-3-3 t12 dual tiling |
| Properties | Vertex-transitive |
Dual tiling
Related polyhedra and tiling
| Uniform (4,3,3) tilings | |||||||||||
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| Symmetry: [(4,3,3)], (*433) | [(4,3,3)]+, (433) | ||||||||||
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| 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 | |||||||||||
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| 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 | ||||
| Symmetry *n32 [1+,2n,3] = [(n,3,3)] |
Spherical | Euclidean | Compact Hyperbolic | Paracompact | ||
|---|---|---|---|---|---|---|
| *233 [1+,4,3] = [3,3] |
*333 [1+,6,3] = [(3,3,3)] |
*433 [1+,8,3] = [(4,3,3)] |
*533 [1+,10,3] = [(5,3,3)] |
*633... [1+,12,3] = [(6,3,3)] |
*∞33 [1+,∞,3] = [(∞,3,3)] | |
| Coxeter Schläfli |
 =  h2{4,3} |
 = h2{6,3} |
= h2{8,3} |
 =  h2{10,3} |
 =  h2{12,3} |
 =  h2{∞,3} |
| Cantic figure |
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| Vertex | 3.6.2.6 | 3.6.3.6 | 3.6.4.6 | 3.6.5.6 | 3.6.6.6 | 3.6.∞.6 |
 Domain |
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| Wythoff | 2 3 | 3 | 3 3 | 3 | 4 3 | 3 | 5 3 | 3 | 6 3 | 3 | ∞ 3 | 3 |
| Dual figure |
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| Face | V3.6.2.6 | V3.6.3.6 | V3.6.4.6 | V3.6.5.6 | V3.6.6.6 | V3.6.∞.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
Wikimedia Commons has media related to Uniform tiling 3-6-4-6.
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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