Cantic octagonal tiling
Cantic octagonal tiling | |
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![]() 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 |
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}.
Dual tiling
Related polyhedra and tiling
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 | ||||||||||
![]() | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() | |||
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 | ||
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*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 | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() |
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 | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() |
Wythoff | 2 3 | 3 | 3 3 | 3 | 4 3 | 3 | 5 3 | 3 | 6 3 | 3 | ∞ 3 | 3 |
Dual figure | ![]() | ![]() | ![]() | |||
Face | V3.6.2.6 | V3.6.3.6 | V3.6.4.6 | V3.6.5.6 | V3.6.6.6 | V3.6.∞.6 |
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 3-6-4-6.
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.
External links
- Weisstein, Eric W. "Hyperbolic tiling". MathWorld.
- Weisstein, Eric W. "Poincaré hyperbolic disk". MathWorld.
- Hyperbolic and Spherical Tiling Gallery Archived 2013-03-24 at the Wayback Machine
- KaleidoTile 3: Educational software to create spherical, planar and hyperbolic tilings
- Hyperbolic Planar Tessellations, Don Hatch
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