| 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 |
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}.
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Dual tiling
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 | |||
| 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)] | |
| CoxeterSchläfli | = h2{4,3} | = h2{6,3} | = h2{8,3} | = h2{10,3} | = h2{12,3} | = h2{∞,3} |
| Canticfigure | ||||||
| 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 |
| Dualfigure | ||||||
| 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
Wikimedia Commons has media related to Uniform tiling 3-6-4-6.- 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