Quarter order-6 square tiling
| Quarter order-6 square tiling | |
|---|---|
 Poincaré disk model of the hyperbolic plane | |
| Type | Hyperbolic uniform tiling |
| Vertex figure | 3.4.6.6.4 |
| Schläfli symbol | q{4,6} |
| Coxeter diagram |     =   =   =   or  or or |
| Dual | ? |
| Properties | Vertex-transitive |
In geometry, the quarter order-6 square tiling is a uniform tiling of the hyperbolic plane. It has Schläfli symbol of q{4,6}. It is constructed from *3232 orbifold notation, and can be seen as a half symmetry of *443 and *662, and quarter symmetry of *642.
Images
Projections centered on a vertex, triangle and hexagon:
Related polyhedra and tiling
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| Vertex figure |
66 | (3.4.3.4)2 | 3.4.6.6.4 | 6.4.6.4 | ||||
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| 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)} |
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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 |
See also
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.
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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