| 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
| Similar H2 tilings in *3232 symmetry | ||||||||
|---|---|---|---|---|---|---|---|---|
| Coxeter diagrams |  | | |  | ||||
 |  |  | | | |  | | |
| | | | | |||||
| Vertex figure | 66 | (3.4.3.4)2 | 3.4.6.6.4 | 6.4.6.4 | ||||
| Image |  |  | |  | ||||
| Dual |  |  | ||||||
| Uniform (4,4,3) tilings | ||||||||||
|---|---|---|---|---|---|---|---|---|---|---|
| Symmetry: [(4,4,3)] (*443) | [(4,4,3)]+ (443) | [(4,4,3+)] (3*22) | [(4,1+,4,3)] (*3232) | |||||||
 | | | | | | |   | | | |
| | | | | | | | | | | |
 |  |  |  |  |  |  |  |  |  | |
| h{6,4} t0(4,4,3) | h2{6,4} t0,1(4,4,3) | {4,6}1/2 t1(4,4,3) | h2{6,4} t1,2(4,4,3) | h{6,4} t2(4,4,3) | r{6,4}1/2 t0,2(4,4,3) | t{4,6}1/2 t0,1,2(4,4,3) | s{4,6}1/2 s(4,4,3) | hr{4,6}1/2 hr(4,3,4) | h{4,6}1/2 h(4,3,4) | q{4,6} h1(4,3,4) |
| Uniform duals | ||||||||||
 |  |  |  | |||||||
| 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-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
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