| Pentahexagonal tiling |
|---|
| Poincaré disk model of the hyperbolic plane |
| Type | Hyperbolic uniform tiling |
| Vertex configuration | (5.62 |
| Schläfli symbol | r{6,5} or { 6 5 } {\displaystyle {\begin{Bmatrix}6\\5\end{Bmatrix}}} |
| Wythoff symbol | 2 | 6 5 |
| Coxeter diagram | |
| Symmetry group | [6,5], (*652) |
| Dual | Order-6-5 rhombille tiling |
| Properties | Vertex-transitive edge-transitive |
In geometry, the pentahexagonal tiling is a uniform tiling of the hyperbolic plane. It has Schläfli symbol of r{6,5} or t1{6,5}.
Uniform colorings
Related polyhedra and tiling
| Uniform hexagonal/pentagonal tilings vte |
|---|
| Symmetry: [6,5], (*652) | [6,5]+, (652) | [6,5+], (5*3) | [1+,6,5], (*553) |
| | | | | | | | | |
| | | | | | | | | |
| {6,5} | t{6,5} | r{6,5} | 2t{6,5}=t{5,6} | 2r{6,5}={5,6} | rr{6,5} | tr{6,5} | sr{6,5} | s{5,6} | h{6,5} |
| Uniform duals |
| | | | | | | | | |
| | | | | | | | | |
| V65 | V5.12.12 | V5.6.5.6 | V6.10.10 | V56 | V4.5.4.6 | V4.10.12 | V3.3.5.3.6 | V3.3.3.5.3.5 | V(3.5)5 |
| *5n2 symmetry mutations of quasiregular tilings: (5.n)2 vte |
|---|
| Symmetry *5n2 [n,5] | Spherical | Hyperbolic | Paracompact | Noncompact |
| *352 [3,5] | *452 [4,5] | *552 [5,5] | *652 [6,5] | *752 [7,5] | *852 [8,5]... | *∞52 [∞,5] | [ni,5] |
| Figures | | | | | | | | |
| Config. | (5.3)2 | (5.4)2 | (5.5)2 | (5.6)2 | (5.7)2 | (5.8)2 | (5.∞)2 | (5.ni)2 |
| Rhombic figures | | | | | | | | |
| Config. | V(5.3)2 | V(5.4)2 | V(5.5)2 | V(5.6)2 | V(5.7)2 | V(5.8)2 | V(5.∞)2 | V(5.∞)2 |
| Symmetry mutation of quasiregular tilings: (6.n)2 vte |
|---|
| Symmetry *6n2 [n,6] | Euclidean | Compact hyperbolic | Paracompact | Noncompact |
| *632 [3,6] | *642 [4,6] | *652 [5,6] | *662 [6,6] | *762 [7,6] | *862 [8,6]... | *∞62 [∞,6] | [iπ/λ,6] |
| Quasiregular figures configuration | 6.3.6.3 | 6.4.6.4 | 6.5.6.5 | 6.6.6.6 | 6.7.6.7 | 6.8.6.8 | 6.∞.6.∞ | 6.∞.6.∞ |
| Dual figures |
| Rhombic figures configuration | V6.3.6.3 | V6.4.6.4 | V6.5.6.5 | V6.6.6.6 | V6.7.6.7 | V6.8.6.8 | V6.∞.6.∞ | |
| [(5,5,3)] reflective symmetry uniform tilings |
|---|
| | | | | | |
- John H. Conway, Heidi Burgiel, Chaim Goodman-Strauss, The Symmetries of Things 2008, ISBN978-1-56881-220-5 (Chapter 19, The Hyperbolic Archimedean Tessellations)
- "Chapter 10: Regular honeycombs in hyperbolic space". The Beauty of Geometry: Twelve Essays. Dover Publications. 1999. ISBN0-486-40919-8. LCCN.
See also
External links