Related Polyhedra and Tilings
The rhombille tiling is a part of a set of uniform dual tilings, corresponding to the dual of the trihexagonal tiling.
| Symmetry:, (*632) | +, (632) | , (*333) | , (3*3) | |||||||
|---|---|---|---|---|---|---|---|---|---|---|
| {6,3} | t0,1{6,3} | t1{6,3} | t1,2{6,3} | t2{6,3} | t0,2{6,3} | t0,1,2{6,3} | s{6,3} | h{6,3} | h1,2{6,3} | |
| Uniform duals | ||||||||||
| V6.6.6 | V3.12.12 | V3.6.3.6 | V6.6.6 | V3.3.3.3.3.3 | V3.4.12.4 | V.4.6.12 | V3.3.3.3.6 | V3.3.3.3.3.3 | ||
This tiling is a part of a sequence of rhombic polyhedra and tilings with Coxeter group symmetry, starting from the cube, which can be seen as a rhombic hexahedron where the rhombi are squares. The nth element in this sequence has a face configuration of V3.n.3.n.
| Symmetry *n32 |
Spherical | Euclidean | Hyperbolic tiling | ||||
|---|---|---|---|---|---|---|---|
| *332 Td |
*432 Oh |
*532 Ih |
*632 p6m |
*732 |
*832 |
*∞32 |
|
| Quasiregular figures configuration |
3.3.3.3 |
3.4.3.4 |
3.5.3.5 |
3.6.3.6 |
3.7.3.7 |
3.8.3.8 |
3.∞.3.∞ |
| Coxeter diagram | |||||||
| Dual (rhombic) figures configuration |
V3.3.3.3 |
V3.4.3.4 |
V3.5.3.5 |
V3.6.3.6 |
V3.7.3.7 |
V3.8.3.8 |
V3.∞.3.∞ |
| Coxeter diagram | |||||||
The rhombille tiling is periodic, meaning that it has a two-dimensional group of symmetries, but there also exist aperiodic tilings based on rhombi, notably the Penrose tiling which uses two kinds of rhombi with 36° and 72° acute angles. Another aperiodic tiling, the sphinx tiling, is like the rhombille tiling based on the hexagonal lattice.
The rhombille tiling has *632 symmetry, but vertices can be colored with alternating colors on the inner points leading to a *333 symmetry.
| Image | (2 colors) |
(3 colors) |
|---|---|---|
| Symmetry | p6m, (*632) | p3m1, ], (*333) |
| Coxeter |
Read more about this topic: Rhombille Tiling
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