Topological Relations
This tiling is related to the trihexagonal tiling by dividing the triangles and hexagons into central triangles and merging neighboring triangles into kites.
This tiling is topologically related to three catalan solids, with face configurations 3.4.n.4, and the sequence continues into tilings of the hyperbolic plane. These face-transitive figures have (*n32) reflectional symmetry.
V3.4.3.4 (*332) and (*432) |
V3.4.4.4 (*432) |
V3.4.5.4 (*532) |
V3.4.6.4 (*632) |
V3.4.7.4 (*732) |
The deltoidal trihexagonal tiling is a part of a set of uniform dual tilings, corresponding to the dual of the rhombitrihexagonal tiling.
| Wythoff | 3 | 6 2 | 2 3 | 6 | 2 | 6 3 | 2 6 | 3 | 6 | 3 2 | 6 3 | 2 | 6 3 2 | | | 6 3 2 | |||
|---|---|---|---|---|---|---|---|---|---|---|---|
| Schläfli | {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} | h0{6,3} | h1,2{6,3} | |
| Coxeter | |||||||||||
| Image Vertex figure |
6.6.6 |
3.12.12 |
3.6.3.6 |
6.6.6 |
{36} |
3.4.6.4 |
4.6.12 |
3.3.3.3.6 |
(3.3)3 |
3.3.3.3.3.3 |
|
| Uniform duals | |||||||||||
| Coxeter | |||||||||||
| Image Vertex figure |
V6.6.6 |
V3.12.12 |
V3.6.3.6 |
V6.6.6 |
V3.3.3.3.3.3 |
V3.4.6.4 |
V4.6.12 |
V3.3.3.3.6 |
V(3.3)3 |
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Read more about this topic: Deltoidal Trihexagonal Tiling
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