| Snub hexagonal tiling | |
|---|---|
| Type | Semiregular tiling |
| Vertex configuration | 3.3.3.3.6 |
| Schläfli symbol | s{6,3} |
| Wythoff symbol | | 6 3 2 |
| Coxeter-Dynkin | |
| Symmetry | p6, [6,3]+, 632 |
| Dual | Floret pentagonal tiling |
| Properties | Vertex-transitive chiral |
Vertex figure: 3.3.3.3.6 |
|
In geometry, the Snub hexagonal tiling (or snub trihexagonal tiling) is a semiregular tiling of the Euclidean plane. There are four triangles and one hexagon on each vertex. It has Schläfli symbol of s{3,6}.
Conway calls it a snub hexatille, constructed as a snub operation applied to a hexagonal tiling (hexatille).
There are 3 regular and 8 semiregular tilings in the plane. This is the only one which does not have a reflection as a symmetry.
Contents |
This tiling is part of sequence of snubbed polyhedra with vertex figure (3.3.3.3.p) and Coxeter-Dynkin diagram . These face-transitive figures have (n32) rotational symmetry.
(3.3.3.3.3) (332) |
(3.3.3.3.4) (432) |
(3.3.3.3.5) (532) |
3.3.3.3.6 (632) |
3.3.3.3.7 (732) |
3.3.3.3.8 (832) |
There is only one uniform coloring of a snub hexagonal tiling. (Naming the colors by indices (3.3.3.3.6): 11213.)