| Truncated hexagonal tiling | |
|---|---|
| Type | Semiregular tiling |
| Vertex configuration | 3.12.12 |
| Schläfli symbol | t0,1{6,3} |
| Wythoff symbol | 2 3 | |
| Coxeter-Dynkin | |
| Symmetry | p6m, [6,3], *632 |
| Dual | Triakis triangular tiling |
| Properties | Vertex-transitive |
Vertex figure: 3.12.12 |
|
In geometry, the truncated hexagonal tiling is a semiregular tiling of the Euclidean plane. There are 2 dodecagons (12-sides) and one triangle on each vertex.
As the name implies this tiling is constructed by a truncation operation applies to a hexagonal tiling, leaving dodecagons in place of the original hexagons, and new triangles at the original vertex locations. It is given an extended Schläfli symbol of t0,1{6,3}.
Conway calls it a truncated hextille, constructed as a truncation operation applied to a hexagonal tiling (hextille).
There are 3 regular and 8 semiregular tilings in the plane.
Contents |
There is only one uniform coloring of a truncated hexagonal tiling. (Naming the colors by indices around a vertex: 122.)
The dodecagonal faces can be distorted into hexagramatic facets:
This tiling is topologically related as a part of sequence of uniform truncated polyhedra with vertex configurations (3.2n.2n), and [n,3] Coxeter group symmetry.
3.4.4 |
3.6.6 |
3.8.8 |
3.10.10 |
3.12.12 |
3.14.14 |
3.16.16 |
3.∞.∞ |
There are 3 regular and 8 semiregular tilings in the plane.