Truncated hexagonal tiling
Semiregular tiling of a plane
| Truncated hexagonal tiling | |
|---|---|
| Type | Semiregular tiling |
| Vertex configuration | 3.12.12 |
| Schläfli symbol | t{6,3} |
| Wythoff symbol | 2 3 | 6 |
| Coxeter diagram | |
| Symmetry | p6m, [6,3], (*632) |
| Rotation symmetry | p6, [6,3]+, (632) |
| Bowers acronym | Toxat |
| Dual | Triakis triangular tiling |
| Properties | Vertex-transitive |
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 applied 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 t{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.
01Uniform colorings
There is only one uniform coloring of a truncated hexagonal tiling. (Naming the colors by indices around a vertex: 122.)
02Topologically identical tilings
The dodecagonal faces can be distorted into different geometries, such as:
Sources and credits
This article is adapted from the Wikipedia article “Truncated hexagonal tiling”, written by its contributors and licensed under CC BY-SA 4.0. Fathomly has changed the layout, removed citation markers, navigation and maintenance notices, and adjusted punctuation. This adapted version is shared under the same license. For references, see the original article.
Images, from Wikimedia Commons:
- Tiling truncated 6 simple.svg by Watchduck You can name the author as "T. Piesk", "Tilman Piesk" or "Watchduck"., CC BY 4.0
- Contracted truncated hexagonal tilings.png by Tomruen, CC BY-SA 4.0
- Wallpaper group-p6m-6.jpg by Unknown author, Public domain
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