Truncated hexagonal tiling
| 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 |
[edit] Uniform colorings
There is only one uniform coloring of a truncated hexagonal tiling. (Naming the colors by indices around a vertex: 122.)
[edit] Related polyhedra and tilings
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.
[edit] See also
[edit] References
- John H. Conway, Heidi Burgiel, Chaim Goodman-Strass, The Symmetries of Things 2008, ISBN 978-1-56881-220-5 [1]
- Grünbaum, Branko ; and Shephard, G. C. (1987). Tilings and Patterns. New York: W. H. Freeman. ISBN 0-716-71193-1. (Chapter 2.1: Regular and uniform tilings, p.58-65)
- Williams, Robert (1979). The Geometrical Foundation of Natural Structure: A Source Book of Design. Dover Publications, Inc. p. 39. ISBN 0-486-23729-X.
[edit] External links
- Weisstein, Eric W., "Semiregular tessellation" from MathWorld.
- Richard Klitzing, 2D Euclidean tilings, o3x6x - toxat - O7
 |
This geometry-related article is a stub. You can help Wikipedia by expanding it. |
