Truncated hexagonal tiling
- Truncated hexagonal tiling
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).
Related polyhedra and tilings
This tiling is topologically related as a part of sequence of uniform truncated polyhedra with vertex figure (3.2n.2n), and continues into the hyperbolic plane. These vertex-transitive figures have (*n32) reflectional symmetry.
There are 3 regular and 8 semiregular tilings in the plane.
There is only one uniform coloring of a truncated hexagonal tiling. (Naming the colors by indices around a vertex: 122.) The tiling colors shown in the table is a mixture of 3 types of colored-vertices (a 3-uniform coloring).
See also
* Tilings of regular polygons
* List of uniform tilings
References
* John H. Conway, Heidi Burgiel, Chaim Goodman-Strass, "The Symmetry of Things" 2008, ISBN 978-1-56881-220-5 [http://www.akpeters.com/product.asp?ProdCode=2205]
* (Chapter 2.1: "Regular and uniform tilings", p.58-65)
* Williams, Robert "The Geometrical Foundation of Natural Structure: A Source Book of Design" New York: Dover, 1979. p39
External links
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