Snub hexagonal tiling

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 of the semiregular tilings which does not have a reflection as a symmetry.

This tiling is part of sequence of snubbed polyhedra with vertex figure (3.3.3.3.p) and Coxeter-Dynkin diagram .

There is only one uniform coloring of a snub hexagonal tiling. (Naming the colors by indices (3.3.3.3.6): 11213.)

ee 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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