Trihexagonal tiling

In geometry, the trihexagonal tiling is a semiregular tiling of the Euclidean plane. There are two triangles and two hexagons alternating on each vertex. It has Schläfli symbol of "t₁{6,3}".

Conway calls it a hexadeltille, combining alternate elements from a hexagonal tiling (Hextille) and triangular tiling (deltille).

There are 3 regular and 8 semiregular tilings in the plane.

There are two distinct uniform colorings of a trihexagonal tiling. (Naming the colors by indices on the 4 faces around a vertex (3.6.3.6): 1212, 1232.)

Related polyhedra and tilings

This tiling is topologically part of sequence of rectified polyhedra with vertex figure (3.n.3.n) and (*n32) reflectional symmetry.

This tiling is also topologically part of sequence of polyhedra and tilings with vertex figure (3.2n.3.2n) and (*n33) reflectional symmetry.

See also

* Tilings of regular polygons
* List of uniform tilings
* Kagome lattice

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. p38

External links

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