Rhombitrihexagonal tiling

Rhombitrihexagonal tiling
Type	Semiregular tiling
Vertex configuration	3.4.6.4
Schläfli symbol	t0,2{6,3}
Wythoff symbol	3 | 6 2
Coxeter-Dynkin
Symmetry	p6m, [6,3], *632
Dual	Deltoidal trihexagonal tiling
Properties	Vertex-transitive
Vertex figure: 3.4.6.4

In geometry, the rhombitrihexagonal tiling is a semiregular tiling of the Euclidean plane. There are one triangle, two squares, and one hexagon on each vertex. It has Schläfli symbol of t_0,2{3, 6}.

Conway calls it a rhombihexadeltille. It can be considered a cantellated or expanded hexagonal tiling by Johnson's operational language.

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

Uniform colorings

There is only one uniform coloring in a rhombitrihexagonal tiling. (Naming the colors by indices around a vertex (3.4.6.4): 1232.)

Related polyhedra and tilings

This tiling is topologically related as a part of sequence of cantellated polyhedra with vertex figure (3.4.n.4), and continues as tilings of the hyperbolic plane. These vertex-transitive figures have (*n32) reflectional symmetry.

(3.4.3.4) (*332)	(3.4.4.4) (*432)	(3.4.5.4) (*532)
(3.4.6.4) (*632)	(3.4.7.4) (*732)	(3.4.8.4) (*832)

Gallery

An ornamental version

The game Kensington

See also

• Tilings of regular polygons
• List of uniform tilings

References

• 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. ISBN 0-486-23729-X.  p40
• John H. Conway, Heidi Burgiel, Chaim Goodman-Strass, The Symmetries of Things 2008, ISBN 978-1-56881-220-5 [1] (Chapter 21, Naming Archimedean and Catalan polyhedra and tilings.
• Weisstein, Eric W., "Uniform tessellation" from MathWorld.
• Weisstein, Eric W., "Semiregular tessellation" from MathWorld.
• Richard Klitzing, 2D Euclidean tilings, x3o6x - rothat - O8