Truncated trihexagonal tiling

Truncated trihexagonal tiling
Type	Semiregular tiling
Vertex configuration	4.6.12
Schläfli symbol	t0,1,2{6,3}
Wythoff symbol	2 6 3 |
Coxeter-Dynkin
Symmetry	p6m, [6,3], *632
Dual	Bisected hexagonal tiling
Properties	Vertex-transitive
Vertex figure: 4.6.12

In geometry, the truncated trihexagonal tiling is a semiregular tiling of the Euclidean plane. There are one square, one hexagon, and one dodecagon on each vertex. It has Schläfli symbol of t_0,1,2{3,6}.

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

Other names

• Great rhombitrihexagonal tiling
• Rhombitruncated trihexagonal tiling
• Omnitruncated hexagonal tiling, omnitruncated triangular tiling
• Conway calls it a truncated hexadeltille, constructed as a truncation operation applied to a trihexagonal tiling (hexadeltille).

Uniform colorings

There is only one uniform coloring of a truncated trihexagonal tiling, with faces colored by polygon sides.

A 2-uniform coloring allows for alternately colored hexagons.

Related polyhedra and tilings

This tiling is topologically related as a part of sequence of omnitruncated polyhedra with vertex figure (4.6.2p) and Coxeter-Dynkin diagram . The following forms exist as tilings of the hyperbolic plane, starting with the truncated triheptagonal tiling. This set of polyhedra are zonohedrons.

(4.6.4)	(4.6.6)	(4.6.8)	(4.6.10)
(4.6.12)	(4.6.14)	(4.6.16)	(4.6.18)

See also

• Tilings of regular polygons
• List of uniform tilings

References

• Williams, Robert (1979). The Geometrical Foundation of Natural Structure: A Source Book of Design. Dover Publications, Inc. p. 41. ISBN 0-486-23729-X. 
• John H. Conway, Heidi Burgiel, Chaim Goodman-Strass, The Symmetries of Things 2008, ISBN 978-1-56881-220-5 [2]

External links

• Weisstein, Eric W., "Uniform tessellation" from MathWorld.
• Weisstein, Eric W., "Semiregular tessellation" from MathWorld.
• Richard Klitzing, 2D Euclidean tilings, x3x6x - othat - O9