Great rhombitrihexagonal tiling

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Great rhombitrihexagonal tiling
Type	Uniform tiling
Vertex figure	4.6.12
Schläfli symbol
Wythoff symbol	2 6 3 |
Coxeter-Dynkin
Symmetry	p6m
Dual	Bisected hexagonal tiling
Properties	Vertex-transitive
4.6.12
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In geometry, the Great rhombitrihexagonal tiling (or Omnitruncated trihexagonal tiling) is a semiregular tiling of the Euclidean plane. There are one square, one hexagon, and one dodecagon (12-sides) on each vertex. It has Schläfli symbol of t_0,1,2{3,6}.

Conway calls it a truncated hexadeltille.

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

This tiling is topologically related as a part of sequence of omnitruncated polyhedra with vertex figure (4.6.2n). This set of polyhedra are zonohedrons.

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

There is only one uniform colorings of a Great rhombitrihexagonal tiling. (Naming the colors by indices around a vertex: 123.)

[edit] See also

• Tilings of regular polygons
• List of uniform tilings

[edit] References

• Robert Williams The Geometrical Foundation of Natural Structure: A Source Book of Design New York: Dover, 1979. p41