Truncated hexagonal tiling

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Truncated hexagonal tiling
Type	Uniform tiling
Vertex figure	3.12.12
Schläfli symbol	t{6,3}
Wythoff symbol	2 3 | 6 3 3 | 3
Coxeter-Dynkin
Symmetry	p6m
Dual	Triakis triangular tiling
Properties	Vertex-transitive
3.12.12
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In geometry, the truncated hexagonal tiling is a semiregular tiling of the Euclidean plane. There are 2 dodecagons (12-sides) and one triangle on each vertex. It has Schläfli symbol of t_0,1{6,3} or t_1,2{3,6}.

Conway calls it a truncated hextille.

This tiling is topologically related as a part of sequence of uniform truncated polyhedra with vertex figure (3.2n.2n), and continues into the hyperbolic plane.

(3.4.4)

(3.6.6)

(3.8.8)

(3.10.10)

(3.12.12)

(3.14.14)

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

There is only one uniform colorings of a truncated hexagonal tiling. (Naming the colors by indices around a vertex: 122.) The coloring shown is a mixture of 3 types of colored-vertices.

[edit] See also

• Tilings of regular polygons
• List of uniform tilings

[edit] 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 The Geometrical Foundation of Natural Structure: A Source Book of Design New York: Dover, 1979. p39