Snub hexagonal tiling

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Snub hexagonal tiling
Type	Uniform tiling
Vertex figure	3.3.3.3.6
Schläfli symbol	s{6,3}
Wythoff symbol	| 6 3 2
Coxeter-Dynkin
Symmetry	p6
Dual	Floret pentagonal tiling
Properties	Vertex-transitive
3.3.3.3.6
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In geometry, the Snub hexagonal tiling (or snub trihexagonal tiling) is a semiregular tiling of the Euclidean plane. There are four triangles and one hexagon on each vertex. It has Schläfli symbol of s{3,6}.

Conway calls it a snub hexatille.

There are 3 regular and 8 semiregular tilings in the plane. This is the only one of the semiregular tilings which does not have a reflection as a symmetry.

This tiling is topologically related as a part of sequence of snubbed polyhedra with vertex figure (3.3.3.3.n).

(3.3.3.3.3)

(3.3.3.3.4)

(3.3.3.3.5)

3.3.3.3.6

3.3.3.3.7

There is only one uniform coloring of a snub hexagonal tiling. (Naming the colors by indices (3.3.3.3.6): 11213.)

[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