Snub hexagonal tiling

Snub hexagonal tiling
Type	Semiregular tiling
Vertex configuration	3.3.3.3.6
Schläfli symbol	s{6,3}
Wythoff symbol	| 6 3 2
Coxeter-Dynkin
Symmetry	p6, [6,3]+, 632
Dual	Floret pentagonal tiling
Properties	Vertex-transitive chiral
Vertex figure: 3.3.3.3.6

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, constructed as a snub operation applied to a hexagonal tiling (hexatille).

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

Related polyhedra and tilings

This tiling is part of sequence of snubbed polyhedra with vertex figure (3.3.3.3.p) and Coxeter-Dynkin diagram . These face-transitive figures have (n32) rotational symmetry.

(3.3.3.3.3) (332)	(3.3.3.3.4) (432)	(3.3.3.3.5) (532)
3.3.3.3.6 (632)	3.3.3.3.7 (732)	3.3.3.3.8 (832)

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

See also

• Tilings of regular polygons
• List of uniform tilings

References

• John H. Conway, Heidi Burgiel, Chaim Goodman-Strass, The Symmetries of Things 2008, ISBN 978-1-56881-220-5 [1]
• 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.  p.39

External links

• Weisstein, Eric W., "Uniform tessellation" from MathWorld.
• Weisstein, Eric W., "Semiregular tessellation" from MathWorld.
• Richard Klitzing, 2D Euclidean tilings, s3s6s - snathat - O11