Snub trihexagonal tiling

Snub trihexagonal tiling
Type	Semiregular tiling
Vertex configuration	3.3.3.3.6
Schläfli symbol	sr{6,3} or $s{\begin{Bmatrix}6\\3\end{Bmatrix}}$
Wythoff symbol	| 6 3 2
Coxeter diagram
Symmetry	p6, [6,3]+, (632)
Rotation symmetry	p6, [6,3]+, (632)
Bowers acronym	Snathat
Dual	Floret pentagonal tiling
Properties	Vertex-transitive chiral

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}.

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 vertex-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 planar tilings

References

• Grünbaum, Branko ; and Shephard, G. C. (1987). Tilings and Patterns. New York: W. H. Freeman. ISBN 0-716-71193-1.{{cite book}}: CS1 maint: multiple names: authors list (link) (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