Elongated triangular tiling

Elongated triangular tiling
Type	Semiregular tiling
Vertex configuration	3.3.3.4.4
Schläfli symbol	{3,6}:e
Wythoff symbol	2 | 2 (2 2)
Coxeter-Dynkin	None
Symmetry	cmm, [∞,2+,∞], 2*22
Dual	Prismatic pentagonal tiling
Properties	Vertex-transitive
Vertex figure: 3.3.3.4.4

In geometry, the elongated triangular tiling is a semiregular tiling of the Euclidean plane. There are three triangles and two squares on each vertex.

Conway calls it a isosnub quadrille.

There are 3 regular and 8 semiregular tilings in the plane. This tiling is related to the snub square tiling which also has 3 triangles and two squares on a vertex, but in a different order. It is also the only uniform tiling that can't be created as a Wythoff construction. It can be constructed as alternate layers of apeirogonal prisms and apeirogonal antiprisms.

Uniform colorings

There is only one uniform coloring of an elongated triangular tiling. (Naming the colors by indices around a vertex (3.3.3.4.4): 11122.) A second nonuniform coloring 11123 also exists. The coloring shown is a mixture of 12134 and 21234 colorings.

See also

• Tilings of regular polygons

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 (1979). The Geometrical Foundation of Natural Structure: A Source Book of Design. Dover Publications, Inc. ISBN 0-486-23729-X.  p37

External links

• Weisstein, Eric W., "Uniform tessellation" from MathWorld.
• Weisstein, Eric W., "Semiregular tessellation" from MathWorld.
• Richard Klitzing, 2D Euclidean tilings, elong( x3o6o ) - etrat - O4