# Elongated triangular tiling

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Elongated triangular tiling

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 Euclidean 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.

This 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.

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.

ee also

* Tilings of regular polygons

References

* (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. p37

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