| 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 |
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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.[1]
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.
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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.