Elongated triangular tiling
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| Elongated triangular tiling | |
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| Type | Uniform tiling |
|---|---|
| Vertex figure | 3.3.3.4.4 |
| Schläfli symbol | {3,6}:e |
| Wythoff symbol | 2 | 2 (2 2) |
| Coxeter-Dynkin | none |
| Symmetry | cmm |
| Dual | Prismatic pentagonal tiling |
| Properties | Vertex-transitive |
 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.
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.
This is also the only uniform tiling that can't be created as a Wythoff construction.
There is only one uniform colorings of an elongated triangular tiling. (Naming the colors by indices around a vertex (3.3.3.4.4): 11122.) Second nonuniform coloring 11123 also exists. The coloring shown is a mixture of 12134 and 21234 colorings.
[edit] See also
[edit] 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 The Geometrical Foundation of Natural Structure: A Source Book of Design New York: Dover, 1979. p37
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