Truncated square tiling
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| Truncated square tiling | |
|---|---|
 |
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| Type | Uniform tiling |
| Vertex figure | 4.8.8 |
| Schläfli symbol | t{4,4} |
| Wythoff symbol | 2 | 4 4 | 4 4 2 |
| Coxeter-Dynkin |    |
| Symmetry | p4m |
| Dual | Tetrakis square tiling |
| Properties | Vertex-transitive |
 4.8.8 |
|
In geometry, the truncated square tiling is a semiregular tiling of the Euclidean plane. There is one square and two octagons on each vertex. This is the only edge-to-edge tiling by regular convex polygons which contains an octagon. It has Schläfli symbol of t0,1{4,4}.
Other names used for this pattern include Mediterranean tiling and octagonal tiling.
It is topologically related to the polyhedron truncated octahedron, 4.6.6
There are 3 regular and 8 semiregular tilings in the plane.
There are two distinct uniform colorings of a truncated square tiling. (Naming the colors by indices around a vertex (4.8.8): 122, 123.) The three colors can be considered from the same Wythoff construction, with the square degenerating into lines by two different ways.
 2 colors: 113 |
 3 colors: 123 |
 2 colors: 223 |
[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. p40
[edit] External links
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