Truncated square tiling

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Truncated square tiling
Truncated square tiling
Type Uniform tiling
Vertex figure 4.8.8
Schläfli symbol t{4,4}
Wythoff symbol 2 | 4 4
4 4 2 |
Coxeter-Dynkin Image:CDW_ring.pngImage:CDW_4.pngImage:CDW_ring.pngImage:CDW_4.pngImage:CDW_dot.png
Image:CDW_ring.pngImage:CDW_4.pngImage:CDW_ring.pngImage:CDW_4.pngImage:CDW_ring.png
Symmetry p4m
Dual Tetrakis square tiling
Properties Vertex-transitive
Truncated square tiling
4.8.8
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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}.

Conway calls it a truncated quadrille.

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.)


2 colors: 122

3 colors: 123

[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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