Tetrakis square tiling
| Tetrakis square tiling | |
|---|---|
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| Type | Dual semiregular tiling |
| Faces | 45-45-90 triangle |
| Face configuration | V4.8.8 |
| Symmetry group | *442 |
| Dual | Truncated square tiling |
| Properties | face-transitive |
In geometry, the tetrakis square tiling is a tiling of the Euclidean plane. It is square tiling with each square divided into four triangles from the center point, forming an infinite arrangement of lines.
Conway calls it a kisquadrille[1], represented by a kis operation that adds a center point and triangles to replace the faces of a square tiling (quadrille). It is also called the Union Jack lattice because of the similitude of its unit cell to the UK flag.
It is labeled V4.8.8 because each isosceles triangle face has two types of vertices: one with 4 triangles, and two with 8 triangles.
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[edit] Dual tiling
It is the dual tessellation of the truncated square tiling which has one square and two octagons at each vertex.[2]
[edit] Related polyhedra and tilings
It is topologically related to the polyhedron tetrakis hexahedron, V4.6.6
The symmetry type is:
- with the coloring: cmm; a primitive cell is 8 triangles, a fundamental domain 2 triangles (1/2 for each color)
- with the dark triangles in black and the light ones in white: p4g; a primitive cell is 8 triangles, a fundamental domain 1 triangle (1/2 each for black and white)
- with the edges in black and the interiors in white: p4m; a primitive cell is 2 triangles, a fundamental domain 1/2
[edit] See also
[edit] Notes
- ^ John H. Conway, Heidi Burgiel, Chaim Goodman-Strass, The Symmetries of Things 2008, ISBN 978-1-56881-220-5 [1] (Chapter 21, Naming Archimedean and Catalan polyhedra and tilings, p288 table)
- ^ Weisstein, Eric W., "Dual tessellation" from MathWorld.
[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 (1979). The Geometrical Foundation of Natural Structure: A Source Book of Design. Dover Publications, Inc. p. 40. ISBN 0-486-23729-X.
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