• Source: Snub square tiling

In geometry, the snub square tiling is a semiregular tiling of the Euclidean plane. There are three triangles and two squares on each vertex. Its Schläfli symbol is s{4,4}.
Conway calls it a snub quadrille, constructed by a snub operation applied to a square tiling (quadrille).
There are 3 regular and 8 semiregular tilings in the plane.




Uniform colorings


There are two distinct uniform colorings of a snub square tiling. (Naming the colors by indices around a vertex (3.3.4.3.4): 11212, 11213.)




Circle packing


The snub square tiling can be used as a circle packing, placing equal diameter circles at the center of every point. Every circle is in contact with 5 other circles in the packing (kissing number).




Wythoff construction


The snub square tiling can be constructed as a snub operation from the square tiling, or as an alternate truncation from the truncated square tiling.
An alternate truncation deletes every other vertex, creating a new triangular faces at the removed vertices, and reduces the original faces to half as many sides. In this case starting with a truncated square tiling with 2 octagons and 1 square per vertex, the octagon faces into squares, and the square faces degenerate into edges and 2 new triangles appear at the truncated vertices around the original square.
If the original tiling is made of regular faces the new triangles will be isosceles. Starting with octagons which alternate long and short edge lengths, derived from a regular dodecagon, will produce a snub tiling with perfect equilateral triangle faces.
Example:




Related tilings























= Related k-uniform tilings

=
This tiling is related to the elongated triangular tiling which also has 3 triangles and two squares on a vertex, but in a different order, 3.3.3.4.4. The two vertex figures can be mixed in many k-uniform tilings.




= Related topological series of polyhedra and tiling

=
The snub square tiling is third in a series of snub polyhedra and tilings with vertex figure 3.3.4.3.n.

The snub square tiling is third in a series of snub polyhedra and tilings with vertex figure 3.3.n.3.n.




See also



List of uniform planar tilings
Snub (geometry)
Snub square prismatic honeycomb
Tilings of regular polygons
Elongated triangular tiling




References



John H. Conway, Heidi Burgiel, Chaim Goodman-Strauss, The Symmetries of Things 2008, ISBN 978-1-56881-220-5 [1]
Klitzing, Richard. "2D Euclidean tilings s4s4s - snasquat - O10".
Grünbaum, Branko; Shephard, G. C. (1987). Tilings and Patterns. New York: W. H. Freeman. ISBN 0-7167-1193-1. (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. ISBN 0-486-23729-X. p38
Dale Seymour and Jill Britton, Introduction to Tessellations, 1989, ISBN 978-0866514613, pp. 50–56, dual p. 115




External links


Weisstein, Eric W. "Semiregular tessellation". MathWorld.

Kata Kunci Pencarian:

• Daftar bentuk matematika
• Snub square tiling
• Square tiling
• Cairo pentagonal tiling
• List of Euclidean uniform tilings
• List of mathematical shapes
• Snub order-6 square tiling
• Snub pentapentagonal tiling
• List of polygons, polyhedra and polytopes
• Snub tetraheptagonal tiling
• Cubic honeycomb