Cairo pentagonal tiling

Infobox face-uniform tiling


Type = Dual semiregular tiling
Face_List = irregular pentagons
Symmetry_Group = p4g
or 4*2 and 442
Face_Type = V3.3.4.3.4
Dual = Snub square tiling
Property_List = face-transitive
In geometry, the Cairo pentagonal tiling is a dual semiregular tiling of the Euclidean plane.

Conway calls it a 4-fold pentille.

It is given its name because it appears on the streets of Cairo and in many Islamic decorations.

This tiling can be seen as the union of two flattened perpendicular hexagonal tilings. Each hexagon is divided into four pentagons.

Related tilings

As a dual to the snub square tiling the geometric proportions are fixed for this tiling. However it can be adjusted to other geometric forms with the same topological connectivity and different symmetry. For example, this rectangular tiling is topologically identical.

ee also

* Tilings of regular polygons
* List of uniform planar tilings

References

* John H. Conway, Heidi Burgiel, Chaim Goodman-Strass, "The Symmetry of Things" 2008, ISBN 978-1-56881-220-5 [http://www.akpeters.com/product.asp?ProdCode=2205]
* (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. p38
* Wells, David, "The Penguin Dictionary of Curious and Interesting Geometry." London: Penguin, p. 23, 1991.

External links

*
* http://home.flash.net/~markthom/html/alhambra.html
* http://www.geocities.com/williamwchow/java/j8.htm
* http://www.decrete.com/stencils/basketweave