Cairo pentagonal tiling

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Cairo pentagonal tiling

Type	Dual semiregular tiling
Faces	irregular pentagons
Edges	Infinite
Vertices	Infinite
Face configuration	V3.3.4.3.4
Symmetry group	p4g
Dual	Snub square tiling
Properties	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.

1 Geometric variations
2 See also
3 References
4 External links

[edit] Geometric variations

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.

Basketweave tiling

Cairo tiling overlay

[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. p38
Wells, David, The Penguin Dictionary of Curious and Interesting Geometry. London: Penguin, p. 23, 1991.