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In geometry, the 'Cairo pentagonal tiling' is a dual semiregular tiling of the Euclidean plane.
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.

Contents

Geometric variations

See also

References

External links

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

See also

★ Tilings of regular polygons

★ List of uniform planar tilings

References

★ Tilings and Patterns, Grünbaum, Branko ; and Shephard, G. C., , , W. H. Freeman, 1987, 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.

External links

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★ http://www.mathsyear2000.co.uk/explorer/morphing/05newfromold.shtml

★ http://home.flash.net/~markthom/html/alhambra.html

★ http://www.geocities.com/williamwchow/java/j8.htm

★ http://www.decrete.com/stencils/basketweave