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Encyclopedia > Cairo pentagonal tiling
Cairo pentagonal tiling
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 planar, face-uniform

In geometry, the Cairo pentagonal tiling is a dual semiregular tiling of the Euclidean plane. This article needs to be cleaned up to conform to a higher standard of quality. ... Look up pentagon in Wiktionary, the free dictionary. ... In geometry, a face configuration is notational description of a face-uniform polyhedron. ... The symmetry group of an object (e. ... In geometry, polyhedra are associated into pairs called duals, where the vertices of one correspond to the faces of the other. ... In geometry, the snub square tiling is a semiregular tiling of the Euclidean plane. ... Something is called planar if it is made up of flat planes, or pertaining to planes. ... In geometry, a polyhedron is face-uniform when all its faces have the same shape and size (technically, when all faces are congruent). ... Table of Geometry, from the 1728 Cyclopaedia. ...


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. In geometry, the hexagonal tiling is a regular tiling of the Euclidean plane. ... A regular hexagon. ... This is an article about the geometrical shape. ...

Contents

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. In geometry, the snub square tiling is a semiregular tiling of the Euclidean plane. ...


Basketweave tiling

Cairo tiling overlay

Download high resolution version (1587x1587, 940 KB)Illustration of p4g type Wallpaper group (bathroom floor tiling) File links The following pages link to this file: Wallpaper group Talk:Wallpaper group Categories: Public domain images ...

See also

This article needs to be cleaned up to conform to a higher standard of quality. ... This table shows the 11 uniform tilings of the plane, and their dual tilings. ...

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.

Branko Grünbaum is a mathematician who works mainly in geometry and is considered a founder of discrete geometry. ... This is a disambiguation page — a navigational aid which lists other pages that might otherwise share the same title. ...

External links

  • Weisstein, Eric W., Cairo Tessellation at MathWorld.
  • 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

  Results from FactBites:
 
Alhambra (204 words)
The unit cell of the Cairo tiling is a pentagon, but the tiling can also be viewed as two sets of hexagons intersecting at right angles.
A move consists of covering one of the pentagons on the board with a tile from your hand, and drawing another tile from the bag to bring the total to four again.
A tile may not be played onto a cell where either the horizontally- or vertically-oriented hexagon already contains a tile of that color.
  More results at FactBites »


 
 

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