| Cairo pentagonal tiling | |
|---|---|
| Type | Dual semiregular tiling |
| Faces | irregular pentagons |
| Face configuration | V3.3.4.3.4 |
| Symmetry group | 4*2 and 442 |
| Dual | Snub square tiling |
| Properties | face-transitive |
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. It is one of 14 known isohedral pentagon tilings.
Conway calls it a 4-fold pentille.[1]
This tiling can be seen as the union of two flattened perpendicular hexagonal tilings. Each hexagon is divided into four pentagons. These are not regular pentagons: their sides are not equal, and their angles in sequence are 120°, 120°, 90°, 120°, 90°.
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It is the dual of the snub square tiling, made of two squares and three equilateral triangles around each vertex.[2]
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 |