Cairo pentagonal tiling
Encyclopedia
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 tiling
s.
Conway
calls it a 4-fold pentille.
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°.
of the snub square tiling, made of two squares and three equilateral triangles around each vertex.
Geometry
Geometry arose as the field of knowledge dealing with spatial relationships. Geometry was one of the two fields of pre-modern mathematics, the other being the study of numbers ....
, 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 tiling
Pentagon tiling
In geometry, a pentagon tiling is a tiling of the plane by pentagons. A regular pentagonal tiling on the Euclidean plane is impossible because the internal angle of a regular pentagon, 108 is not a divisor of 360...
s.
Conway
John Horton Conway
John Horton Conway is a prolific mathematician active in the theory of finite groups, knot theory, number theory, combinatorial game theory and coding theory...
calls it a 4-fold pentille.
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°.
Dual tiling
It is the dualDual polyhedron
In geometry, polyhedra are associated into pairs called duals, where the vertices of one correspond to the faces of the other. The dual of the dual is the original polyhedron. The dual of a polyhedron with equivalent vertices is one with equivalent faces, and of one with equivalent edges is another...
of the snub square tiling, made of two squares and three equilateral triangles around each vertex.
Related polyhedra and 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. Basketweave tiling |
 Cairo tiling overlay |