Under a religious prohibition on depicting life-like figures, Islamic artists designed elaborate abstract decorations. Their designs are based on
calligraphy, abstract representations of foliage and intricate tessellations. Tessellations are regular patterns of tiles that cover surfaces without overlapping or leaving any gaps.
Just three types of regular polygon tessellate by themselves: equilateral triangles, squares and regular hexagons. In order to tessellate, the sum of the
angles around each vertex or point where the tiles meet must be 360°. For example, the angles of a square are 90°, so four squares meet at each vertex in the tessellation.
Using combinations of two or more different regular polygons it is possible to produce eight semi-regular tessellations. They are known as the
Archimedean tessellations, because they were first tabulated by Archimedes in a work that is now lost. One example is the tessellation of equilateral triangles, squares and regular hexagons in which two squares, a
triangle and a hexagon surround each meeting point. The sum of the angles meeting at each of these points is 2 x 90° + 60° + 120° = 360°.
Many of the designs of Islamic artists are based on the three regular tessellations and the eight semi-regular tessellations. The decorations on many
Islamic buildings are breath-taking in their intricacy. Such designs have been employed throughout the centuries, and throughout the Islamic world from Spain to India.
The 20th Century artist M. C. Escher was strongly influenced by the tessellating mosaics decorating the Alhambra Palace and La Mezquita mosque at
Cordoba. Escher studied these patterns and made many drawings during visits to Spain in 1926 and 1936. He described tessellations as the richest source of inspiration that he had ever tapped. Escher considered that
it was unfortunate that Moslem artists had restricted themselves to purely abstract geometrical designs.
One of the ways in which Escher developed his own unique style of tessellation was that his tiles were not simply polygons, they usually represented a
variety organisms such as fish, birds or even people.