allahallahThere are exactly 17 different types of infinite patterns based on different combinations of the 4 actions that produce symmetry. The goal of classification is to identify what kinds of symmetries exist in the pattern, and what basic shape is being repeated in the pattern which produces these symmetries.

allahallahA pattern can be thought of as existing on a net or grid that supports the underlying structure. Every pattern has a basic "building block" shape which, when repeated on the net, fitting together in various ways, produces an infinite field of pattern. There are five of these basic building block shapes (called unit cell shapes):

allahallah(1) parallelogram, (2) rectangle, (3) centered rectangle, (4) square, and (5) hexagonal.

The first step in classification is to identify what net block the pattern is using:



Scanned from Symmetries of Islamic Geometrical Patterns


allahallah Symmetric patterns are classified based on the unit cell shape. Each different kind of pattern is given a standardized abbreviation. The numbers and letters of the abbreviation are a short-hand way of saying what kinds of symmetrical actions are performed on the unit cell shape in order to produce the pattern. This table lists the 17 different pattern types, and an explanation of the notation follows it.

Explanation of the notation:

1) The first symbol is a c if the unit cell shape is a centered rectangle, for all other unit cell shapes the first symbol is a p.

2) The second symbol indicates the level of rotation symmetry in the pattern (the number of degrees the unit cell shape must be rotated in order to form the pattern). A 1 indicates no rotation symmetry, a 2 indicates 60 degrees of rotation symmetry, a 3 indicates 120 degrees of rotation symmetry, and so on, a 6 (360 degrees) being the highest number.

3) The third symbol is an m if the unit cell shape contains a mirror reflection. If the symbol is g, then it contains a glide reflection. If the third symbol is a 1, then there is no reflection.

4) The fourth symbol is either an m or a g if there is a mirror reflection or glide reflection in another direction within the unit cell shape.

Where applicable, the short-hand notation is given in parenthesis, and this is the notation usually used.


allahallahLet's move ahead to see how these pattern types are expressed in Islamic Art.