Geometric patterns make up one of the three nonfigural types of decoration in Islamic art, which also include calligraphy and vegetal patterns. Whether isolated or used in combination with nonfigural ornamentation or figural representation, geometric patterns are popularly associated with Islamic art, largely due to their aniconic quality. These abstract designs not only adorn the surfaces of monumental Islamic architecture but also function as the major decorative element on a vast array of objects of all types. While geometric ornamentation may have reached a pinnacle in the Islamic world, the sources for both the shapes and the intricate patterns already existed in late antiquity among the Greeks, Romans, and Sasanians in Iran. Islamic artists appropriated key elements from the classical tradition, then complicated and elaborated upon them in order to invent a new form of decoration that stressed the importance of unity and order. The significant intellectual contributions of Islamic mathematicians, astronomers, and scientists were essential to the creation of this unique new style.
Consisting of, or generated from, such simple forms as the circle and the square, geometric patterns were combined, duplicated, interlaced, and arranged in intricate combinations, thus becoming one of the most distinguishing features of Islamic art. However, these complex patterns seem to embody a refusal to adhere strictly to the rules of geometry. As a matter of fact, geometric ornamentation in Islamic art suggests a remarkable amount of freedom; in its repetition and complexity, it offers the possibility of infinite growth and can accommodate the incorporation of other types of ornamentation as well. In terms of their abstractness, repetitive motifs, and symmetry, geometric patterns have much in common with the so-called arabesque style seen in many vegetal designs. Calligraphic ornamentation also appears in conjunction with geometric patterns.
The four basic shapes, or “repeat units,” from which the more complicated patterns are constructed are: circles and interlaced circles; squares or four-sided polygons; the ubiquitous star pattern, ultimately derived from squares and triangles inscribed in a circle; and multisided polygons. It is clear, however, that the complex patterns found on many objects include a number of different shapes and arrangements, allowing them to fit into more than one category.