Symmetries of Islamic geometrical patterns / by Syed Jan Abas and Amer Shaker Salman ; with forewords by Ahmed Moustafa and Sir Michael Atiyah.

Includes bibliographical references (pages 389-393) and index.

1. Islamic patterns and their geometrical structures. 1.1. Islamic patterns: an introduction. 1.2. Geometrical strategies and structures. 1.3. Concluding remarks -- 2. In praise of pattern, symmetry, unity & Islamic art. 2.1. In praise of pattern. 2.2. In praise of unity. 2.3. In praise of Islamic art. 2.4. Concluding remarks -- 3. The gateway from Islamic patterns to invariance and groups. 3.1. An example of symmetries of an Islamic pattern. 3.2. The key property of symmetric objects. 3.3. The symmetry group of an Islamic pattern. 3.4. Symmetry and groups in general. 3.5. The two grand questions and one that is grandest. 3.6. Concluding remarks -- 4. Classification, identification and construction of the seventeen types of two-dimensional periodic patterns. 4.1. Classification of patterns. 4.2. Examples of the seventeen types of patterns from Islamic art. 4.3. Identifying the seventeen pattern types. 4.4. Tile-based algorithms for the seventeen pattern types. 4.5. Concluding remarks -- 5. Islamic patterns and their symmetries. 5.1. Concluding remarks.