An ancient rule for constructing dodecagonal quasiperiodic patterns

The discovery of complex dodecagonal patterns in historical Islamic architecture is generating a renewed interest into understanding the mathematical principles of traditional Islamic geometry. By employing a compass and a straightedge, ancient craftsmen utilized consistent design principles that allowed for diverse geometric expressions to be realized throughout the ancient world. Derived from these principles, a global multi-level structural model is proposed that provides a general guiding principle for constructing a wide variety of infinite dodecagon-based quasiperiodic patterns.