A Novel System Combining Additive Patterns and Polygonal Structures

Abstract

This study examines the structural relationships among patterns with six-fold motifs in Islamic art and proposes a ruler-and-compass method based on dividing a 90-degree corner into six equal parts to generate patterns. This approach enables the systematic construction of various geometric designs within square and √3-unit cells, providing a practical design grammar for contemporary applications. The research demonstrates how this method reveals the connections between historical patterns and deepens the understanding of shared design principles in Islamic art. A key contribution of this study is the introduction of the SES-APPS system (Additive Patterns and Polygonal Structures), which combines modular design elements with polygonal frameworks. The study also presents methods for applying these patterns to k-uniform systems and complex polyhedral forms, such as the cuboctahedron, and offers new possibilities for both theoretical exploration and practical design in the field of Islamic geometric ornament.