A 7-Fold System for Creating Islamic Geometric Patterns Part 1: Historical Antecedents

Jay Bonner and Marc Pelletier
Proceedings of Bridges 2012: Mathematics, Music, Art, Architecture, Culture (2012)
Pages 141–148 Regular papers


A comprehensive set of 7-fold polygonal sub-grid elements produces very beautiful Islamic geometric patterns characterized by distinctive 14 and 7-pointed stars. The tessellating characteristic of these polygonal elements represents a systematic approach to creating geometric designs with 7-fold symmetry. While a number of historical examples of 7-fold Islamic geometric patterns exist, there is insufficient evidence from the historical record to establish the degree to which designers of the past were aware of this as a system per se. The employment of a limited set of repetitive polygonal elements onto which pattern lines are applied aligns this 7/14 System with other systematic approaches to creating Islamic geometric patterns. In particular, this 7/14 System has direct parallels with the historically ubiquitous 5/10 System. As with other polygonal systems, the 7/14 System offers tremendous design potential for the creation of new geometric patterns. As demonstrated in Part 2 of this paper, the contemporary expression of this design system includes the creation of quasicrystalline and self-similar designs with recursive symmetry.