Interlocking Star Polygons in Persian Architecture: The Special Case of the Decagram in Mosaic Designs

Abstract

This article analyzes a particular series of Persian mosaic designs illustrated in historical scrolls and appearing on the surfaces of historical monuments. The common element in these designs is a special ten-pointed star polygon, called a decagram for convenience; it is the dominant geometric shape in several polyhedral tessellations. This decagram can be created through the rotation of two concentric congruent regular pentagons with a radial distance of 36° from each others’ central angles. To create a decagram-based interlocking pattern, however, a craftsman-mathematician would need to take careful steps to locate a fundamental region. A modular approach to pattern-making seems to be more applicable for this design than compass-straightedge constructions. Such designs include patterns that are sometimes called aperiodic or quasi-periodic tilings in the language of modern mathematics.