The Topkapı Scroll's Thirteen-Pointed Star Polygon Design

B. Lynn Bodner
Proceedings of Bridges 2012: Mathematics, Music, Art, Architecture, Culture (2012)
Pages 157–164 Regular papers


This paper will explore the Topkapı Scroll sketch known as Catalog Number 30, the only repeat unit, that, when replicated using symmetry operations, creates an overall pattern consisting of "nearly regular" thirteen-pointed stars, regular sixteen-pointed stars as well as irregularly-shaped pentagonal stars. Since there are no known written instructions explaining how this repeat unit was generated, we set out to see if we could recreate this highly unusual design using only the simplest of Euclidean construction techniques that may have been known to, and used by, master builders during medieval times.