Decorating Regular Polyhedra Using Historical Interlocking Star Polygonal Patterns — A Mathematics and Art Case Study

Reza Sarhangi
Proceedings of Bridges 2014: Mathematics, Music, Art, Architecture, Culture (2014)
Pages 243–252 Regular Papers


This paper reports on the application of some historical interlocking patterns for the embellishment of the regular polyhedra (Platonic and Kepler-Poinsot solids). Such patterning can be extended to cover surfaces of some other convex and non-convex solids. In this regard, first the Shamseh n/k star polygon method and the radial grid method will be employed, and step-by-step geometric constructions will be demonstrated, then the girih tile modularity method will be used to explore more patterning designs. Then, the girih tile modularity is used to explore more patterning designs.