Transforming Squares to Strips in Expanded Polyhedral Forms

David Reimann
Proceedings of Bridges 2017: Mathematics, Art, Music, Architecture, Education, Culture
Pages 435–438 Short Papers


An interesting connection between two polyhedra construction techniques is presented. The first method replaces edges with squares connected at corners. The second method constructs forms using strips or sticks using a strict over-under-under-over pattern. It is shown how these two techniques can be thought of as two possibilities in a continuum of edge deformations. Example constructions are shown for the five Platonic solids, the cuboctahedron, and the icosidodecahedon. A construction using a serpentine edge is also shown.