Spiky Soccer Balls: Generalized Polar Zonohedral Clusters
Laura Marotta and Brian Redmond

Proceedings of Bridges 2025: Mathematics and the Arts
Pages 463–466
Short Papers

Abstract

We extend Webster’s method for generating polar zonohedral clusters by removing the requirement that the seed polyhedron be circumscribable. Applying this construction to Kleetopes of the dodecahedron, we produce spiky forms that can be faceted by connecting adjacent zonohedral poles to produce truncations of the icosahedron, resulting in various soccer ball-like forms. We analyze the relationship between truncation, pyramid height, and edge length ratios, providing an explicit formula linking these parameters. These considerations inspired our art submission featuring generalized polar zonohedral domes forming a standard truncated icosahedron, with the spiky form appearing as negative space within the clusters.

Files