Magnetic Sphere Constructions

Henry Segerman and Rosa Zwier
Proceedings of Bridges 2017: Mathematics, Art, Music, Architecture, Education, Culture
Pages 79–86 Regular Papers

Abstract

We investigate constructions made from magnetic spheres. We give heuristic rules for making stable constructions of polyhedra and planar tilings from loops and saddles of magnetic spheres, and give a theoretical restriction on possible configurations, derived from the Poincaré-Hopf theorem. Based on our heuristic rules, we build relatively stable new planar tilings, and, with the aid of a 3D printed scaffold, a construction of the buckyball. From our restriction, we argue that the dodecahedron is probably impossible to construct. We finish with a simplified physical model, within which we show that a hexagonal loop is in static equilibrium.

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