Minkowski Sums and Spherical Duals

John M. Sullivan
Bridges London: Mathematics, Music, Art, Architecture, Culture (2006)
Pages 117–122

Abstract

At Bridges 2001, Zongker and Hart [8] gave a construction for “blending” two polyhedra using an overlay of dual spherical nets. The resulting blend, they noted, is the Minkowski sum of the original polyhedra. They considered only a restricted class of polyhedra, with all edges tangent to some common sphere. This note defines spherical duals of general convex polyhedra and proves that the Zongker/Hart construction is always valid. It can be used visually, for instance, to “morph” from any polyhedron to any other.

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