The Hoberman Switch Pitch Throwing Ball is a $12 toy that instantiates a dual polyhedron: every time you throw it, it turns inside-out; there's a wealth of scientific literature that explains how this works, including this open-access paper from the Journal of the International Association for Shell and Spatial Structures. Here's JWZ's summary: "The curved body panels that make it look like a sphere hide an internal structure that is a cube; or really, two tetrahedrons embedded in a cube; and when it its its activation energy, the tetrahedron becomes its dual, swapping faces and vertices."
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