Place magnets, ideally point dipoles, at the vertices of a polyhedron. What orientations of the dipoles minimize potential energy? This can be generalized to any collection of points in space.
Inspired by the toy of spherical neodymium magnets. An icosahedron made of 12 of them and an octahedron made of 6 of them are stable, but tetrahedron and cube seem not.
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