Tom has a set of particles that repel each other with a force of whose strength is proportional to where is the distance of separation between any pair of particles.
If Tom puts 8 of these particles into a rigid, frictionless sphere and allows them to come to rest, they'll align to the vertices of a certain -faced polyhedron.
What is
For example, if Tom puts 4 of the particles into the sphere, they'll come to rest at the vertices of a regular tetrahedron, as shown.