The cuboctahedric Higgs oscillator from the rational Calogero model

We exclude the center of mass of the N-particle rational Calogero model and consider the angular part of the resulting Hamiltonian. We show that it describes the motion of the particle on an (N - 2)-dimensional sphere interacting with N(N - 1)/2 force centers with Higgs oscillator potential. In the case of a four-particle system, these force centers define the vertexes of an Archimedean solid called a cuboctahedron.