  In (Fusco et. al., 2011) several periodic orbits of the Newtonian N-body
problem have been found as minimizers of the Lagrangian action in suitable sets
of T-periodic loops, for a given T>0. Each of them share the symmetry of one
Platonic polyhedron.
  In this paper we first present an algorithm to enumerate all the orbits that
can be found following the proof in (Fusco et. al., 2011). Then we describe a
procedure aimed to compute them and study their stability. Our computations
suggest that all these periodic orbits are unstable. For some cases we produce
a computer-assisted proof of their instability using multiple precision
interval arithmetic.
