  The regular-geometric-figure solution to the $N$-body problem is presented in
a very simple way. The Newtonian formalism is used without resorting to a more
involved rotating coordinate system. Those configurations occur for other kinds
of interactions beyond the gravitational ones for some special values of the
parameters of the forces. For the harmonic oscillator, in particular, it is
shown that the $N$-body problem is reduced to $N$ one-body problems.
