  In this paper, we investigate periodic vibrations of a group of particles
with a dihedral configuration in the plane governed by the Lennard-Jones and
Coulomb forces. Using the gradient equivariant degree, we provide a full
topological classification of the periodic solutions with both temporal and
spatial symmetries. In the process, we provide with general formulae for the
spectrum of the linearized system which allows us to obtain the critical
frequencies of the particle motions which indicate the set of all critical
periods of small amplitude periodic solutions emerging from a given stationary
symmetric orbit of solutions.
