  The role of discrete (or point-group) symmetries is discussed in the
framework of the Cluster Shell Model which describes the splitting of
single-particle levels in the deformed field of cluster potentials. We discuss
the classification of the eigenstates for the cases of a triangular and
tetrahedral configuration of alpha-particles in terms of the irreducible
representations of the double point groups D'(3h) and T'(d), respectively, and
show how the discrete symmetry of a given eigenstate can be determined.
Finally, we derive the Coriolis coupling for each one of these geometrical
configurations.
