Dipole-induced-dipole polarizabilities of symmetric clusters

Symmetry arguments are applied to the determination of closed-form solution s to the classical dipole-induced-dipolemodel of interaction polarizabiliti es for polyhedral clusters of cubic and icosahedral symmetry. Analytical co nditions for the range of applicability of the model and onset of the 'pola rization catastrophe' are given. These conditions are expressed as transfor med versions of the hyperbolic curve of divergence that is already present in the classical case of an interacting pair. Clusters based on the cube an d the icosahedron support unique patterns of induced dipoles, but other phy sically accessible distributions are found for the octahedron (equatorial d ipoles antiparallel to a large central moment), tetrahedron and dodecahedro n (central and mean cage dipole moments antiparallel).