ENSEMBLES OF SINGULARITIES GENERATED BY SURFACES WITH POLYHEDRAL SYMMETRY

The role of the symmetries in the topology of sets of Lagrangian singu larities is studied in a simple physical model: the envelope of the ra ys emanating from a convex wave front invariant under the action of po lyhedral groups. New point singularities are found of integer index an d located at the vertices of the polyhedron or of its reciprocal. This remarkable layout results from the interplay between the symmetries o f the singularities, the polyhedral symmetries, and the topology of th e wave front. An application to fine-particle magnetic systems is give n.