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Ensembles of Singularities Generated by Surfaces with Polyhedral Symmetry
Phys. Rev. Lett. 81, 1547 – Published 24 August, 1998
DOI: https://doi.org/10.1103/PhysRevLett.81.1547
Abstract
The role of the symmetries in the topology of sets of Lagrangian singularities is studied in a simple physical model: the envelope of the rays emanating from a convex wave front invariant under the action of polyhedral groups. New point singularities are found of integer index and located at the vertices of the polyhedron or of its reciprocal. This remarkable layout results from the interplay between the symmetries of the singularities, the polyhedral symmetries, and the topology of the wave front. An application to fine-particle magnetic systems is given.
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