SU(N) MONOPOLES AND PLATONIC SYMMETRY

We discuss the ADHMN construction for SU(N) monopoles and show that a particular simplification arises in studying charge N - 1 monopoles wi th minimal symmetry breaking. Using this we construct families of tetr ahedrally symmetric SU(4) and SU(5) monopoles. In the moduli space app roximation, the SU(4) one-parameter family describes a novel dynamics where the monopoles never separate, but rather, a tetrahedron deforms to its dual. We find a two-parameter family of SU(5) tetrahedral monop oles and compute some geodesics in this submanifold numerically. The d ynamics is rich, with the monopoles scattering either once or twice th rough octahedrally symmetric configurations. (C) 1997 American Institu te of Physics.