  We discuss the ADHMN construction for SU(N) monopoles and show that a
particular simplification arises in studying charge N-1 monopoles with minimal
symmetry breaking. Using this we construct families of tetrahedrally symmetric
SU(4) and SU(5) monopoles. In the moduli space approximation, 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 monopoles and compute some geodesics
in this submanifold numerically. The dynamics is rich, with the monopoles
scattering either once or twice through octahedrally symmetric configurations.
