  The dynamics of n slowly moving fundamental monopoles in the SU(n+1) BPS
Yang-Mills-Higgs theory can be approximated by geodesic motion on the
4n-dimensional hyperkahler Lee-Weinberg-Yi manifold. In this paper we apply a
variational method to construct some scaling geodesics on this manifold. These
geodesics describe the scattering of n monopoles which lie on the vertices of a
bouncing polyhedron; the polyhedron contracts from infinity to a point,
representing the spherically symmetric n-monopole, and then expands back out to
infinity. For different monopole masses the solutions generalize to form
bouncing nested polyhedra. The relevance of these results to the dynamics of
well separated SU(2) monopoles is also discussed.
