  It is shown that there exists a charge five monopole with octahedral symmetry
and a charge seven monopole with icosahedral symmetry. A numerical
implementation of the ADHMN construction is used to calculate the energy
density of these monopoles and surfaces of constant energy density are
displayed. The charge five and charge seven monopoles look like an octahedron
and a dodecahedron respectively. A scattering geodesic for each of these
monopoles is presented and discussed using rational maps. This is done with the
aid of a new formula for the cluster decomposition of monopoles when the poles
of the rational map are close together.
