OCTAHEDRAL AND DODECAHEDRAL MONOPOLES

It is shown that there exists a charge five monopole with octahedral s ymmetry and a charge seven monopole with icosahedral symmetry. A numer ical implementation of the ADHMN construction is used to calculate the energy density of these monopoles and surfaces of constant energy den sity are displayed. The charge five and charge seven monopoles look li ke an octahedron and a dodecahedron, respectively. A scattering geodes ic for each of these monopoles is presented and discussed using ration al maps. This is done with the aid of a new formula for the cluster de composition of monopoles when the poles of the rational map are close together.