Relative Equilibrium Configurations of Point Vortices on a Sphere

The problem of constructing and classifying equilibrium and relative equilibrium configurations of point vortices on a sphere is studied. A method which enables one to find any such configuration is presented. Configurations formed by the vortices placed at the vertices of Platonic solids are considered without making the assumption that the vortices possess equal in absolute value circulations. Several new configurations are obtained.