  We describe the linear and nonlinear stability and instability of certain
symmetric configurations of point vortices on the sphere forming relative
equilibria. These configurations consist of one or two rings, and a ring with
one or two polar vortices. Such configurations have dihedral symmetry, and the
symmetry is used to block diagonalize the relevant matrices, to distinguish the
subspaces on which their eigenvalues need to be calculated, and also to
describe the bifurcations that occur as eigenvalues pass through zero.
