The morphology of the uniform Lennard-Jones-dipole-dipole cluster with 13 centers (LJDD)(13) is investigated over a relatively wide range of values of the dipole moment. We introduce and compare several necessary modifications of the basin-hopping algorithm for global optimization to improve its efficiency. We develop a general algorithm for T=0 Brownian dynamics in curved spaces, and a graph theoretical approach necessary for the elimination of dissociated states. We find that the (LJDD)(13) cluster has icosahedral symmetry for small to moderate values of the dipole moment. As the dipole moment increases, however, its morphology shifts to an hexagonal antiprism, and eventually to a ring. (C) 2004 American Institute of Physics.