  Arrangement of interacting particles on a sphere is historically a well known
problem, however, ordering of particles with anisotropic interaction, such as
the dipole-dipole interaction, has remained unexplored. We solve the
orientational ordering of point dipoles on a sphere with fixed positional order
with numerical minimization of interaction energy and analyze stable
configurations depending on their symmetry and degree of ordering. We find that
a macrovortex is a generic ground state, with various discrete rotational
symmetries for different system sizes, while higher energy metastable states
are similar, but less ordered. We observe orientational phase transitions and
hysteresis in response to changing external field both for the fixed sphere
orientation with respect the field, as well as for a freely-rotating sphere.
For the case of a freely rotating sphere, we also observe changes of the
symmetry axis with increasing field strength.
