  We perform numerical simulations of purely repulsive soft colloidal particles
interacting via a generalized elastic potential and constrained to a
two-dimensional plane and to the surface of a spherical shell. For the planar
case, we compute the phase diagram in terms of the system's rescaled density
and temperature. We find that a large number of ordered phases becomes
accessible at low temperatures as the density of the system increases, and we
study systematically how structural variety depends on the functional shape of
the pair potential. For the spherical case, we revisit the generalized Thomson
problem for small numbers of particles N <= 12 and identify, enumerate and
compare the minimal energy polyhedra established by the location of the
particles to those of the corresponding electrostatic system.
