  We show that the ground state of a dipolar Bose gas in a cylindrically
symmetric harmonic trap has a rich phase diagram, including droplet crystal
states in which a set of droplets arrange into a lattice pattern that breaks
the rotational symmetry. An analytic model for small droplet crystals is
developed and used to obtain a zero temperature phase diagram that is
numerically validated. We show that in certain regimes a coherent low-density
halo surrounds the droplet crystal giving rise to a novel phase with localized
and extended features.
