  We investigate the novel density distributions acquired by a dipolar
Bose-Einstein condensed gas confined in a box potential, with special focus on
the effects of supersolidity. Differently from the case of harmonic trapping,
the ground state density reveals a strong depletion in the bulk region and an
accumulation of atoms near the walls, well separated from the bulk, as a
consequence of the competition between the attractive and the repulsive nature
of the dipolar force. In a quasi two-dimensional geometry characterized by
cylindrical box trapping, we observe the emergence of a ring-like configuration
near the boundary of the box, reveling peculiar supersolid and crystal effects
in a useful range of parameters. In the case of square box trapping the density
oscillations along the edges, caused by the enhanced accumulation of atoms near
the vertices, exhibit interesting analogies with the case of box trapped one
dimensional configurations. For sufficiently large values of the atom number
also the bulk region can exhibit supersolidity, the resulting geometry
reflecting the symmetry of the confining potential even for large systems.
