  We theoretically investigate supersolidity in three-dimensional dipolar
Bose-Einstein condensates. We focus on the role of trap geometry in determining
the dimensionality of the resulting droplet arrays, which range from
one-dimensional to zigzag, through to two-dimensional supersolids in circular
traps. Supersolidity is well established in one-dimensional arrays, and may be
just as favorable in two-dimensional arrays provided that one appropriately
scales the atom number to the trap volume. We develop a tractable variational
model--which we benchmark against full numerical simulations--and use it to
study droplet crystals and their excitations. We also outline how exotic ring
and stripe states may be created with experimentally-feasible parameters. Our
work paves the way for future studies of two-dimensional dipolar supersolids in
realistic settings.
