  We explore spatial symmetry breaking of a dipolar Bose Einstein condensate in
the thermodynamic limit and reveal a critical point in the phase diagram at
which crystallization occurs via a second order phase transition. This behavior
is traced back to the significant effects of quantum fluctuations in dipolar
condensates, which moreover stabilize a new supersolid phase, namely a regular
honeycomb pattern with maximal modulational contrast and near-perfect
superfluidity.
