  We present a formal demonstration that light can simultaneously exhibit a
superfluid behavior and spatial long-range order when propagating in a photonic
crystal with self-focussing nonlinearity. In this way, light presents the
distinguishing features of matter in a "supersolid" phase. We show that this
supersolid phase provides the stability conditions for nonlinear Bloch waves
and, at the same time, permits the existence of topological solitons or defects
for the envelope of these waves. We use a condensed matter analysis instead of
a standard nonlinear optics approach and provide numerical evidence of these
theoretical findings.
