  Supersolid is an exotic state of matter, showing crystalline order with a
superfluid background, observed recently in dipolar Bose-Einstein condensate
(BEC) in a trap. Here, we present exact solutions of the desired Bloch form in
the self-trapped free-floating quantum fluid. Our general solutions of the
amended nonlinear Schr{\"o}dinger equation, governing the mean-field and beyond
mean-field dynamics, are obtained through a M{\"o}bius transform, connecting a
wide class of supersolid solutions to the ubiquitous cnoidal waves. The
solutions yield the constant condensate, supersolid behavior and the
self-trapped droplet in different parameter domains. The lowest residual
condensate is found to be exactly one-third of the constant background.
