  We analyze the physics of self-bound droplets in a doubly dipolar
Bose-Einstein condensate (DDBEC) composed by particles with both electric and
magnetic dipole moments. Using the particularly relevant case of dysprosium, we
show that the anisotropy of the doubly-dipolar interaction potential is highly
versatile and nontrivial, depending critically on the relative orientation and
strength between the two dipole moments. This opens novel possibilities for
exploring intriguing quantum many-body physics. Interestingly, by varying the
angle between the two dipoles we find a dimensional crossover from quasi
one-dimensional to quasi two-dimensional self-bound droplets. This opens a so
far unique scenario in condensate physics, in which a dimensional crossover is
solely driven by interactions in the absence of any confinement.
