Abstract
Recent experiments with degenerate molecular gases dressed by elliptically polarized microwave fields have opened new avenues for engineering dipolar interactions. We identify a set of symmetries of the interaction potential, which generate degeneracies among the interaction parameters, and use these to classify the resulting spatial symmetries and equilibrium shapes of the gases. Exploiting these symmetries we analyze solutions including beyond-meanfield quantum fluctuations, and develop complementary variational results. We then map out the phase diagram of self-bound droplets and characterize their key properties.