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We demonstrate a supersolid-like spatially-periodic square- andhoneycomb-lattice crystallization of droplets, in addition to thecommonly-studied triangular-lattice crystallization, in acylindrically-symmetric quasi-two-dimensional trapped dipolar condensate, usinga beyond-mean-field model including a quantum-fluctuation Lee-Huang-Yang-typeinteraction. These three types of crystallization of droplets may appear forthe same atomic interactions and the same trap frequencies. The energy $E$ ofall three crystallization as a function of number $N$ of atoms satisfy theuniversal scaling relation $E\sim N^{0.4}$ indicating that all threearrangements of the droplets should be energetically probable processes ofphenomenological interest. The state of square-lattice crystallization may havethe central site occupied or unoccupied, corresponding to a parity-symmetric orparity-antisymmetric state, respectively. The state of square-latticecrystallization with the occupied central site and the state oftriangular-lattice crystallization, for a fixed $N$, constitute twoquasi-degenerate ground states while the other states are low-lying excitedstates. This makes the square-lattice crystallization with the occupied centralsite an ideal candidate for future experimental observation.

Supersolid-like square- and honeycomb-lattice crystallization of droplets in a dipolar condensate