We study the application of a square perturbing lattice to the naturally forming hexagonal arrays of dipolar droplets in a dipolar Bose-Einstein condensate. We find that the application of the lattice causes spontaneous pattern formation and leads to frustration in some regimes. For certain parameters, the ground state has neither the symmetry of the intrinsic hexagonal supersolid nor the symmetry of the square lattice. These results may give another axis on which to explore dipolar Bose-Einstein condensates and to probe the nature of supersolidity.

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• Dipolar atoms
• Bose gases