Using a recently introduced formulation of the ground-state inverse design problem for a targeted lattice [W. Piñeros et al., J. Chem. Phys. 144, 084502 (2016)], we discover purely repulsive and isotropic pair interactions that stabilize low-density truncated square and truncated hexagonal crystals, as well as promote their assembly in Monte Carlo simulations upon isochoric cooling from a high-temperature fluid phase. The results illustrate that the primary challenge to stabilizing very open two-dimensional lattices is to design interactions that can favor the target structure over competing stripe microphases.
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