  Using a recently introduced formulation of the ground-state inverse design
problem for a targeted lattice [Pi\~neros 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.
