  We present a direct method for solving the inverse problem of designing
isotropic potentials that cause self-assembly into target lattices. Each
potential is constructed by matching its energy spectrum to the reciprocal
representation of the lattice to guarantee that the desired structure is a
ground state. We use the method to self-assemble complex lattices not
previously achieved with isotropic potentials, such as a snub square tiling and
the kagome lattice. The latter is especially interesting because it provides
the crucial geometric frustration in several proposed spin liquids.
