A nonadditive hard-sphere (NAHS) reference model for ionic liquids with truncated ion ion pair interaction potentials represented by collision diameters defined as sigma(ij) = sigma(1 + delta(ij)epsilon) (using the Kronecker delta) is investigated. In a reference 1:1 ionic salt (e.g., AB = NaCl), the nonadditivity parameter (epsilon) is positive; hence, like ions interact with a larger diameter than unlike ions; that is, sigma(AA) = sigma(BB) = (1 + epsilon)sigma(AB) The NAHS model is found to show remarkable similarity of structure to the full-Hamiltonian for electrostatic charged ion models of ionic liquids, their crystalline phases, and freezing properties. Molecular dynamics computations are used to show that the structures of ionic liquids and crystals are determined mainly by short-range geometric and symmetry effects rather than the long-range electrostatic potentials. A preliminary phase diagram for nonadditive hard spheres has been determined for the range of positive nonadditivity for stable cubic lattices CsCl (body-centered), rock salt, NaCl (simple cubic), and sphelerite ZnS (tetrahedral). Model NAHS ionic liquids obey a scaling law for the freezing temperature T-f = T-0(1 + epsilon)(3), where T-0 is the HS freezing temperature. NAHS is an effective reference model, analogous to the HS model for molecular and atomic liquids, as a starting point for describing the structures and phase diagrams of ionic liquids and crystals.