We developed two modeling approaches to rationalize the formation of the experimentally observed lattices from differently sized NP building blocks. First, we constructed a simple geometric model based on varying the sizes of NPs arranged in a given lattice (AB and A3B4), where the NPs interact via contact potentials. According to this model, a lattice will be stable only if oppositely charged NPs are in direct contact; when the NP sizes are such that the oppositely charged NPs cannot be in contact (due to geometric constraints), another lattice will form in which the NPs can regain favorable contacts. It follows from geometric considerations (Supplementary Section 6.1) that the CsCl-type and Th3P4-type lattices will fail to form when the size ratio of the oppositely charged NPs is greater than ~1.37 and ~2.08, respectively. These considerations suggest that the Th3P4-type lattice should be stable over a relatively large range of NP size ratios, which is in qualitative agreement with the experimental findings (Supplementary Fig. ).