In this paper we propose a new equilibrium model of the interactions between receptors, ligands, and G-proteins--the cubic ternary complex (CTC) model. The CTC model is a generalization of the extended ternary complex model of Samama et al. (1993). It incorporates all the features of that model but differs in that it also allows G-proteins to bind to inactive receptors. The addition of this feature produces a complete equilibrium description of the three-way interactions between ligand, receptor, and G-proteins. We show that the standard equilibrium receptor-occupancy models of pharmacology are equivalent to the hierarchical log-linear models of statistics. Using this equivalence, we derive the completeness of the CTC model from both a graphical and a statistical perspective. In its simplest instance (one receptor, one G-protein, and one ligand) the CTC model consists of eight receptor species that can be graphically visualized as occupying the vertices of a cube. Statistically, the CTC model is a saturated three-factor log-linear model. Viewed statistically or graphically, other equilibrium binary and ternary complex models are subsets of the CTC model.