Our ability to synthesize faceted nanoparticles of tunable shapes and sizes has opened up many intriguing applications of such particles. However, our progress in understanding, modeling, and simulating their collective rheology, phase behavior, and self-assembly has been hindered by the lack of analytical interparticle interaction potentials. Here, we present one of the first analytical models for the van der Waals interaction energy between faceted nanoparticles. The model was derived through various approximations that reduce the usual six-dimensional integral over particle volumes to a series of two-dimensional integrals over particle interaction areas with closed-form solutions. Comparison and analyses of energies obtained from the analytical model with those computed from exact atomistic calculations show that the model approximations lead to insignificant errors in predicted energies across all relevant particle configurations. We demonstrate that the model yields accurate energies for diverse particle shapes including nanocubes, triangular prisms, faceted rods, and square pyramids, while yielding many orders of magnitude improvement in computational efficiency compared to atomistic calculations. To make the model more accessible and to demonstrate its applicability, an open-source graphical user interface application implementing the model for nanocubes in arbitrary configurations has been developed. We expect that the analytical model will accelerate future investigations of faceted nanoparticles that require accurate calculation of interparticle interactions.