We propose a model for the electronic structure of SmB6 suggested by new transport measurements in combination with analyses of the magnetic susceptibility and lattice energetics. Our model successfully describes the resistivity, Hall effect, magnetic susceptibility, and Mössbauer isomer shift in this material. In addition, it predicts an anomaly in the low-temperature specific heat. Analysis of the lattice energetics shows that the rigidity of the boron lattice is responsible for the fact that Sm ions on equivalent sites can occur with the 4f shell in either the 4f5 or the 4f6 configuration. A relationship among the compressibilities of the rare-earth hexaborides is predicted on the basis of this analysis.