The cohesive energetics of three phases of solid cubic rubidium chloride, the zinc blende structured 4:4 phase, the 6:6 sodium chloride polymorph and the 8:8 phase with the cesium chloride structure, are computed using a non-empirical fully ionic model. The rearrangement energies needed to convert free anions to their optimal states in-crystal, two-body inter-ionic potentials, plus the further contributions arising from electron correlation, are reported. The 'optimal' anion-anion potentials, computed by using at each geometry the optimal wavefunction, are compared with the 'frozen' potential using the same wavefunction at all geometries.The lattice energy of the 4:4 structure is predicted to be some 40 kJ mol-1 smaller than that of either the 6:6 or the 8:8 phases. Introduction of the Axilrod-Teller triple dipole dispersion interactions and the vibrational zero point energy predicts the 8:8 phase to lie 3.2 kJ mol-1 lower in energy than the 6:6 structure. This is both consistent with radius ratio arguments and supported by two separate experiments that strongly suggest that the 8:8 phase is favoured over the 6:6 structure at low temperatures even though the latter is more stable at ambient temperatures. A shell model description is presented for the ion-induced dipole interactions that arise both in small clusters and in crystals encapsulated in nanotubes. The elastic constants and entropy at 300 K predicted for the 6:6 phase from this model by using the GULP program agree well with experiment. A smaller entropy is predicted for the 8:8 structure.