The structural and electronic properties of bulk cubic and tetragonal tungsten trioxide are investigated using a periodic boundary condition ab initio Hartree-Fock method; a posteriori density functional corrections are used to estimate the effect of electron correlation on the energy. The farces involved in the bonding between metal and oxygen are examined to shed light on the crystal chemistry of the compound. While the cubic phase is highly ionic, the symmetry distortion leading to the tetragonal phase causes an increase in covalence between tungsten and its nearest oxygen. The observed instability of cubic WO3 is explained by its higher energy (0.80 eV per formula unit) with respect to the tetragonal phase. We attribute this energy,oy difference to the increased covalence observed in the latter phase. The calculated structural parameters for tetragonal WO3 agree with available experimental data. A layered structure emerges from our calculations for tetragonal WO3; when the effect of applying pressure is examined, only the interlayer spacing is appreciably modified. This softer degree of freedom results in a lower value of the bulk modulus when compared to that of the cubic phase. In the range of experimentally obtainable pressures, the order of stability of the two phases cannot be reversed, and the cubic structure remains unstable with respect to the tetragonal structure.