We have studied the structure of ice-VI by examining all ice-rule-allowed structures in its primary unit cell of 10 water molecules with first principles methods. A significant amount of static distortions in the oxygen positions away from their crystallographic positions are found, which is in good agreements with significant higher-order terms in the atomic displacement parameters obtained from X-ray and neutron diffraction data. Structural anomalies (such as exceptionally short OH bonds and small H-O-H angles) noted in conventional crystal structure refinements were not seen in our ab initio calculations, and it is evident that these structural anomalies arose from oversimplified models in which static distortions are not properly accounted for. Our results also show that the molecular geometry of water in ice-VI is similar to but richer than those in ice-Ih and ice-VII. Larger distortions in bond lengths/angles and correlation between the molecular geometry and the neighboring environments were found. Different proton-ordering schemes proposed in the literature were examined, and our calculations provide evidence in favor of a ferroelectric phase of the proton-ordered counterpart of ice-VI at about 80 K.