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The structural symmetry and molecular separation in water and ice remain uncertain. We present herewith a solution to unifying the density, the structure order and symmetry, the size (H-O length d H ), and the separation (d OO  = d L  + d H  or the O:H length d L ) of molecules packing in water and ice in terms of statistic mean. This solution reconciles: i) the d L  and the d H  symmetrization of the O:H-O bond in compressed ice, ii) the d OO  relaxation of cooling water and ice and, iii) the d OO  expansion of a dimer and between molecules at water surface. With any one of the d OO , the density ρ(g·cm −3 ), the d L , and the d H , as a known input, one can resolve the rest quantities using this solution that is probing conditions or methods independent. We clarified that: i) liquid water prefers  statistically  the mono-phase of tetrahedrally-coordinated structure with fluctuation, ii) the low-density phase (supersolid phase as it is strongly polarized with even lower density) exists only in regions consisting molecules with fewer than four neighbors and, iii) repulsion between electron pairs on adjacent oxygen atoms dictates the cooperative relaxation of the segmented O:H-O bond, which is responsible for the performance of water and ice.

Size, separation, structural order and mass density of molecules packing in water and ice