The general mathematical constraints for thermomechanical equilibrium of partial melts under hydrostatic or nearly hydrostatic stress conditions are well known. However, melt phase geometries under equilibrium conditions have previously been understood only qualitatively. Because of its importance in determining bulk physical and chemical properties of partially molten regions of the crust and the mantle, we have computed the geometries of the liquid phase for a range of melt fractions and dihedral angles. We describe here a theoretical interfacial topology model and its associated calculational algorithms which yield numerically precise equilibrium solid-liquid interfacial surfaces where the only costraints imposed on the system are constant mean curvature and constant wetting angle in accordance with equilibrium. The calculated geometries are used to determine the permeability of partial melts to fluid flow, interfacial areas, surface energy, minimum channel cross section, surface mean curvature, and maximum trappable melt fraction for melt fractions up to 5% and wetting angles between 20¿ and 80¿. For wetting angles less than 60¿ the melt is distributed in an interconnected network of channels along the grain edges, and therefore melt mobilization is possible as soon as melt forms. For wetting angles greater than 60¿ the melt phase will be distributed in isolated pockets at the grain corners if the melt fraction is less than a critical value, whereas an interconnected network of melt channels will be established if the critical melt fraction is exceeded. Wetting angle exerts a first-order control on the permeability of partially molten systems through its effect on the connectivity of the melt phase. Once a connected melt phase has formed, the permeability is only mildly sensitive to wetting angle.