The implementation of a method for the exact evaluation of the volume and surface area of cavities and free volumes in polydisperse sphere packings is described. The generalization of an algorithm for Voronoi tessellation by Tanemura et al. is presented, employing the radical plane construction, as a part of the method. We employ this method to calculate the equation of state for monodisperse and polydisperse hard-sphere fluids, crystals, and for the metastable amorphous branch up to random close packing or jamming densities. We compute the distribution of free volumes, and compare with previous results employing a heuristic definition of free volume. We show the efficacy of the method for analyzing protein structure, by computing various quantities such as the distribution of sizes of buried cavities and pockets, the scaling of solvent accessible area to the corresponding occupied volume, the composition of residues lining cavities, etc.
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