Voronoi polyhedra' are geometrical objects that serve as a computational tool for investigating aspects of molecular architecture. They have recently been used to study solvation2 in aqueous solution. They have been known for many years, and their application to crystallography is well documented? Work in this laboratory during the past few years has shown the feasibility and utility of employing Voronoi polyhedra to study solvation effects, specifically the geometry of the solvent sheath of a q ~a t e d ~-~ molecules.
Chemists', and specifically protein chemists', interest in Voronoi polyhedra has been aimed at trying to ascertain volumes of proteins (and of voids) for biologically interesting molecules. Richards7 has used Voronoi polyhedra to assign molecular volumes of proteins, as have Gellatly and Finney? Recently, Baranyai and Ruff9 have used a modified Voronoi polyhedron definition to study adjacency (neighboring identities) in molten alkali halides. Interest in Voronoi polyhedra exists outside of chemistry in computer science and allied fields. Thus Guibas and Stolfi" address the problem of generating Voronoi polyhedra, citing a literature that is completely orthogonal to the chemists' and physicists' citation lists.
Renewed interest in the speed of Voronoi polyhedron generation has shown itself in the paper by Medvedev," who introduces a new algorithm for generating Voronoi polyhedra, and compares his algorithm to that of Tanemura et al.I2 Both Medvedev