The most important concepts and methods used in studying the geometrical an
d topological properties of crystal structures are considered, and a critic
al analysis of their potentialities for state-of-the-art crystal chemistry
is performed. A new stereoatomic model of crystal structure is suggested in
which atoms and atom groups are represented by their Voronoi-Dirichlet pol
yhedra. The fundamental difference between this model and the known applica
tions of the Voronoi-Dirichlet polyhedra to crystal-chemical analysis is in
the use of a number of rules, principles, and procedures based on the phys
ically justified correlation between the characteristics of the domain of i
nfluence of an atom in the structure and those of its Voronoi-Dirichlet pol
yhedron. Numerous examples demonstrate the universality of the stereoatomic
model, which allows one to appreciably automate the crystal-chemical analy
sis of both individual compounds and entire classes of inorganic and coordi
nation compounds.