Determination of the centroid or 'the best centre' of a coordination polyhedron

The geometric parameters related to the point in the coordination polyhedron having the minimum variation of distances to the vertices ('the centroid of the coordination polyhedron') are proposed as a measure of polyhedral irregularity or deformation. The numerical method for the determination of the centroid coordinates is described. Knowing these coordinates, the radius of the sphere circumscribed to the coordination polyhedron, the degree of sphericity of coordination, the principal axes of the ellipsoid fitted to the polyhedron and the displacement of the central atom from the centroid are calculated. These quantities are measures for various aspects of irregularity in the coordination polyhedron. The centroid calculation has been applied to the family of ABS(2)-type sulfides with cations in slightly to highly deformed octahedral coordinations.