Tb. Zunic et E. Makovicky, DETERMINATION OF THE CENTROID OR THE BEST CENTER OF A COORDINATION POLYHEDRON, Acta crystallographica. Section B, Structural science, 52, 1996, pp. 78-81
The geometric parameters related to the point in the coordination poly
hedron having the minimum variation of distances to the vertices ('the
centroid of the coordination polyhedron') are proposed as a measure o
f 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 coordinati
on polyhedron, the degree of sphericity of coordination, the principal
axes of the ellipsoid fitted to the polyhedron and the displacement o
f the central atom from the centroid are calculated. These quantities
are measures for various aspects of irregularity in the coordination p
olyhedron. The centroid calculation has been applied to the family of
ABS(2)-type sulfides with cations in slightly to highly deformed octah
edral coordinations.