The geometrical characteristics of cubo-octahedral, icosahedral, body-
centered cubic, and simple cubic clusters are systematically studied a
nd enumerated as a function of the number of sites in the cluster. The
various types of sites and the number of first nearest-neighbors for
each one of the structures are analyzed. One-parameter analytic expres
sions, to calculate the total number of sites in the cluster, those at
the surface, the number of sites of the various kinds, the dispersion
, the number of bonds, and the average coordination number, are presen
ted. In the dispersion relationships, we studied the contributions ari
sing from the face, vertex, and edge sites. The average coordination n
umber of the core, the one of the surface and between the core and the
surface are also calculated. (C) 1997 Acta Metallurgica Inc.