How icosahedral are icosahedral clusters?

Icosahedral symmetry, not contemplated within the crystallographic space groups, is nevertheless present to a high degree of perfection in a variety of clusters, in molecular, ionic, covalent or metallic structures. The application of continuous shape measures to those structures allows for a quantification of the degree of icosahedral symmetry present in each case, a first necessary step for a deeper discussion of the factors that favor the adoption of the icosahedron as a stable structural motif. Examples analyzed include boranes and carbaboranes, main group, rare earth or transition metal clusters, ligand-bridged polynuclear complexes and sets of donor atoms in mono- or polynuclear complexes. Specific examples are found of structures that appear along the minimal distortion pathways from the icosahedron to the cuboctahedron or the anticuboctahedron. (C) 2010 Elsevier B.V. All rights reserved.