Description of metallic and covalent clusters with icosahedral symmetry: The polytope model

Compact and tetravalent clusters with icosahedral local or global symmetries are generated by mapping from ideal structures in curved space onto a tangent euclidean 3D space. The observed elastic energy of the clusters can thus be interpreted as an intrinsic curvature associated to a frustrated local order. It is then proposed a kind of classification of the very rich family of possible clusters using a limited set of parameters. (orig.)