Polyhedral structures with an odd number of vertices: nine-coordinate metal compounds.

The stereochemistry of nine-coordinate transition-metal and rare-earth compounds has been studied by means of continuous shape measures (CShM) and related tools. Several reference nine-vertex polyhedra have been defined and their minimal distortion interconversion paths established. A theoretical shape map is presented in which the structures can be placed according to their distances in CShM space to the capped square antiprism and the tricapped trigonal prism, which are the most common polyhedra in nine-coordinate compounds. The structures of almost 2000 metal coordination spheres in molecular and extended solid-state compounds have been analyzed. Clear stereochemical trends can be established for subsets of these compounds grouped according to the nature of their ligands, which include families of compounds spread along the interconversion paths between the capped square antiprism and the capped cube, or between the tricapped trigonal prism and the tridiminished icosahedron.