Stereochemistry of compounds with coordination number ten.

The stereochemistry of ten-coordinate rare-earth and transition-metal compounds is studied from the point of view of continuous shape measures (CShM) and derived tools. A total of 19 ideal ten-vertex polyhedra belonging to 12 different symmetry point groups have been considered, from which nine are retained for the description of the stereochemistries of all studied compounds. The structures of the coordination spheres are analyzed by families, according to the denticity and topology of the ligands. Some ligand topologies are seen to consistently favor usually neglected ideal polyhedra, such as the capped trigonal cupola.