The structural significance of the number of skeletal bonding electron-pairs in carboranes, the higher boranes and borane anions, and various transition-metal carbonyl cluster compounds

The skeletal structures of carboranes, the higher boranes and borane anions, and many transition-metal carbonyl cluster species are related to the number of skeletal bonding electron-pairs they contain; species with n skeletal atoms adopt closo-structures if held together by (n+ 1) pairs, nido-structures if held together by (n+ 2) pairs, and arachno-structures if held together by (n+ 3) pairs of skeletal bonding electrons.