A simple model of the bonding and doping of a series of icosahedral-boride insulators is presented. Icosahedral borides contain clusters of boron atoms that occupy the 12 vertices of icosahedra. This particular series of icosahedral borides share both the stoichiometry B 12X2, where X denotes a group V element (P or As), and a common lattice structure. The inter-icosahedral bonding of these icosahedral borides is contrasted with that of B 12O 2 and with that of α-rhombohedral boron. Knowledge of the various types of inter-icosahedral bonding is used as a basis to address effects of inter-icosahedral atomic substitutions. The inter-icosahedral bonding is maintained when an atom of a group V element is replaced with an atom of a group IV element, thereby producing a p-type dopant. However, changes of inter-icosahedral bonding occur upon replacing an atom of a group V element with an atom of a group VI element or with a vacancy. As a result, these substitutions do not produce effective n-type dopants. Moreover, partial substitution of boron atoms for atoms of group V elements generally renders these materials p-type semiconductors.