An LCAO—MO systematization of polyhedral molecules such as BNHN is undertaken. Peculiarities of polyhedral systems, such as inapplicability of nearest-neighbor assumption and increased number of parameters are discussed within the framework of a Hückel type of theory. It is found that inclusion of hydrogen atoms does not affect predictions of closed shells, but is important in determining electronic transitions. Various physical factorizations of the secular equations, such as the in-surface, apex-equatorial, and ring-polar separations are critically examined. A computer program for calculations on molecules of up to 15 atoms is described and used to obtain the energy levels of a variety of polyhedral molecules.