BN alternants with barons and nitrogens fully replacing alternant sets
of carbons in an alternant hydrocarbon form a special class of specie
s of natural interest. The Huckel model for general BN alternants and
certain extended Huckel models for ''regular'' BN alternants are shown
to be simply soluble in terms of the eigensolutions for the correspon
ding alternant hydrocarbons. The difference in the electronegativities
for boron and nitrogen implies the opening of HOMO-LUMO gaps for alte
rnant BN clusters-or equivalently the opening of band gaps (at the Fer
mi energy) for BN alternant polymers. Infinite classes first of octahe
dral-symmetry fullerenoid cages and second of ''buckytube'' polymers a
re considered.