  We report all-electron, density-functional calculations with large Gaussian
polarization basis set of the recently synthesized octahedral B24N24 cage that
is perfectly round by symmetry, and boron-nitride (BN) clusters that its
existence might suggest. We consider whether it is energetically possible that
the two halves of this round cage could cap the BN nanotubes, modeled by B28N28
and B32N32. The energetics show that BN nanotubes with such round caps, are
only slightly less favorable than the BN clusters containing six squares as the
only defects in the otherwise perfect hexagonal lattice. A larger B96N96
octahedral cage formed from B24N24 by adding sufficient hexagons to isolate all
squares is not very favorable energetically. The squares protrude noticeably
from its otherwise round surface.
