  Based on a simple general relation for the Lorentz field, the precise values
are obtained for the energies of ferromagnetic and basic antiferromagnetic
states in sc, bcc, fcc, and diamond cubic lattices. Within both the
'nearest-neighbor' and group-theoretic approaches, a large variety of
antiferromagnetic states revealed as corresponding to the lowest energies is
addressed, with recognizing their spherical spin-orientation degeneracy, which
turns out to be rather special in fcc lattices.
