  We extend the theory of ground states of classical Heisenberg spin systems
published previously by a closer investigation of the convex Gram set of $N$
spins. This is relevant for the present purpose since the set of ground states
of a given spin system corresponds to a face of Gram set. The investigation of
the Gram set is facilitated by the determination of its symmetry group. The
case of the general spin triangle is completely solved and illustrated by a
couple of examples.
