15-13U

It is shown that the ground state of a system of classical spins on a asymmetric triangular lattice with interactions within an elementary triangular plaquette can be constructed by minimizing the single plaquette energy density function. Even in the case when all the three angles between pairs of spins on the plaquette are different, there exist five types of global ground-state configurations. The most complicated of these is a spiral four sublattice ordering. On the base of this outcome the experimentally observed spin disorder in NiGa$_2$S$_4$ and FeGa$_2$S$_4$ compounds is explained.