  The phase behavior of a two-dimensional colloidal system subject to a
commensurate triangular potential is investigated. We consider the integer
number of colloids in each potential minimum as rigid composite objects with
effective discrete degrees of freedom. It is shown that there is a rich variety
of phases including ``herring bone'' and ``Japanese 6 in 1'' phases. The
ensuing phase diagram and phase transitions are analyzed analytically within
variational mean-field theory and supplemented by Monte Carlo simulations.
Consequences for experiments are discussed.
