The stability of three possible icosahedral phases (called here vertex, edge, and face models, respectively) in a diblock copolymer melt is examined, with higher harmonics included in the density-wave mean field theory developed by Leibler. Two cases are examined : (1) diblock copolymer melt with constant coupling vertices, and (2) diblock copolymer melt with general coupling vertices in which, unlike all the previous studies on the effect of higher order harmonics in diblock copolymer melt, the calculation is performed exactly. We find that icosahedral phases are always metastable and the mean-field phase diagram of the diblock copolymer is unchanged.