We have prepared a new calix[4]arene-based lipid containing glutamic acid as the hydrophilic group. The α-amine and the γ-carboxylic acid groups of the glutamic acid moiety allowed a continuous change in the state of the headgroup from cationic to zwitterionic and then to anionic with increasing pH. Accompanying this headgroup change, micelles of the lipid underwent a morphological transformation from spherical to cylindrical and again to spherical. The morphological transition was ascribed to the change in the lipid conformation corresponding to the pH conditions. Interestingly, at acidic and basic pH, the spherical micelles demonstrated monodispersity in terms of the aggregation number, which agreed with the vertex numbers of Platonic solids, indicating the formation of Platonic micelles. At acidic and basic pH, the lipid conformations were almost identical, but there was a slight difference in the hydrophilic volume, which might affect the packing behavior of the lipid in micelles and account for the difference in the aggregation number. This study clearly demonstrates the precise pH-controllable aggregation number of micelles, which belong to the Platonic micelle systems.