We have recently introduced the concept of "Platonic micelles", the preference of spherical micelles to specific aggregation numbers mostly coinciding with the number of faces of platonic solids. This effect was observed on bulky, mostly calix[4]arene-based surfactant systems with small aggregation numbers. The preferred aggregation numbers result in better sphere coverage, highliting the packing and the "protection" of hydrophobic cores from the aqueous solvent as the most important factor for this preference. In the present study we further explore the interactions that drive the packing of the highly charged PACaL3 surfactant into highly symmetrical hexameric micelles. We performed a series of molecular dynamics simulations that yielded a large set of structures and an ensemble in good agreement with the experimental Small Angle X-ray Scattering data was selected. The geometry and the rigidity of the calix[4]arene group with proper tail length and headgroup volume are the driving forces for the high symmetry and monodispersity of the micelle. The charge of the headgroups is mainly responsible for inhibiting the formation of higher order structures. Sodium, shown to be important for the stability of the micelle, is not directly interacting with the micelle implying that the calix[4]arene ring is a C2ν symmetry conformation.