Stability and geometry of the lyotropic periodic cubic mesophases are consi
dered in the framework of a general symmetry based phenomenological approac
h. A limited number of cubic structural types is shown to be formed by amph
iphilic molecular aggregates: due to the specific nature of self-organizing
units, The related thermodynamic models predict topology of phase diagrams
and specific features of transitions between isotropic, lamellar, cubic bi
continuous and cubic micellar phases.