  The Fourier approach and theories of space groups and color symmetries are
used to systematically generate and compare bicontinuous cubic structures in
the framework of a Ginzburg-Landau model for ternary amphiphilic systems. Both
single and double structures are investigated; they correspond to systems with
one or two monolayers in a unit cell, respectively. We show how and why single
structures can be made to approach triply periodic minimal surfaces very
closely, and give improved nodal approximations for G, D, I-WP and P surfaces.
We demonstrate that the relative stability of the single structures can be
calculated from the geometrical properties of their interfaces only. The single
gyroid G turns out to be the most stable bicontinuous cubic phase since it has
the smallest porosity. The representations are used to calculate distributions
of the Gaussian curvature and 2H-NMR bandshapes for C(P), C(D), S, C(Y) and
F-RD surfaces.
