U. S. Schwarz and G. Gompper 
Stability of bicontinuous cubic phases in
ternary amphiphilic systems with spontaneous curvature  
J. Chem. Phys. 112: 3792 - 3802 (2000)

We study the phase behavior of ternary amphiphilic systems in the
framework of a curvature model with non-vanishing spontaneous
curvature.  The amphiphilic monolayers can arrange in different ways
to form micellar, hexagonal, lamellar and various bicontinuous cubic
phases. For the latter case we consider both single structures (one
monolayer) and double structures (two monolayers).  Their interfaces
are modeled by the triply periodic surfaces of constant mean
curvature of the families G, D, P, C(P), I-WP and F-RD. The
stability of the different bicontinuous cubic phases can be
explained by the way in which their universal geometrical properties
conspire with the concentration constraints.  For vanishing
saddle-splay modulus $\bar \kappa$, almost every phase considered
has some region of stability in the Gibbs triangle.  Although
bicontinuous cubic phases are suppressed by sufficiently negative
values of the saddle-splay modulus $\bar \kappa$, we find that they
can exist for considerably lower values than obtained previously.
The most stable bicontinuous cubic phases with decreasing $\bar
\kappa < 0$ are the single and double gyroid structures since they
combine favorable topological properties with extreme volume
fractions.