  We investigate the stability of seven inverse bicontinuous cubic phases ($G$,
$D$, $P$, $C(P)$, $S$, $I-WP$, $F-RD$) in lipid-water mixtures based on a
curvature model of membranes. Lipid monolayers are described by parallel
surfaces to triply periodic minimal surfaces. The phase behavior is determined
by the distribution of the Gaussian curvature on the minimal surface and the
porosity of each structure. Only $G$, $D$ and $P$ are found to be stable, and
to coexist along a triple line. The calculated phase diagram agrees very well
with experimental results for 2:1 lauric acid/DLPC.
