The amphiphiles' hydrocarbon tails are contained on the inside of the micelle and hence the polar-apolar interface of the aggregates has a positive mean curvature, by definition (it curves away from the polar phase).
The structures of the normal topology micellar cubic phases that are formed by some types of amphiphiles (e.g. the oligoethyleneoxide monoalkyl ether series of non-ionic surfactants are the subject of debate.
When thin film samples of micellar cubic phases are viewed under a polarising microscope they appear dark and featureless.
Small air bubbles trapped in these preparations tend to appear highly distorted and occasionally have faceted surfaces.
It was observed that a reverse micellar cubic phase with Fd3m (Q227) symmetry formed in a ternary system of an amphiphilic diblock copolymer (EO17BO10, where EO represents ethylene oxide and BO represents butylene oxide), water, and p-xylene.