Topological defects in bicontinuous phases

It is shown that in balanced bicontinuous cubic lyotropic crystals two types of dislocations are possible. The first, trivial type of dislocations preserves the orientability of the surfactant bilayer. Dislocations of the second, Mobius type make the bilayer non-orientable. Upon melting of the cubic phase into the sponge phase, crystal order is destroyed but Mobius dislocations persist by virtue of topological continuity as disorientation: a new kind of topological defects which, by definition, alter the orientability of the bilayer.