Abstract

We study the phase separation of binary lipid mixtures that form bicontinuous cubic phases. The
competition between the nonuniform Gaussian membrane curvature and line tension leads to a very rich
phase diagram, where we observe symmetry breaking of the membrane morphologies and reentrant
phenomena due to the formation of bridges between segregated domains. Upon increasing the line tension
contribution, we also find faceting of lipid domains that we explain using a simple argument based on the
symmetry of the underlying surface and topology.