  We study the phase separation of binary lipid mixtures that form bicontinuous
cubic phases. The competition between non-uniform 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 facetting of lipid domains that we explain
using a simple argument based on the symmetry of the underlying surface and
topology.
