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We study the phase separation of binary lipid mixtures that form bicontinuouscubic phases. The competition between non-uniform Gaussian membrane curvatureand line tension leads to a very rich phase diagram, where we observe symmetrybreaking of the membrane morphologies and reentrant phenomena due to theformation of bridges between segregated domains. Upon increasing the linetension contribution, we also find facetting of lipid domains that we explainusing a simple argument based on the symmetry of the underlying surface andtopology.

Phase Separation on Bicontinuous Cubic Membranes: Symmetry Breaking, Re-entrant and Domain Facetting