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Types of membrane geometries with different mean and Gaussian curvatures. (a) A vesicle with positive mean curvature and positive Gaussian curvature. (b) A tubule with positive mean curvature and zero Gaussian curvature. (c) The cubic phase lm3m with negative Gaussian curvature. (d) The inverted hexagonal phase HII with negative mean curvature and zero Gaussian curvature. The principal directions are shown in grey.
