Some theoretical shapes of red blood cells are presented, reproducing the well-known transition between the normally observed biconcave disk and the sphere. The curvature elasticity of the bounding membrane and the enclosed volume are assumed to control the shape. The membrane must have a spontaneous curvature opposite to the curvature of the sphere if flattened forms rather than elongated ones are to be stable.
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Helfrich et al. (1975) studied this question.