Through building some initial shapes which are similar to target shapes in Surface Evolver, after a long time of evolvement, we obtain the starfish vesicles with D2h and D3h symmetry, which are supported by experiment. Through tracing the eigenvalues of Hessian matrix of different shapes, we find that between the oblate and the star-fish vesicles, and between the oblate and prolate vesicles, there are two discontinuous phase transformation, and the biconcave triangular shapes and the biconcave elliptic shapes are usually unstable in the SC model.