  Polyhedral vesicles with a large bending modulus of the membrane such as the
gel phase lipid membrane were studied using a Brownian dynamics simulation. The
vesicles exhibit various polyhedral morphologies such as tetrahedron and cube
shapes. We clarified two types of line defects on the edges of the polyhedrons:
cracks of both monolayers at the spontaneous curvature of monolayer $C_{\text
{0}}<0$, and a crack of the inner monolayer at $C_{\text {0}}\ge0$. Around the
latter defect, the inner monolayer curves positively. Our results suggested
that the polyhedral morphology is controlled by $C_{\text {0}}$.
