We infer scaling of the shape and energy of a space-enclosing elastic sheet such as a large fullerene ball of linear dimension R. Stretching deformation is crucial in determining the optimal shape, in conjunction with bending. The asymptotic shape of a symmetrical fullerene ball is a flat-sided polyhedron whose edges have an average curvature radius of order R^2/3. The predicted asymptotic energy is concentrated in these edges and is of order R^1/3. Analogous edges with this scaling property should occur generally in elastic sheets with discrete disclinations.