ASYMPTOTIC SHAPE OF ELASTIC NETWORKS

The shapes of large decorated icosahedron elastic networks are determi ned by minimizing the total elastic energy. In agreement with recent t heoretical predictions, it is found that the asymptotic shape is a fla t-sided polyhedron in which the radius of curvature at the edges scale s as N-1/3, where N is proportional to the surface area. The total ene rgy of these networks scales as N-1/6. Extremely large system sizes ar e needed to observe this behavior. It is also shown that for sufficien tly large networks, the mean curvature is negative over a large portio n of the triangular faces of the icosahedron. Analogous scaling behavi or should occur generally at ridges connecting discrete disclinations in elastic sheets.