Asymptotic shape of elastic networks

The shapes of large decorated icosahedron elastic networks are determined by minimizing the total elastic energy. In agreement with recent theoretical predictions, it is found that the asymptotic shape is a flat-sided polyhedron in which the radius of curvature at the edsges scales as ${\mathit{N}}^{1/3}$, where N is proportional to the surface area. The total energy of these networks scales as ${\mathit{N}}^{1/6}$. Extremely large system sizes are needed to observe this behavior. It is also shown that for sufficiently large networks, the mean curvature is negative over a large portion of the triangular faces of the icosahedron. Analogous scaling behavior should occur generally at ridges connecting discrete disclinations in elastic sheets.