Slightly broken icosahedral symmetry advances Thomson problem

To advance Thomson problem we generalize physical principles suggested by Caspar and Klug (CK) to model icosahedral capsids. Proposed simplest distortions of the CK spherical arrangements yield new-type trial structures very close to the lowest energy ones. In the region 600<N<1000, where N is the number of particles in the structure, we found 40 new spherical crystals with the lowest ever seen energies and curvature-induced topological defects being not the well-known elongated scars but flatten pentagons. These crystals have N values prohibited in the CK model and demonstrate a new way to combine the local hexagonal order and spherical geometry.