Abstract

The difficulty of constructing ordered states on spheres was recognized by J. J. Thomson, who discovered the electron and then attempted regular tilings of the sphere in an ill-fated attempt to explain the periodic table. We discuss how protein packings in virus shells solve a related “Thomson problem”, and the remarkable modifications in the theory necessary to account for grain boundary scars in colloidal particles packed on spheres. We then apply related ideas to the folding strategies and shapes of pollen grains during dehydration. The grain can be modeled as a pressurized high-Young-modulus sphere with a weak sector and a nonzero spontaneous curvature. In the absence of such a weak sector, these shells crumple irreversibly under pressure via a strong first order phase transition. The weak sectors eliminate the hysteresis and allow easy re-hydration at the pollination site, somewhat like the collapse and subsequent reassembly of a folding chair.