  Many spherical viruses encapsulate their genome in protein shells with
icosahedral symmetry. This process is spontaneous and driven by electrostatic
interactions between positive domains on the virus coat proteins and the
negative genome. We model the effect of the icosahedral charge distribution
from the protein shell instead of uniform using a mean-field theory. We find
that the non-uniform charge distribution strongly affects the optimal genome
length, and that it can explain the experimentally observed phenomenon of
overcharging of virus and virus-like particles.
