  Viruses are biological nanosystems with a capsid of protein-made capsomer
units that encloses and protects the genetic material responsible for their
replication. Here we show how the geometrical constraints of the
capsomer-capsomer interaction in icosahedral capsids fix the form of the
shortest and universal truncated multipolar expansion of the two-body
interaction between capsomers. The structures of many of the icosahedral and
related virus capsids are located as single lowest energy states of this
potential energy surface. Our approach unveils relevant features of the natural
design of the capsids and can be of interest in fields of nanoscience and
nanotechnology where similar hollow convex structures are relevant.
