Abstract
Phenomena such as protein folding, crystallisation, self-assembly, and the observation of magic number clusters in molecular beams are all the result of non-random searches. Analysis of the underlying potential energy surface may provide a unifying framework to explain how such events occur as the result of a guided exploration of the landscape. In particular, icosahedral shells composed of 12 pentagonal pyramids are found to be thermodynamically favourable and kinetically accessible when the pyramids are not too spiky and not too flat. Hence, viruses with icosahedral capsids not only minimise the genetic material required to encode the repeated subunits, but may also utilise the favourable properties of a potential energy surface that effectively directs self-assembly.