A local rule-based theory is developed which shows that the self-assembly of icosahedral virus shells may depend on only the lower-level interactions of a protein subunit with its neighbors-i.e., on local rules rather than on larger structural building blocks. The local rule theory provides a framework for understanding the assembly of icosahedral viruses. These include both viruses that fall in the quasiequivalence theory of Caspar and Klug and the polyoma virus structure, which violates quasi-equivalence and has puzzled researchers since it was first observed. Local rules are essentially templates for energetically favorable arrangements. The tolerance margins for these rules are investigated through computer simulations. When these tolerance margins are exceeded in a particular way, the result is a "spiraling" malformation that has been observed in nature.