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We address here a theoretical basis for the icosahedral symmetry that is observed so commonly for viral capsids, i.e., the single-protein-thick rigid shells that protect the viral genome. In particular, we outline the phenomenological hamiltonian approach developed recently (see Zandi, R., Reguera, D., Bruinsma, R., Gelbart, W.M. and Rudnick, J. (2004), Original of icosahedral symmetry in viruses, Proc. Natl. Acad. Sci., 101, 15556–15560) to account for the overwhelming prevalence of the Caspar-Klug “T-number” structures that are found for “spherical” viruses. We feature the role of “conformational switching energies” defining the competing multimeric states of the protein subunits. The results of Monte Carlo simulation of this model are argued to shed light as well on the mechanical properties and genome release mechanism for these viruses.