An analysis of all possible icosahedral viral capsids is proposed. It takes into accountthe diversity of coat proteins and their positioning in elementary pentagonal andhexagonal configurations, leading to definite capsid size. We show that theself-organization of observed capsids during their production implies a definitecomposition and configuration of elementary building blocks. The exact number of differentprotein dimers is related to the size of a given capsid, labeled by itsT-number. Simple rules determining these numbers for each value ofT are deduced and certain consequences concerning the probabilities ofmutations and evolution of capsid viruses are discussed.
