The structure and assembly of icosahedral virus capsids composed of one or more gene products and displaying quasi-equivalent subunit associations are discussed at three levels. The principles of quasi-equivalence and the related geodesic dome formation are first discussed conceptually and the geometric basis for their construction from two-dimensional assembly units is reviewed. The consequences for such an assembly when three-dimensional protein subunits are the associating components are then discussed with the coordinates of cowpea chlorotic mottle virus (CCMV) used to generate hypothetical structures in approximate agreement with the conceptual models presented in the first section. Biophysical, molecular genetic, and atomic structural data for CCMV are then reviewed, related to each other, and incorporated into an assembly model for CCMV that is discussed with respect to the modular, chemical nature of the viral subunit structure. The concepts of quasi-equivalence are then examined in some larger virus structures containing multiple subunit types and auxiliary proteins and the need for additional control points in their assembly are considered. The conclusion suggests that some viral assembly principles are limited paradigms for protein associations occurring in the broader range of cell biology including signal transduction, interaction of transcription factors and protein trafficking.