This study concerns the self-assembly of virus-like particles (VLPs) composed of an icosahedral virus protein coat encapsulating a functionalized spherical nanoparticle core. The recent development of efficient methods for VLP self-assembly has opened the way to structural studies. Using electron microscopy with image reconstruction, the structures of several VLPs obtained from brome mosaic virus capsid proteins and gold nanoparticles were elucidated. Varying the gold core diameter provides control over the capsid structure. The number of subunits required for a complete capsid increases with the core diameter. The packaging efficiency is a function of the number of capsid protein subunits per gold nanoparticle. VLPs of varying diameters were found to resemble to three classes of viral particles found in cells (T=1, 2, and 3). As a consequence of their regularity, VLPs form three-dimensional crystals under the same conditions as the wild-type virus. The crystals represent a form of metallodielectric material that exhibits optical properties influenced by multipolar plasmonic coupling.