The orientation and location of the 240 hexons comprising the outer protein shell of adenovirus have been determined. Electron micrographs of the capsid and its fragments were inspected for the features of hexon known from the X-ray crystallographic model as described in the accompanying paper. A capsid model is proposed with each facet comprising a small p3 net of 12 hexons, arranged as a triangular sextet with three outer hexon pairs. The sextet is centrally placed about the icosahedral threefold axis, with its edges parallel to those of the facet. The outer pairs project over the facet edges on one side of the icosahedral twofold axes at each edge. The model capsid is defined by the underlying icosahedron, of edge 445 A, upon which hexons are arranged. The hexons are thus bounded by icosahedra with insphere radii of 336 A and 452 A. A quartet of hexons forms the asymmetric unit of an icosahedral hexon shell, which can be closed by the addition of pentons at the 12 vertices. Considering the hexon trimer as a complex structure unit, its interactions in the four topologically distinct environments are very similar, with conservation of at least two-thirds of the inter-hexon bonding. The crystal-like construction explains the flat facets and sharp edges characteristic of adenovirus. Larger "adenovirus-like" capsids of any size could be formed using only one additional topologically different environment. The construction of adenovirus illustrates how an impenetrable protein shell can be formed, with highly conserved intermolecular bonding, by using the geometry of an oligomeric structure unit and symmetry additional to that of the icosahedral point group. This contrasts with the manner suggested by Caspar & Klug (1962), in which the polypeptide is the structure unit, and for which the number of possible bonding configurations required of a structure unit tends to infinity as the continuously curved capsid increases in size. The known structures of polyoma and the plant viruses with triangulation number equal to 3 are evaluated in terms of hexamer-pentamer packing, and evidence is presented for the existence of larger subunits than the polypeptide in both cases. It is suggested that spontaneous assembly can occur only when exact icosahedral symmetry relates structure units or sub-assemblies, which would themselves have been formed by self-limiting closed interactions. Without such symmetry, the presence of scaffolding proteins or nucleic acid is necessary to limit aggregation.