Electron microscopy of human immunodeficiency virus (HIV) has provided evidence for a virion model which when sectioned, consists of a circular envelope surrounding an inner conical core. When sections are perpendicular to the core axis, the envelope is still circular, but the tapered core appears as a dot near the center of the envelope. An observation inconsistent with the present model is the frequent finding of an electron-lucent "polygonal window" associated with the virion envelope. Here, we provide evidence for a new model of HIV. This model, which accounts for the polygonal windows and the shape of the envelope, places the conical core inside a regular polyhedron that lies just under the envelope. We tested the validity of various polyhedrons with three-dimensional computer graphics which emulate thin section electron microscopy. With this technique, about 2000 computer-generated "thin sections" of HIV-models were compared with electron micrographs of HIV. A structure consistent with the computer-generated data reveals a detailed model for HIV with the following features; (a) the conical core is inside an envelope-associated capsid having icosadeltahedral symmetry. This envelope-associated capsid is 60-sided and contains 32 vertices, 20 of which have hexagonal symmetry and 12 of which have pentagonal symmetry, (b) the inner rodlike core abuts the inside of any 2 opposing hexagonal vertices, (c) the pentagonal vertices do not support the inner core. A comparison of these results with that of Gelderblom et al. (Gelderblom HR, Hausmann EHS, Ozel M, Pauli G, Koch MA: Fine structure of HIV and immunolocalization of structural proteins. Virology 156: 171, 1987), suggests that the p17 polypeptide is a component of the envelope-associated icosadeltahedral capsid. This computer emulation technique provides a thorough test of this model of HIV, but does not constitute proof. Additional testing methods such as bidirectional metal shadowing and freeze etching will be needed to confirm this new virion structure. Additionally, this computer technique may be useful for testing the proposed morphology for cell organelles.