The Phycodnaviridae, Iridoviridae and related viruses, with diameters of 1500-2000 A, are formed from large trigonal arrays of hexagonally close-packed capsomers forming the faces of icosahedra [Yan et al. (2000), Nature Struct. Biol. 7, 101-103; Nandhagopal et al. (2002), Proc. Natl Acad. Sci. USA, 99, 14758-14763]. Caspar and Klug predicted that such structures could be assembled from hexameric capsomers [Caspar & Klug (1962), Cold Spring Harbor. Symp. Quant. Biol. 27, 1-24], as was subsequently found in numerous icosahedral viruses. During the course of evolution, some viruses, including the virus families mentioned above, replaced hexameric capsomers with pseudo-hexameric trimers by gene duplication. In large dsDNA icosahedral viruses, the capsomers are organized into 'pentasymmetrons' and 'trisymmetrons'. The interactions between the trimeric capsomers can be divided into three groups, one between similarly oriented trimers and two between oppositely oriented trimers (trimers related by an approximately sixfold rotation). The interactions within a trisymmetron belong to the first class, whereas those between trisymmetrons and within the pentasymmetron are of the other two types. Knowledge of these distances permits a more accurate fitting of the atomic structure of the capsomer into the cryo-electron microscopy (cryoEM) reconstruction of the whole virus. The adoption of pseudo-hexagonal capsomers places these viruses into a subset of the Caspar and Klug surface lattices.