Some non-enveloped virus capsids assemble from multiple copies of a single type of coat-protein (CP). The comparative energetics of the diverse CP-CP interfaces present in such capsids likely govern virus assembly-disassembly mechanisms. The T = 3 icosahedral capsids comprise 180 CP copies arranged about two-, three-, five- and six-fold axes of (quasi-)rotation symmetry. Structurally diverse CPs can assemble into T = 3 capsids. Specifically, the Leviviridae CPs are structurally distinct from the Bromoviridae, Tombusviridae and Tymoviridae CPs which fold into the classic "jelly-roll" fold. However, capsids from across the four families are known to disassemble into dimers. To understand whether the overall symmetry of the capsid or the structural details of the CP determine virus assembly-disassembly mechanisms, we analyze the different CP-CP interfaces that occur in the four virus families. Previous work studied protein homodimer interfaces using interface size (relative to the monomer) and hydrophobicity. Here, we analyze all CP-CP interfaces using these two parameters and find that the dimerization interface (present between two CPs congruent through a two-fold axis of rotation) has a larger relative size in the Leviviridae than in the other viruses. The relative sizes of the other Leviviridae interfaces and all the jelly-roll interfaces are similar. However, the dimerization interfaces across families have slightly higher hydrophobicity, potentially making them stronger than other interfaces. Finally, although the CP-monomers of the jelly-roll viruses are structurally similar, differences in their dimerization interfaces leads to varied dimer flexibility. Overall, differences in CP-structures may induce different modes of swelling and assembly-disassembly in the T = 3 viruses.