Geminiviruses are major plant pathogens that threaten food security globally. They have a unique architecture built from two incomplete icosahedral particles, fused to form a geminate capsid. However, despite their importance to agricultural economies and fundamental biological interest, the details of how this is realized in 3D remain unknown. Here we report the structure of Ageratum yellow vein virus at 3.3?Å resolution, using single-particle cryo-electron microscopy, together with an atomic model that shows that the N-terminus of the single capsid protein (CP) adopts three different conformations essential for building the interface between geminate halves. Our map also contains density for ~7 bases of single-stranded DNA bound to each CP, and we show that the interactions between the genome and CPs are different at the interface than in the rest of the capsid. With additional mutagenesis data, this suggests a central role for DNA binding-induced conformational change in directing the assembly of geminate capsids.