The nodavirus Flock house virus (FHV) has a bipartite, positive-sense RNA genome that is packaged into an icosahedral particle displaying T=3 symmetry. The high-resolution X-ray structure of FHV has shown that 10 bp of well-ordered, double-stranded RNA are located at each of the 30 twofold axes of the virion, but it is not known which portions of the genome form these duplex regions. The regular distribution of double-stranded RNA in the interior of the virus particle indicates that large regions of the encapsidated genome are engaged in secondary structure interactions. Moreover, the RNA is restricted to a topology that is unlikely to exist during translation or replication. We used electron cryomicroscopy and image reconstruction to determine the structure of four types of FHV particles that differed in RNA and protein content. RNA-capsid interactions were primarily mediated via the N and C termini, which are essential for RNA recognition and particle assembly. A substantial fraction of the packaged nucleic acid, either viral or heterologous, was organized as a dodecahedral cage of duplex RNA. The similarity in tertiary structure suggests that RNA folding is independent of sequence and length. Computational modeling indicated that RNA duplex formation involves both short-range and long-range interactions. We propose that the capsid protein is able to exploit the plasticity of the RNA secondary structures, capturing those that are compatible with the geometry of the dodecahedral cage.