Understanding how biological sequences encode structural and functional information is a fundamental scientific challenge. For RNA viral genomes, the information encoded in the sequence extends well-beyond their protein coding role to the role of intra-sequence base pairing in viral packaging, replication, and gene expression. Working with the Pariacoto virus as a model sequence, we investigate the compatibility of predicted base pairings with the dodecahedral cage known from crystallographic studies. To build a putative secondary structure, we first analyze different possible configurations using a combinatorial model of RNA folding. We give results on the trade-offs among types of loop structures, the asymptotic degree of branching in typical configurations, and the characteristics of stems in "well-determined" substructures. These mathematical results yield insights into the interaction of local and global constraints in RNA secondary structures, and suggest new directions in understanding the folding of RNA viral genomes.