  The structural organisation of the viral genome within its protein container,
called the viral capsid, is an important aspect of virus architecture. Many
single-stranded (ss) RNA viruses organise a significant part of their genome in
a dodecahedral cage as a RNA duplex structure that mirrors the symmetry of the
capsid. Bruinsma and Rudnick have suggested a model for the structural
organisation of the RNA in these cages. It is the purpose of this paper to
further develop their approach based on results from the areas of graph theory
and DNA network engineering. We start by suggesting a scenario for pariacoto
virus, a representative of this class of viruses, that is energetically more
favorable than those derived previously. We then show that it is a
representative of a whole family of cage structures that abide to the same
construction principle, and then derive the energetically optimal configuration
for a second family of cage structures along similar lines. Finally, we give
reasons for the conjecture that these two families are more likely to occur in
nature than other scenarios.
