Artificial protein cages have great potential in diverse fields including as vaccines and drug delivery vehicles. TRAP-cage is an artificial protein cage notable for the way in which the interface between its ring-shaped building blocks can be modified such that the conditions under which cages disassemble can be controlled. To date, TRAP-cages have been constructed from homo-11mer rings, i.e., hendecamers. This is interesting as convex polyhedra with identical regular faces cannot be formed from hendecamers. TRAP-cage overcomes this limitation due to intrinsic flexibility, allowing slight deformation to absorb any error. The resulting TRAP-cage made from 24 TRAP 11mer rings is very close to regular with only very small errors necessary to allow the cage to form. The question arises as to the limits of the error that can be absorbed by a protein structure in this way before the formation of an apparently regular convex polyhedral becomes impossible. Here we use a naturally occurring TRAP variant consisting of twelve identical monomers (i.e., a dodecamer) to probe these limits. We show that it is able to form an apparently regular protein cage consisting of twelve TRAP rings. Comparison of the cryo-EM structure of the new cage with theoretical models and related cages gives insight into the rules of cage formation and allows us to predict other cages that may be formed given TRAP-rings consisting of different numbers of monomers.