Much effort has gone into finding peptides that bind potentially useful nanoparticles, but relatively little effort has focused on the scaffolds that organize these peptides into useful nanostructures. Chaperonins are protein complexes with 14 - 18 protein subunits that self-assemble into double-ring complexes and function as scaffolds for peptides or amino acids that bind metallic and semiconductor quantum dots. The utility of chaperonins as scaffolds depends on their structure and their ability to self-assemble into double-rings and higher-order structures, such as filaments and two-dimensional arrays. To better understand the structure of chaperonins, we constructed a model of a group II chaperonin and, based on this model, genetically constructed five mutant subunits with significant deletions. We expressed these mutants as recombinant proteins and observed by native polyacrylamide gel electrophoresis (PAGE) and transmission electron microscopy (TEM) that they all self-assembled into double rings. Our model predicted and TEM confirmed that these deletions did not significantly change the 17 nm diameter of the wild-type double rings, but decreased their height and opened their central cavities. Four of the five mutants formed higher-order structures: chains of rings, bundles of chains or filaments, and two-dimensional arrays, which we suggest can be useful nanostructures.