We tell our story of an investigation to discover how to expand Buckminster Fuller's foldable circle, model-building method to other great circle geometries. We discovered that Fuller's method can be generalized by the introduction of what we call supercircles (buildable constructs that are essentially circular, but have more than 360 degrees of arc). We outline our techniques for building the models and identify relationships to the relevant elements of polyhedron geometry, spherical trigonometry, group theory, combinatorics and graph theory. In the process we have identified a number of interesting mathematical questions which may lead to a theory of great circle foldabilities.