The current work is organized as follows. In the following section the particle-in-a-box problem will be more fully introduced and contextualized historically. A syntax is then suggested that unifies the landscape of model quantum systems, and is aimed to help scientists navigate the literature, and the facets of the physics and chemistry described by the models. As will be seen, the confining shape, the 'box' the particle(s) are placed in, has a profound effect on their behavior. In its simplest form the box is two dimensional and the range of permissible shapes are bounded by the platonic ideals of the square and the circle. To connect these two shapes, we introduce the Superformula. This remarkably flexible mathematical construct has been used to describe biological, chemical, and physical phenomena 5 , but is simple enough in its functional form to be accessible to a student with a secondary education. The use of the Superformula as a model of confinement will be similarly reviewed. Summary remarks conclude the paper.