Folding Paper Shopping Bags

One of the most ubiquitous examples of origami is the common paper shopping bag. In a common model of paper folding, there are a finite number of creases, between which the paper must stay rigid and flat, as if made of plastic or metal plates connected by hinges. We show that (maybe surprisingly), the paper shopping bag cannot be flattened under this model using the usual pattern of creases. This raises the question of what foldings are possible in this model? We introduce some techniques for foldability analysis, and show that the bag may be flattened by adding new creases, or by adding new material between creases.