Graphs and Combinatorics
We pose and answer several questions concerning the number of ways to fold a polygon to a polytope, and how many polytopes can be obtained from one polygon; and the analogous questions for unfolding polytopes to polygons. Our answers are, roughly: exponentially many, or nondenumerably infinite.
Demaine, Erik D.; Demaine, Martin L.; Lubiw, Anna; and O'Rourke, Joseph, "Enumerating Foldings and Unfoldings Between Polygons and Polytopes" (2002). Computer Science: Faculty Publications. 63.