Mathematicians have long been asking the question: Can a given convex polyhedron can be unfolded into a polygon and then refolded into any other convex polyhedron? One facet of this question investigates the space of polyhedra that can be realized from folding a given polygon. While convex polygons are relatively well understood, there are still many open questions regarding the foldings of non-convex polygons. We analyze these folded realizations and their volumes derived from the polygonal family of `L-shapes,' parallelograms with another parallelogram removed from a corner. We investigate questions of maximal volume, diagonal flipping, and topological connectedness and discuss the family of polyhedra that share a L-shape polygonal net.
Dinan, Emily; Nadeau, Alice; and Odegard, Isaac
"Folding concave polygons into convex polyhedra: The L-Shape,"
Rose-Hulman Undergraduate Mathematics Journal: Vol. 16:
1, Article 13.
Available at: https://scholar.rose-hulman.edu/rhumj/vol16/iss1/13