Abstract:

A folding of a polygon is a gluing of the points on the perimeter together to form a polyhedron. We will examine a particular type of folding known as the zipper folding where the perimeter of the polygon is identified starting from a specified point gluing together points equidistant from the starting point (as measured along the perimeter), which “zips” up the boundary of the polygon into a polyhedron. We classify and compute the combinatorially distinct convex foldings of a diamond shape which are obtained via a zipper folding along the boundary of the shape. In the process, we explore computational aspects of this problem; in particular, we outline several useful techniques for computing both the edge set of the final polyhedron and its three-dimensional coordinates.