In this paper, we present a framework for studying folding problems from a motion-planning
perspective. The version of the motion-planning problem we consider is that of determining …

Unfolding a convex polyhedron into a simple planar polygon is a well-studied problem. In
this paper, we study the limits of unfoldability by studying nonconvex polyhedra with the …

Packaging products such as telephones and two-way radios after assembly is a common
manufacturing task. Carton folding is a packaging operation typically performed by human …

We define a simple orthogonal polyhedron to be a three-dimensional polyhedron with the
topology of a sphere in which three mutually-perpendicular edges meet at each vertex. By …

Three open problems on folding/unfolding are discussed:(1) Can every convex polyhedron
be cut along edges and unfolded at to a single nonoverlap** piece?(2) Given gluing …

Rapid advancement in technology has made virtual 3D models popular and increasingly
affordable. However, 3D displays alone are usually insufficient for a complete understanding …

Is every edge unfolding of every Platonic solid overlapfree? The answer is yes. In other
words, if we develop a Platonic solid by cutting along its edges, we always obtain a flat …

Folding and unfolding problems have been implicit since Albrecht Dürer in the early 1500's
[Dür77], but have not been studied extensively until recently. Over the past few years, there …

We show that every orthogonal polyhedron of genus g ≤ 2 g≤ 2 can be unfolded without
overlap while using only a linear number of orthogonal cuts (parallel to the polyhedron …

An unfolding of a polyhedron is produced by cutting the surface and flattening to a single,
connected, planar piece without overlap (except possibly at boundary points). It is a long …