Middlebury College
Department of Computer Science Seminar
Unfolding Polyhedra
Robin Flatland
Associate Professor of Computer Science
Siena College
An unfolding of a polyhedron is a set of cuts that can be applied to its surface so that it can be unfolded flat as a single piece without overlap. Often what is desired is an edge-unfolding in which the cuts are restricted to the polyhedron's edges. For example, an edge-unfolding for a soccer ball shape is shown below. People have been interested in finding unfoldings since at least 1525, when painter and printmaker Albrecht Dürer published a book containing edge-unfoldings for many convex polyhedra. Today applications of polyhedra unfolding arise in manufacturing processes that construct three-dimensional objects by bending sheet metal. Very little, however, is known about what shape classes can and cannot be unfolded, with the biggest open question being whether or not all convex polyhedra have edge-unfoldings.
In this talk I will give an introduction to polyhedra unfolding, discuss recent progress in unfolding orthogonal polyhedra, and present several easily accessible open problems.
Friday, November 18, 2005
12:20 p.m. to 1:15 p.m.
McCardell Bicentennial Hall 538
Lunch will be provided at 12:05 p.m.
All are welcome to attend!