A natural and well-studied problem in algorithmic graph theory and network optimization is
that of computing a\shortest path" between two nodes, s and t, in a graph whose edges …

We present an algorithm for determining the shortest path between any two points along the
surface of a polyhedron which need not be convex. This algorithm also computes for any …

The subject of Discrete Geometry and Convex Polytopes has received much attention in
recent decades, with an explosion of the work in the field. This book is an introduction …

We introduce the notion of a star unfolding of the surface \calP of a three-dimensional
convex polytope with n vertices, and use it to solve several problems related to shortest …

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 …

In this paper, we study unfoldings of orthogonal polyhedra. More precisely, we de ne two
special classes of orthogonal polyhedra, orthostacks and orthotubes, and show how to …

We present an optimal-time algorithm for computing (an implicit representation of) the
shortest-path map from a fixed source s on the surface of a convex polytope P in three …

In 1525, the painter Albrecht D urer introduced the notion of a net of a polytope, and
published nets for some of the Platonian and Archimedian polyhedra, along with directions …

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 …