It is shown that there are examples of distinct polyhedra, each with a Hamiltonian path of edges, which when cut, unfolds the surfaces to a common net. In particular, it is establ...
Given a convex polyhedron with n vertices and F faces, what is the fewest number of pieces, each of which unfolds to a simple polygon, into which it may be cut by slices along edg...
The main motivation here is a question: whether any polyhedron which can be subdivided into convex pieces without adding a vertex, and which has the same vertices as a convex poly...
We consider the problems of straightening polygonal trees and convexifying polygons by continuous motions such that rigid edges can rotate around vertex joints and no edge crossing...