Rigidity of Polyhedra


Are triangulated polyhedral surfaces rigid?

Euler first proposed the rigidity conjecture in the 18th century, stating that all embedded polyhedral surfaces are rigid. Early in the 19th century, Cauchy proved that any convex polyhedron in R3 with rigid faces, but hinged at the edges, was in fact completely rigid (i.e., it could not be subjected to small perturbations). However the "rigidity conjecture" that any (not necessarily convex) polyhedron homeomorphic to a sphere was rigid was disproved by Connelly, who described a simple example of an 18-faced, 11-vertex polyhedron that may be "flexed."

This page is a computational geometry student project for the course 308-507A taught by Professor Godfried Toussiant of McGill University, Monrtreal, Canada. You can look at other students' projects by clicking here.

NEXT: Timeline of Rigidity Theories

Illustrated by Jonathan Shum
Center for Intelligent Machines
McGill University, Montreal, Canada.