## Rigidity of Polyhedra

### Introduction

*Are triangulated polyhedral surfaces rigid? *
Euler first proposed the rigidity conjecture in the
18^{th} century, stating that all embedded
polyhedral surfaces are rigid. Early in the
19^{th} 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.