Flexible polyhedron

A flexible polyhedron is a polyhedron that, if physically constructed with rigid plates for faces and hinges as edges, can deform in shape. A polyhedron that cannot deform at all is known as rigid, and a polyhedron that can deform but only infinitesimally is known as shaky. All convex polyhedra are rigid, as proven by Cauchy. The bellows conjecture, proven in 1997, states that the volume of a flexible polyhedron is constant as it is deformed.

Klaus Steffen found a 14-face flexible polyhedron made of only triangles, which has been proven minimal for a polyhedron with only triangular faces.