ABSTRACT
If a convex polyhedron in 3-space has the property that the collection of faces containing a given vertex do not all lie in the same plane, then the 2-skeleton of that polyhedron is infinitesimally rigid. J. J. Stoker extends Augustin Louis Cauchy's rigidity theorem to some more general 3-dimensional polyhedra, including special types of non-convex ones and polyhedra with boundary. A polyhedron each of whose vertices is the sole point of the polyhedron which intersects some plane. The boundary of the 3-dimensional polyhedron of Cauchy's theorem is the set of 0, 1, and 2-dimensional faces, the 2-skeleton. Cauchy's proof involved a mixture of topological arguments and arguments from elementary geometry. It is invariant under the operation of dissecting the polyhedron into a finite number of pieces and reassembling them to form a new polyhedron, which is therefore scissors congruent to the first.
