A sufficient condition for a polyhedron to be rigid

Abstract

We study oriented connected closed polyhedral surfaces with non-degenerate triangular faces in three-dimensional Euclidean space, calling them polyhedra for short. A polyhedron is called flexible if its spatial shape can be changed continuously by changing its dihedral angles only. We prove that for every flexible polyhedron some integer combination of its dihedral angles remains constant during the flex. The proof is based on a recent result of A. A. Gaifullin and L. S. Ignashchenko.