Rigidity conjecture for geometric nonconvex self-intersecting polyhedra

A geometric polyhedron here may be nonconvex and self-intersecting; its faces, dihedral angles, edge lengths, and partially-flat vertices are understood in the sense of the paper. The nonconvex polyhedron rigidity conjecture. Every geometric, possibly nonconvex and self-intersecting, polyhedron is uniquely determined by its dihedral angles and edge lengths, if it satisfies that (i) every face is convex and (ii) no vertex is partially flat. The result proved in the paper requires an additional condition excluding collinear triples of vertices. The conjecture proposes removing that auxiliary condition and is described as a challenging long-term goal.