The Stoker problem states that the dihedral angles of a convex Euclidean polyhedron determine the angles of each face. In this talk , I will present my recent works joint with Zhizhang Xie and Guoliang Yu that answers positively to Stoker's problem, and proves a more general dihedral rigidity for manifolds with polytope singularities. I will briefly introduce our approach, the index theory of Dirac-type operator on manifold with polytope singularities under certain boundary conditions.