Dehn's result continues to be valid for spherical geometry and hyperbolic geometry. In both of those geometries, two polyhedra that can be cut and reassembled into each other must have the same Dehn invariant. However, as Jessen observed, the extension of Sydler's result to spherical or hyperbolic geometry remains open: it is not known whether two spherical or hyperbolic polyhedra with the same volume and the same Dehn invariant can always be cut and reassembled into each other. Every hyperbolic manifold with finite volume can be cut along geodesic surfaces into a hyperbolic polyhedron, which necessarily has zero Dehn invariant.