A proof of the branching number bound for normal manifolds Original Research Article

We prove that every face of dimension n − 2 of the normal manifold induced by a polyhedron in imagen is contained in precisely four distinct n-dimensional polyhedra of the normal manifold. This result implies that the branching number of the normal manifold is 4 and refines Ralphʹs result which only gave 4 as an upper bound. The proof is based on the well-known fact that every ridge of a polyhedron is contained in precisely two facets.