  In this paper we extend the classical theory of combinatorial manifolds to
the non-homogeneous setting. NH-manifolds are polyhedra which are locally like
Euclidean spaces of varying dimensions. We show that many of the properties of
classical manifolds remain valid in this wider context. NH-manifolds appear
naturally when studying Pachner moves on (classical) manifolds. We introduce
the notion of NH-factorization and prove that PL-homeomorphic manifolds are
related by a finite sequence of NH-factorizations involving NH-manifolds.
