The paper deals with a class of 3-dimensional polyhedra -called pinched manifolds - admitting only the simplest kind of singular points, i. e. points with a neighbourhood PL homeomorphic to the cone over a 2-sphere with holes. Pinched manifolds naturally appear as polyhedra associated to edge-coloured graphs with boundary. In fact, if we delete any set of edges, all coloured c, from a crystallization G of a closed 3-manifold, then the resulting graph represents a pinched manifold. On the other hand, if we delete all such edges from G, we obtain a graph representing the 3-disk D^3. Hence, pinched manifolds could be thougth of as the middle steps of a procedure for constructing a closed 3-manidols from D^3.