On three dimensional stellar manifolds

It is well known that a three dimensional (closed, connected and compact) manifold is obtained by identifying boundary faces from a stellar ball a ⋆ S. The study of S/ ∼, two dimensional stellar sphere S with 2-simplexes identified in pairs leads us to the following conclusion: either a three dimensional manifold is homeomorphic to a sphere or to a stellar ball a⋆S with its boundary 2-simplexes identified in pairs so that S/ ∼ is a finite number of internally flat complexes attached to a finite graph that contains at least one closed circuit. Each of those internally flat complexes is obtained from a polygon where each side may be identified with one or more different other sides. Moreover, Euler characteristic of S/ ∼ is equal to one and the fundamental group of S/ ∼ is not trivial.