  We give a simple combinatoric proof of an exponential upper bound on the
number of distinct 3-manifolds that can be constructed by successively
identifying nearest neighbour pairs of triangles in the boundary of a
simplicial 3-ball and show that all closed simplicial manifolds that can be
constructed in this manner are homeomorphic to $S^3$. We discuss the problem of
proving that all 3-dimensional simplicial spheres can be obtained by this
construction and give an example of a simplicial 3-ball whose boundary
triangles can be identified pairwise such that no triangle is identified with
any of its neighbours and the resulting 3-dimensional simplicial complex is a
simply connected 3-manifold.
