For some early very related classifications see 

1) "[The classification of simplicial 3-spheres with nine vertices into polytopes and nonpolytopes][1]" By Altshuler, Bokowski, Steinberg

2) Neighborly 4-polytopes and neighborly combinatorial 3-manifolds with ten vertices, By Altshuler, Canad J Math 1977

3) Neighborly 4-polytopes with 9 vertices‏
A Altshuler, L Steinberg - Journal of Combinatorial Theory, Series A, 1973‏ 

4) [Enumeration of 3-manifolds with 9 vertices][2] Altshuler and Steinberg

5) [Neighborly 2-manifolds with 12 vertices][3]
A Altshuler, J Bokowski, P Schuchert - journal of combinatorial theory, …, 1996‏ 


6) The complete enumeration of the 4-polytopes and 3-spheres with eight vertices‏  
A Altshuler, L Steinberg - Pacific journal of mathematics, 1985‏ 



  [1]: http://www.sciencedirect.com/science/article/pii/0012365X80900291
  [2]: http://www.sciencedirect.com/science/article/pii/0012365X76901382
  [3]: http://www.sciencedirect.com/science/article/pii/S0097316596900692