A complete classification is given for non-neighborly combinatorial 3-manifolds with nine vertices. It is found that there are 1246 such types, and that they all are spheres. It is shown that 1057 of those spheres are polytopal. i.e. can be realized as boundary complexes of convex 4-polytopes. 115 spheres are non-polytopal, and 74 spheres remain undecided.
ASJC Scopus subject areas
- Theoretical Computer Science
- Discrete Mathematics and Combinatorics