A bound for the splitting of smooth Fano polytopes with many vertices

@article{Assarf2014ABF,
  title={A bound for the splitting of smooth Fano polytopes with many vertices},
  author={Benjamin Assarf and Benjamin Nill},
  journal={Journal of Algebraic Combinatorics},
  year={2014},
  volume={43},
  pages={153-172}
}
The classification of toric Fano manifolds with large Picard number corresponds to the classification of smooth Fano polytopes with large number of vertices. A smooth Fano polytope is a polytope that contains the origin in its interior and is such that the vertex set of each facet forms a lattice basis. Casagrande showed that any smooth d-dimensional Fano polytope has at most 3d vertices. Smooth Fano polytopes in dimension d with at least $$3d-2$$3d-2 vertices are completely known. The main… 
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