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On a Classification of Smooth Fano Polytopes

Abstract : The $d$-dimensional simplicial, terminal, and reflexive polytopes with at least $3d-2$ vertices are classified. In particular, it turns out that all of them are smooth Fano polytopes. This improves previous results of Casagrande (2006) and Øbro (2008). Smooth Fano polytopes play a role in algebraic geometry and mathematical physics. This text is an extended abstract of Assarf et al. (2012).
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Benjamin Assarf, Michael Joswig, Andreas Paffenholz. On a Classification of Smooth Fano Polytopes. 25th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2013), 2013, Paris, France. pp.421-432. ⟨hal-01229748⟩

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