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arXiv · 1206.4827

A classification of smooth convex 3-polytopes with at most 16 lattice points

Anders Lundman
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Abstract

We provide a complete classification up to isomorphism of all smooth convex lattice 3-polytopes with at most 16 lattice points. There exist in total 103 different polytopes meeting these criteria. Of these, 99 are strict Cayley polytopes and the remaining 4 are obtained as inverse stellar subdivisions of such polytopes. We derive a classification, up to isomorphism, of all smooth embeddings of toric threefolds in $\mathbb{P}^N$ where $N\le 15$. Again we have in total 103 such embeddings. Of these, 99 are projective bundles embedded in $\mathbb{P}^N$ and the remaining 4 are blow-ups of such toric threefolds.

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Anders Lundman. 2012-06-21. A classification of smooth convex 3-polytopes with at most 16 lattice points. https://doi.org/10.1007/s10801-012-0363-3

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