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arXiv · 2511.22981

Facet numbers of non-centrally symmetric reflexive polytopes arising from posets

Aki Mori·Kenta Mori·Hidefumi Ohsugi
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Abstract

Twinned chain polytopes form a broad class of non-centrally symmetric reflexive polytopes and exhibit intriguing structures. In the present paper, we show that the number of facets of $d$-dimensional twinned chain polytopes is at most $6^{d/2}$. In case $d$ is even, the equality holds if and only if the polytope is isomorphic to a free sum of $d/2$ copies of del Pezzo polygons. This result contributes a partial answer to Nill's conjecture: the number of facets of a $d$-dimensional reflexive polytope is at most $6^{d/2}$.

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Aki Mori, Kenta Mori, Hidefumi Ohsugi. 2025-11-28. Facet numbers of non-centrally symmetric reflexive polytopes arising from posets. https://arxiv.org/abs/2511.22981

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