Facet Numbers of Non-Centrally Symmetric Reflexive Polytopes Arising from Posets

Abstract

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 $$6^{d/2}$$ 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 $$6^{d/2}$$ 6 d / 2 .