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 .
Fields of Study & Subjects
Advanced Combinatorial Mathematics
Computational Geometry and Mesh Generation
Geometric and Algebraic Topology
Publication details
- Journal / source
- Discrete & Computational Geometry
- Publisher
- Springer Science and Business Media LLC
- Publication date
- 31 August 2026
- Language
- EN