Facets and volume of Gorenstein Fano polytopes

Abstract

It is known that every integral convex polytope is unimodularly equivalent to a face of some Gorenstein Fano polytope. It is then reasonable to ask whether every normal polytope is unimodularly equivalent to a face of some normal Gorenstein Fano polytope. In the present paper, it is shown that, by giving new classes of normal Gorenstein Fano polytopes, each order polytope as well as each chain polytope of dimension $d$ is unimodularly equivalent to a facet of some normal Gorenstein Fano polytopes of dimension $d+1$. Furthermore, investigation on combinatorial properties, especially, Ehrhart polynomials and volume of these new polytopes will be achieved. Finally, some curious examples of Gorenstein Fano polytopes will be discovered.

13 pages, to appear in Mathematische Nachrichten. arXiv admin note: text overlap with arXiv:1507.03221

References in corpus (3)

• Centrally symmetric configurations of order polytopes
• Quadratic Gröbner bases arising from partially ordered sets
• Volume, facets and dual polytopes of twinned chain polytopes

Cited by in corpus (10)

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• The $h^{\ast }$-polynomials of locally anti-blocking lattice polytopes and their $\gamma$-positivity
• Reflexive polytopes arising from partially ordered sets and perfect graphs
• Reflexive polytopes arising from bipartite graphs with $\gamma$-positivity associated to interior polynomials
• Volume, facets and dual polytopes of twinned chain polytopes
• Enriched chain polytopes
• Enriched order polytopes and Enriched Hibi rings
• Reflexive polytopes arising from edge polytopes
• Gorenstein simplices with a given $\delta$-polynomial
• Two enriched poset polytopes