Inclusion-connectivity of reflexive polytopes in higher dimensions

Prove that the graph of d-dimensional reflexive lattice polytopes modulo unimodular equivalence, with adjacency defined by inclusion of representatives in a common lattice, is connected for dimensions d≥5.

Background

The paper defines a graph whose vertices are unimodular-equivalence classes of d-dimensional reflexive lattice polytopes and whose edges join classes admitting nested representatives. It proves that the Gorenstein weak F-equivalence conjecture in dimension d would imply connectedness of this graph.

Connectedness is known for dimensions at most four through classifications and prior results. The authors identify the higher-dimensional cases as unresolved, making this a concrete polyhedral consequence and an independent open problem related to the proposed Gorenstein refinement.