Arbitrary-dimensional reflexive-polytope connectivity conjecture

Determine whether the inclusion-connectivity conjecture holds in every dimension, namely whether all d-dimensional reflexive lattice polytopes modulo unimodular equivalence can be connected to the standard reflexive simplex by a chain of inclusions.

Background

The authors report that the inclusion graph is connected for d≤4. In dimensions two and three, this follows from stronger containment results, while dimension four is covered by classification results modulo unimodular equivalence.

The general higher-dimensional problem remains unresolved and is directly relevant to the proposed Gorenstein weak F-equivalence conjecture, because any such equivalence would induce a chain of nested reflexive ray polytopes.