Gal's conjecture for h*-polynomials

Prove or disprove that if a Gorenstein lattice polytope admits a quadratic triangulation, then its h*-polynomial is γ-positive.

Background

A quadratic triangulation is required to be regular, unimodular, and flag. The conjecture concerns whether this strong triangulation property forces γ-positivity of the h*-polynomial for every Gorenstein lattice polytope.

The flag condition is explicitly essential: without it, the paper notes that even reflexive polytopes with regular unimodular triangulations can have negative γ-coefficients. The problem is identified as a conjecture of Gal and is also cited as Conjecture 3.28 in Ferroni–Higashitani.

References

If a Gorenstein lattice polytope admits a quadratic triangulation, is its $h*$-polynomial $\gamma$-positive?

— Ehrhart Properties under Operations on Lattice Polytopes  (2610.06338 - Liu, 5 Oct 2026) in Section 9, Concluding remarks (Question: Gal's conjecture for h*-polynomials)

They conjectured that a Gorenstein lattice polytope admitting a quadratic triangulation has a $\gamma$-positive $h*$-polynomial Conjecture~3.28.

— Magic positivity for polar duals of pseudo-symmetric smooth Fano polytopes  (2610.06419 - Ohsugi et al., 5 Oct 2026) in Section 1, Introduction