Symmetric edge polytopes are not gamma-positive

Abstract

A conjecture posed by Ohsugi and Tsuchiya (2019) postulates that the Ehrhart $h^{\ast }$-polynomials of symmetric edge polytopes are ${\hat{I}}^3$-positive. We disprove this conjecture by exhibiting an infinite family of counterexamples. The smallest example provided by our construction is a $36$-dimensional symmetric edge polytope.

6 pages, 1 Figure. Comments welcome!