Thin polytopes: lattice polytopes with vanishing local \(h^*\)-polynomial (Q6623607)

A lattice polytope is \textit{thin} if its local \(h^*\)-polynomials vanish. The study of thin simplices was originated by Gelfand, Kapranov, and Zelevinsky; for simplices the local \(h^*\)-polynomial equals the box polynomial.\N\NThe paper starts with a survey of existing results around \(h\)- and \(g\)-polynomials and Ehrhart theory.\N\NThe main results are the complete classification of thin polytopes up to dimension \(3\) and the characterization of thinness for Gorenstein polytopes.