ar X iv : 0 70 6 . 41 78 v 2 [ m at h . C O ] 2 1 Fe b 20 08 Lattice Polytopes of Degree 2

Abstract. A theorem of Scott gives an upper bound for the normalized volume of lattice polygons with exactly i > 0 interior lattice points. We will show that the same bound is true for the normalized volume of lattice polytopes of degree 2 even in higher dimensions. The finiteness of lattice polytopes of degree 2 up to standard pyramids and affine unimodular transformation follows from a theorem of Victor Batyrev. Equivalently, there is only a finite number of quadratic polynomials with fixed leading coefficient being the h∗-polynomial of a lattice polytope.