Ehrhart polynomials of convex polytopes with small volumes

Let P ⊂ R d be an integral convex polytope of dimension d and δ ( P ) = ( δ 0 , δ 1 , … , δ d ) be its δ -vector. By using the known inequalities on δ -vectors, we classify the possible δ -vectors of convex polytopes of dimension d with ∑ i = 0 d δ i ≤ 3 .