Let Δ denote an integral convex polytope of dimension n in a lattice M, and let l_Δ(k) denote the number of lattice points in Δ dilated by a factor of the integer k, l_Δ(k) = #(k Δ intersection M) for k element Z^+. Then l_Δ is a polynomial function in k of degree n with rational coefficients l_Δ(k) = a_n k^n + a_(n - 1) k^(n - 1) + ... + a_0 called the Ehrhart polynomial. Specific coefficients have important geometric interpretations. 1.a_n is the content of Δ.

Dehn invariant | Pick's theorem