 Ehrhart's theorem

Ehrhart's theorem says that the lattice-point count $L_P(n)$ of a $d$-dimensional lattice polytope is a polynomial in the nonnegative integer dilation factor, of degree $d$. For full-dimensional $P\subset {\mathbb{R}}^d$, its leading coefficient is the ordinary volume and its constant coefficient is one. Rational vertices instead generally produce a quasipolynomial.^[ref]