Ehrhart reciprocity ($L_{P^{\circ }}(n)=(-1{)}^d{L}_P(-n)$)

For a $d$-dimensional lattice polytope $P$ and positive integer $n$, Ehrhart reciprocity stateswith relative interior when needed. Negative input means polynomial evaluation, not a negative dilation count. For the unit square, $(1-n{)}^2=(n-1{)}^2$ counts the interior grid points of its $n$th dilation.^[ref]