Let $\mathcal{ P} \subset \mathbb{ R}^d$ be a lattice polytope of dimension $d$. Let $b$ denote the number of lattice points belonging to the boundary of $\mathcal{ P}$ and $c$ that to the interior of $\mathcal{ P}$. It follows from a lower bound theorem of Ehrhart polynomials that, when $c > 0$, the volume of $\mathcal{ P}$ is bigger than or equal to $(dc + (d-1)b - d^2 + 2)/d!$. In the present paper, via triangulations, a short and elementary proof of the minimal volume formula is given.
Categories: math.CO