## Polytopes-The dual mapping question

Can someone help me solve the following question please?

Let v be a vertex of a d-polytope P such that $0 \in intP$ .
Prove that $P^* \cap \{y \in \mathbb{R}^d \mid\left < y, v\right>=1\ \}$ is a facet of $P^{*}$.

The definitions are:
$P^*=\{ y\in\mathbb{R}^{d}\mid\left < x, y\right>\leq 1\ \forall x\in P\}$
and a face of P is the empty set, P itself, or an intersection of P with a supporting hyperplane (i.e.- a hyperplane, such that P is located in one of the halfspaces it determines).
A facet is a face of maximal degree

Thanks