Given an initial polytope bounded by $n$ inequalities $Ex \leq f$ where $E \in \mathcal{R}^{n \times n} $ and $f \in \mathcal{R}^n$, assume we know the set of vertices of this (bounded) polytope.
Now, consider a transformation (matrix $H \in \mathcal{R}^{n \times m}$) composed of m orthonormal columns. Consider a transformed set of inequalities given by $\tilde{E}q \leq \tilde{f}$ where $\tilde{E}= EH$ and $\tilde{E} \in \mathcal{R}^{n \times m}$. And, $\tilde{f}, q \in \mathcal{R}^m$
Can the vertices of the new set of inequalities, $\tilde{E} \leq \tilde{f}$ be computed using the vertices of $Ex \leq f$ ?