This question nicely explains how to go from a vertex representation ($\mathcal{V}$) to a half-space representation ($\mathcal{H}$) of a polytope. But I don't fully understand how to go from a half-space representation to a vertex representation.
I am using the QuickHull algorithm to go from a vertex representation to a half-space representation ($\mathcal{V}\rightarrow\mathcal{H}$). But I should be able to use the same algorithm to go from $\mathcal{H}\rightarrow\mathcal{V}$, given that these problems are equivalent?