I have a non-convex n-dimensional set defined by the constraints:
$$ \frac{n-2}{\sum_{i=1}^{n-1}\frac{1}{v_i}}<v_n $$ $$ 1<v_i<n-1.$$
I am trying to find a Convex Hull of this set. In the 3-dimensional case, it seems like it is sufficient to find a hyperplane that spans through the intersection of concave constraint and bounding surfaces spanned by the second constraint, and then replace the original concave constraint with a linear equation of a plane. Example: 
However, I fail to understand how to do it for 4 and higher dimensions.
Any help would be appreciated.
Update I have recognized that I do not even need a hyperplane equation to solve my problem. It would be sufficient just to understand which $n$ points are on this hyperplane.