HI,

I have a question regarding convex polytopes. Let us say I have the vertices of a polytope which I name as $ V = \{v_1,\cdots,v_k\}$. Each of the $v_k$ are n-dimensional vectors, i.e. $v_k \in R^n$. I would like to know if it is possible to write the polytope as intersection of half-spaces using the information from the vertices, i.e. can I write the polytops as $Ax\leq b, A \in \mathbb{R}^{m \times n}, b \in \mathbb{R}^m, x \in R^n$, where $m$ denotes the number of linear inequalities. Columns of A are not necessarily the vertices of the given polytope. An example, consider a polytope in $R^2_+$ with vertices $\{(0,1),(1,1),(2,0),(0,0)\}$. It can be observed that the corresponding half space representation is $Ax\le b$, where $$A=\begin{pmatrix}\\\ 0 & 1 \\\ 1 & 1 \\\ -1 & 0\\\ 0 & -1\end{pmatrix}, b = (1,2,0,0 )^T$$.

Thank You