Suppose that I want to plot the convex hull of the following set of vectors: namely, \begin{equation} Co(X)=Co\{(1,0,1,1),(0,0,2,1),(0,0,1,2),(0,1,1,1),(1,1,1,0),(1,1,0,1),(1,2,0,0)\} \end{equation} Because the matrix given by the original set of vectors has rank $ 4$ , its convex hull does not lie in a three-dimensional space. However, the matrix given by my original vectors can be translated by subtracting the first vector in such a manner that its convex hull is three-dimensional. In other words, the following convex hull is three-dimensional because the translated matrix has rank $ 3$ and can therefore be plotted: \begin{equation} Co(X^{\prime})=Co\{(0, 0, 0, 0), (-1, 0, 1, 0), (-1, 0, 0, 1), (-1, 1, 0, 0), (0, 1, 0, -1), (0, 1, -1, 0), (0, 2, -1, -1)\} \end{equation}

Hence, my question is simple: can anybody provide some code that plots the convex hull $ Co(X^{\prime})$ ?

Thank you all very much in advance for your time.

PS: In case somebody wants a little bit of background to see where this question comes from, see this question and this other one.