Given a convex polytope defined by $Ax \le b$, with $V = \{ x_1, \ldots, x_n \}$ vertices, I would like to find the maximal distance $\max_{i,j} || x_i - x_j||_2$ as a function of $A$ and $b$ (some upper bound).
Whenever I look for diameter (which is what I would expect) or distance between vertices, I keep finding definitions based on graph theory (e.g. here: https://arxiv.org/pdf/1809.06780.pdf), turning the convex polytope into a graph based on the faces and vertices.
I really want to find the maximal distance between a pair of vertices in the Euclidean sense.
This means to me that either (a) such Euclidean distance is easily obtained by knowing the distance in graph theoretic sense (how?); (b) I am looking for the wrong terms.
Where can I find a hint to that?