Let $\operatorname{conv}(a_1,\ldots,a_m)$ denote the convex hull of $\{a_1,\ldots,a_n\}$. Let $P = \operatorname{conv}(a_1,\ldots,a_p)$ and $Q = \operatorname{conv}(b_1,\ldots,b_q)$ be two convex sets in $\mathbb R^n$.

Definition: An extreme point in a convex set $S$ in $\mathbb R^n$ is a point in $S$ which does not lie in any open line segment joining two points of $S$.

Let $\operatorname{ext}(P)$, $\operatorname{ext}(Q)$ denote the sets of extreme points of $P$, $Q$, respectively. Let $P + Q=\{ a+b : a \in P\text{ and } b\in Q \}$ be the Minkowski sum of $P$ and $Q$.

**Question:** What is $\operatorname{ext}(P+Q)$?

PS1: If not in general, is there any special case where the result is known and has a geometric interpretation?

PS2: I am not sure whether this question is of research level or not. If anybody thinks that this is not proper here please give the references and then vote to close. I have searched it in general but could not find any answer. Thanks in advance.