Let $A = \operatorname{co}(E)$ where $E$ is the subset of $\mathbb{R}^3$ defined by $$E = \{(0,0,1),(0,0,-1)\} \cup \{(1+\cos(\theta), \sin(\theta), 0), \theta \in [0, 2\pi]\}$$ show that $\operatorname{Ext}(A)$ is non-empty and is not closed.
Let $A = \operatorname{co}(E)$ where $E$ is the subset of $\mathbb{R}^3$ defined by
$$E = \{(0,0,1),(0,0,-1)\} \cup \{(1+\cos(\theta), \sin(\theta), 0), \theta \in [0, 2\pi]\}$$
show that $\operatorname{Ext}(A)$ is non-empty and is not closed.