Let $\mathcal{B}(x, r) = \{x \in \mathbb{R}^n | \|x\| \leq r, r \geq 0\}$ be a ball associated with an arbitrary norm $\|\cdot\|$.
Is it possible to express any ball as a polyhedron
$$\mathcal{P} = \{x | Ax \leq b, Bx = g\}?$$
I cannot see an obvious way when I substituting in the definition of the norm, so I guess this is not possible. is this correct?