Suppose that $\pi:(V_1,F_1)\to V_2$ is a linear surjective map, where $V_1$ and $V_2$ are vector spaces and $F_1$ is a Minkowski norm on $V_1$. Let $\Sigma_1$ be the indicatrix on $V_1$, that is the unitary sphere with respect to $F_1$. Define $\Sigma_2:=\pi(\Sigma_1)$.
If $\Sigma_2$ is an indicatrix with respect to some Mnikowski norm on $V_2$?