Suppose I have $n$ linearly independent vectors $v_1, \ldots, v_n$ in $\mathbb R^n$.
Is there an expression for the volume of the following set:
$$ \{x \in \mathbb R^n : |x \cdot v_i| \leq 1 \text{ for all } i\} $$
?
My understanding is that this is the polar set of $\{ \pm v_1, \ldots, \pm v_n\}$.