Mahler's symmetric volume-product conjecture

Let $K$ be a centrally symmetric convex body in $cmathbb{R}^{n}$, and let $\mathcal{P}(K)$ denote its volume product. Let $B_{\infty}^{n}$ be the unit ball of the $\ell_{\infty}$ norm. Symmetric Mahler's conjecture.

$$\mathcal{P}(K) \geq \mathcal{P}(B_{\infty}^{n}) = \frac{4^{n}}{n!}.$$

This is the famous lower-bound conjecture for the volume product of centrally symmetric convex bodies; the source does not state a resolution status.