Strong isotropic constant conjecture for general convex bodies

Let $\mathcal{C}(K)=\lvert K\rvert^2/\det\operatorname{Cov}(K)=1/L_K^{2n}$ for a convex body $K\subseteq\mathbb{R}^n$, and let $\Delta_{n,0}$ be the standard simplex. The strong isotropic constant conjecture for general convex bodies.

$$\mathcal{C}(K)\geq\mathcal{C}(\Delta_{n,0})=\frac{(n+2)^n(n+1)^{n+1}}{(n!)^2}.$$

Equivalently, the isotropic constant is maximized by the simplex among general convex bodies. The conjecture is described as a strong version of the isotropic constant conjecture; its status is not otherwise resolved in the supplied text.