Let $V_n$ be the least real number such that for every convex subset of $\mathbb{R}^n$ with hypervolume $1$ there is a containing simplex with hypervolume $V_n$. What is known about $V_n$? Is there a known general formula? If not, then what is the best known bounds on $V_n$?

Let $V_n$ be the least real number such that for every convex subset of $\mathbb{R}^n$ with hypervolume $1$ there is a containing simplex with hypervolume $V_n$. What is known about $V_n$? Is there a known general formula? If not, then what are the known best bounds for $V_n$?

Let $V_n$ be the least real number such that for every convex subset of $\mathbb{R}^n$ with measure $1$ there is a containing simplex with measure $V_n$. What is known about $V_n$? Is there a known general formula? If not, then what is the best known bounds on $V_n$?

Let $V_n$ be the least real number such that for every convex subset of $\mathbb{R}^n$ with hypervolume $1$ there is a containing simplex with hypervolume $V_n$. What is known about $V_n$? Is there a known general formula? If not, then what is the best known bounds on $V_n$?