Hadwiger's covering conjecture for convex bodies

Let $K$ be a convex body in $\mathbb{R}^n$, meaning a compact convex set with interior points, and let $c(K)$ be the least number of translates of the relative interior of $K$ needed to cover $K$.

Hadwiger's covering conjecture. For each $K\in\mathcal{K}^n$, $c(K)$ is bounded from above by $2^n$, and this upper bound is attained only by parallelotopes.

Hadwiger's covering conjecture concerns the least upper bound of the covering numbers of convex bodies. The source presents it as a longstanding conjecture and gives references for further information; no resolution is stated here.