Zhang's metric dimension conjecture for folded hypercubes

Let $F_n$ be the folded $n$-cube obtained from the hypercube $Q_n$ by identifying each vertex $u$ with its antipode; write $\beta(F_n)$ for its metric dimension. Zhang's conjecture. If $n\ge 5$ is odd, then

$$\beta(F_n)=n-1.$$

Zhang et al. established the upper bound $\beta(F_n)\le n-1$ for odd $n\ge 5$, so the conjecture asserts that this bound is sharp.