Hirsch equality conjecture for non-degenerate axial transportation polytopes

Let $P$ be a non-degenerate $l\times m\times n$ axial transportation polytope with $l,m,n\geq 3$. Its dimension is

$$d=lmn-l-m-n+2.$$

Let $f$ be the number of facets of $P$, and let $G(P)$ be its graph. Hirsch equality conjecture. The diameter of $G(P)$ is equal to $f-d$. The Hirsch conjecture concerns the general upper bound $f-d$ for the diameter of a $d$-dimensional polytope with $f$ facets; the supplied source does not state a resolution of this stronger equality claim, so it remains open.