 Solution

The call constructs dimensions $(d,w,h)$ along the old $(x,y,z)$ axes. To obtain target dimensions $(w,h,d)$ and make an old layer $z=k\text{step}$ become a new layer $y^{\prime }=k\text{step}$, use the cyclic permutationThe new coordinate ranges are immediately $[0,w]$, $[0,h]$, $[0,d]$. Its spatial block is orthogonal with determinant $+1$, since a three-cycle is an even permutation. Hence this is a proper rotation, through $-2\pi /3$ about the axis in direction $(1,1,1)$ under the right-hand convention. No translation is required.