The dimension formula for polytopes of quarter-turn symmetric alternating sign matrices

Let $n \geq 5$ be such that $n \not\equiv 2 \pmod 4$, and set $k = \floor*{n/2}$. The polytope $P_\mathrm{QTSASM}$ is the polytope of quarter-turn symmetric alternating sign matrices of order $n$. Dimension conjecture.

$$\dim P_\mathrm{QTSASM}=\floor*{\frac{(n-1)^2}{4}}-2.$$

This conjectural dimension formula concerns the affine dimension of the polytope described in the preceding results; the supplied text gives no resolution or evidence establishing it.