Spin models and distance-regular graphs of $q$-Racah type

Let $\mathrm{\Gamma }$ denote a distance-regular graph, with vertex set $X$ and diameter $D\ge 3$. We assume that $\mathrm{\Gamma }$ is formally self-dual and $q$-Racah type. We also assume that for each $x\in X$ the subconstituent algebra $T=T(x)$ contains a certain central element $Z=Z(x)$. We use $Z$ to construct a spin model $\mathsf{W}$ afforded by $\mathrm{\Gamma }$. We investigate the combinatorial implications of $Z$. We reverse the logical direction and recover $Z$ from $\mathsf{W}$. We finish with some open problems.