  We construct closed immersions from initial degenerations of the spinor
variety $\mathbb{S}_n$ to inverse limits of strata associated to even
$\Delta$-matroids. As an application, we prove that these initial degenerations
are smooth and irreducible for $n\leq 5$ and identify the log canonical model
of the Chow quotient of $\mathbb{S}_5$ by the action of the diagonal torus of
$\operatorname{GL}(5)$.
