Assume that $k$ is algebraically closed, $K_{X}$ is trivial over $C$ and $X$ has an $snc$-model $\mathscr{Y}$ with reduced special fiber $\mathscr{Y}_{s}$. Assume moreover that $\mathrm{Sk}(X_{K})$ is of dimension $n=\dim(X_{K})$. Then $\mathrm{Sk}(X_{K})$ is an $n$-dimensional closed pseudo-manifold.