Let $X$ be a maximally degenerate $K3$ surface over $K$, and let $\mathscr{X}$ be a good minimal dlt-model over $R$ with reduced special fiber. Then $\mathrm{Sk}(X)$ is homeomorphic to $2$-sphere, and $\Delta(\mathscr{X}^{\mathrm{snc}})$ provides this sphere with a triangulation. Different choice of $\mathscr{X}$ are related by elementary modifications (flops) of type 0, 1 or 2 [FM83, pp.12-15]. An elementary modification of type 0 does not affect the triangulation of $\mathrm{Sk}(X)$ or the map $\rho_{\mathscr{X}}$, because it only changes $\mathscr{X}$ along a curve contained in a two-dimensional open stratum. An elementary modification of type 1 does not modify the triangulation of $\mathrm{Sk}(X)$ but it does alter the map $\rho_{\mathscr{X}}$, because the points of $X^{\mathrm{an}}$ that specialize to the minus one curve that is flipped (but not to its intersection with a double curve) will be mapped to a different vertex of $\mathrm{Sk}(X)$. Finally, an elementary modification of type 2 flips an edge in the triangulation of $\mathrm{Sk}(X)$, but does not alter $\rho_{\mathscr{X}}$ because $\rho_{\mathscr{X}}$ is invariant under blow-ups of strata in snc-models (see Propositions 3.1.7 and 3.1.9 in [MN15]).