Let $A$ be an abelian $K$-variety of dimension $n$. Then the essential skeleton $\mathrm{Sk}(A)$ of $A$ coincides with Berkovich’s canonical skeleton $\Delta(A)$. If $A$ has semi-abelian reduction and $\mathscr{P}$ is a Künnemann-Mumford model of $A$ over $R$, then $\mathscr{P}$ is a good minimal dlt-model that satisfies assumption (2). If $A$ has purely toric reduction, then the non-archimedean SYZ fibration $\rho_{\mathscr{P}}$ coincides with Berkovich’s canonical retraction $\rho_{A}$. In particular, $\rho_{\mathscr{P}}$ is an $n$-dimensional affinoid torus fibration.