For $x\in{X^{\rm an}}$, there is a very affine open neighbourhood $U$ of $x$ in $X$ such that for any open neighbourhood $W$ of $x$ in ${U^{\rm an}}$, there is a compact neighbourhood $V$ of $x$ in $W$ such that ${\rm trop}_{U}(V)$ is a finite union of $d(x)$-dimensional integral $\Gamma$-affine polytopes.