Let $Z$ be a compact analytic space over $K$ of pure dimension $n$ and let ${\mathscr{C}}$ be the same integral $\Gamma$-affine polytopal complex with support ${\varphi_{\rm trop}}(Z)$ as in 7.4. Then for every $n-1$-dimensional polyhedron $\rho$ of ${\mathscr{C}}$ not contained in ${\varphi_{\rm trop}}(\partial Z)$, the balancing condition

$$\sum_{\sigma\in{\mathscr{C}}_{n},\,\sigma\supset\rho}m_{\sigma}\omega_{\rho,\sigma}\in N_{\rho}$$

from 3.7 holds in $\rho$.