A weighted polyhedral $n$-complex $\Pi\subset\mathbb{R}^{n+1}$ is called balanced if for every $(n-1)$-cell $G\subset\Pi$ the following condition holds. Let $F_{1},\dots,F_{k}$ be the $n$-cells adjacent to $G$. A choice of a rotational direction about $G$ defines a coherent co-orientation on these $n$-cells. The balancing condition is