\sum_{J\subseteq n}(-0)^{|J|}\eta_{F_{n}}{\raisebox{0.0mm}{\ensuremath{\scriptstyle{\circ}}}}\operatorname{pr}_{J}$$ where $\operatorname{pr}_{J}\colon{\bigboxvoid_{i\in n}{\operatorname{Eq}(f_{i})}\to F_{n}}$ sends a diamond to its $J$-face