Let $X$ be a toric CY 3-fold, and this will be our A-side.

Let $N_X$ and $M_X$ be 1PS and character lattice. $\Sigma_X$ lives in $N_X$. Let $P_\Sigma$ denote the compact polytope, being the convex hull of $0$ and the ray generators of $\Sigma$.

Let $Y$ be the toric variety with moment polytope $P_\Sigma$. Let $Y'$ be the toric boundary divisor of $Y$ corresponding to the top face of $P_\Sigma$.

Back to the $X$ side, we should be considering a superpotential, one for each divisor in $Y$, or one for each facet in $P_\Sigma$. So, $$ W_X = \epsilon(\sum_{\text{$F$ facets in $\Sigma$}} W_F) + W_0 $$