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 $P_\Sigma$. $Y$ has a mirror skeleton that is living over $(M_Y)_T = (N_X)_T$.

Let $Y'$ be the toric boundary divisor of $Y$ corresponding to the top face.