We continue to use notations from [HZ02].

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  $(\Delta,S),(\Delta^{\vee},T)$ is a dual pair of $d$-dimensional reflexive polytopes with coherent triangulations of their boundaries.

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  $\Delta_{\mathbb{Z}},\Delta^{\vee}_{\mathbb{Z}}$ are the sets of integral points of $\Delta,\Delta^{\vee}$.

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  $\operatorname{SC}(S),\operatorname{SC}(T)$ are the secondary cones in $\mathbb{R}^{\Delta_{\mathbb{Z}}},\mathbb{R}^{\Delta^{\vee}_{\mathbb{Z}}}$ corresponding to the triangulations $S\ast\{0\},T\ast\{0\}$ of $\Delta,\Delta^{\vee}$.

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  $\lambda$ and $\nu$ are integral vectors in the interiors of the respective secondary cones.

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  $X_{T}$ is the toric variety associated to the simplicial fan in $(\mathbb{R}^{d})^{*}$ given by the triangulation $T$.