SL(F_{A^T})$. For precise definitions of these groups, we direct the reader to Section 2. Take the quotient $\tilde G^T:= G^T/ J_{F_{A^T}}$. The Berglund-Hübsch-Krawitz mirror to the orbifold $Z_{A,G} $ is the orbifold $Z_{A^T,G^T} := X_{A^T}/ \tilde G^T$. Chiodo and Ruan proved the classical mirror symmetry statement for the mirror pair $Z_{A,G}$ and $Z_{A^T,G^T}$ is satisfied on the level of Chen-Ruan cohomology [@CR]: $$H^{p,q}_{\text{CR}} ( Z_{A,G} , {\mathbb{C}}) \cong H^{n-1-p,q}_{\text{CR}}(Z_{A^T, G^T}, {\mathbb{C}}).$$

One can compare the mirrors found in Berglund-Hübsch-Krawitz (BHK) mirror duality to the mirrors of Batyrev and Borisov. In Batyrev-Borisov mirror symmetry, a family of Calabi-Yau hypersurfaces in one toric variety all have mirrors that live inside a family of hypersurfaces in a different toric variety. A feature of BHK mirror symmetry is that it proposes possibly distinct mirrors of isolated points of the family in the Calabi-Yau moduli space–not mirrors of families like the work of Batyrev and Borisov. These BHK mirrors of the isolated points may not live in the same family. Suppose one starts with two quasihomogeneous potentials $F_A$ and $F_{A'}$ $$F_A = \sum_{i=0}^n \prod_{j=0}^n x_j^{a_{ij}}; \qquad F_{A'} = \sum_{i=0}^n \prod_{j=0}^n x_j^{a_{ij}'}.$$ Assume that there exist positive integers $q_i, q_i'$ so that $X_A = Z(F_A) \subseteq 