Multiple-mirror conjecture for transpolar VEX multitopes

Let $(\mathcal{D}^{\star}_X,\mathcal{D}_X)$ be a transpolar pair of VEX multitopes. A center-enclosing sub-simplex reduction is a pair of lattice simplices $(\Delta\subset\mathcal{D}^{\star}_X,\nabla\subset\mathcal{D}_X)$. Multiple-mirror conjecture. Multiple mirrors specified by all such center-enclosing sub-simplex reductions are special cases of the mirror mapping extended to anticanonical hypersurfaces in the torus manifolds associated with the full multifans spanned by $(\mathcal{D}^{\star}_X,\mathcal{D}_X)$. The construction predicts a combinatorial network of mirror pairs whose size and variety grow with the complexity of the multitope pair; its general status is open.