  We apply the Berglund-H\"ubsch transpose rule from BHK mirror symmetry to
show that to an $n-1$-dimensional Calabi-Yau orbifold in weighted projective
space defined by an invertible polynomial, we can associate four (possibly)
distinct Sasaki manifolds of dimension $2n+1$ which are $n-1$-connected and
admit a metric of positive Ricci curvature. We apply this theorem to show that
for a given K3 orbifold, there exists four seven dimensional Sasakian manifolds
of positive Ricci curvature, two of which are actually Sasaki-Einstein.
