  The presented paper is a continuation of the series of papers
arXiv:1810.00606 and arXiv:1903.09373. In this paper, utilizing Batyrev and
Borisov's duality construction on nef-partitions, we generalize the recipe in
arXiv:1810.00606 and arXiv:1903.09373 to construct a pair of singular double
cover Calabi--Yau varieties $(Y,Y^{\vee})$ over toric manifolds and compute
their topological Euler characteristics and Hodge numbers. In the
$3$-dimensional cases, we show that $(Y,Y^{\vee})$ forms a topological mirror
pair, i.e., $h^{p,q}(Y)=h^{3-p,q}(Y^{\vee})$ for all $p,q$.
