The presented paper is a continuation of the series of papers [https://academic.oup.com/imrn/advance-article-pdf/doi/10.1093/imrn/rnz259/30788308/rnz259.pdf17, https://dx.doi.org/10.4310/CNTP.2020.v14.n4.a218]. In this paper, utilizing Batyrev and Borisov's duality construction on nef‑partitions, we generalize the recipe in [https://academic.oup.com/imrn/advance-article-pdf/doi/10.1093/imrn/rnz259/30788308/rnz259.pdf17, https://dx.doi.org/10.4310/CNTP.2020.v14.n4.a218] to construct a pair of singular double cover Calabi–Yau varieties (Y,Y⁾ over toric manifolds and compute their topological Euler characteristics and Hodge numbers. In the $3$-dimensional cases, we show that (Y, Y⁾ forms a topological mirror pair, i.e., hp,q (Y ) = h3-p,q (Y⁾ for all $p, q$.
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Hosono et al. (2024) studied this question.
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