An algorithm has been proposed to construct orbifolds of Calabi–Yau manifolds of the Berglund–Hubsch type. This approach has allowed us to obtain all mirror pairs for Calabi–Yau manifolds of this type. As an example, all orbifolds and their mirror pairs have been found for one of the Fermat models. The number of quark and lepton generations, as well as the number of particle types involved only in the gravitational interaction, i.e., dark matter particles, has also been determined for each orbifold.
Aleshin et al. (2026) studied this question.