Polytope duality for families of $K3$ surfaces associated to transpose duality

TL;DR

This paper investigates whether transpose-dual pairs of K3 surfaces, related to Berglund--Hübsch mirror symmetry, can be extended to a polytope duality with lattice duality potential.

Contribution

It explores the extension of transpose-dual pairs of K3 surfaces to a polytope duality framework with lattice duality implications.

Findings

Transpose-dual pairs may extend to polytope duality.

Potential for lattice duality in the polytope duality.

Connections to Berglund--Hübsch mirror symmetry.

Abstract

We consider whether or not transpose-dual pairs, which is a Berglund--H$\ddot{\textnormal{u}}$bsch mirror studied by Ebeling and Ploog \cite{EbelingPloog}, extend to a polytope duality that has a potential to be lattice dual.