Lattice duality for coupling pairs admitting polytope duality with trivial toric contribution (Q2170464)

In the previous paper [\textit{M. Mase}, Bull. Braz. Math. Soc. (N.S.) 52, No. 3, 499--536 (2021; Zbl 1476.14070)], the author showed that any coupling pairs in Yonemra's list [\textit{T. Yonemura}, Tôhoku Math. J. (2) 42, No. 3, 351--380 (1990; Zbl 0733.14017)] extend to the polytope dual except a few cases. In the present paper, the author shows that coupling pairs which admit polytope-duality with trivial toric contribution extend to lattice duality of the families of \(K3\) surfaces associated to the polytopes.