  We study the family of K3 surfaces of Picard rank sixteen associated with the
double cover of the projective plane branched along the union of six lines, and
the family of its Van Geemen-Sarti partners, i.e., K3 surfaces with special
Nikulin involutions, such that quotienting by the involution and blowing up
recovers the former. We prove that the family of Van Geemen-Sarti partners is a
four-parameter family of K3 surfaces with $H \oplus E_7(-1) \oplus E_7(-1)$
lattice polarization. We describe explicit Weierstrass models on both families
using even modular forms on the bounded symmetric domain of type $IV$. We also
show that our construction provides a geometric interpretation, called
geometric two-isogeny, for the F-theory/heterotic string duality in eight
dimensions. As a result, we obtain novel F-theory models, dual to non-geometric
heterotic string compactifications in eight dimensions with two non-vanishing
Wilson line parameters.
