Strong inscribability conjecture in higher rank

A strongly inscribable arrangement is a hyperplane arrangement that has an inscribed zonotope. The rank of an arrangement is the dimension of its essential ambient space. Two arrangements are combinatorially isomorphic when their associated fans are combinatorially isomorphic. A restriction of a reflection arrangement is the arrangement obtained by restricting the reflecting hyperplanes of a finite reflection group to a flat.

Strong inscribability conjecture in higher rank. Every strongly inscribable arrangement of rank $d\geq 3$ is combinatorially isomorphic to the restriction of a reflection arrangement.

The conjecture is supported by computations: the only strongly inscribable arrangements in the Grünbaum–Cuntz catalog found in the paper are restrictions of reflection arrangements. Its general validity remains open.