Solution to the lighting problem for zone bodies

In the paper, the class of zone bodies, which includes, in particular, zonoids (and zonohedrons) is introduced. The lighting problem for this class is solved, thus generalizing earlier results for zonohedrons (H. Martini) and zonoids (V. G. Boltyanskii and P. S. Soltan). Namely, it is proved that the boundary of any $n$-dimensional zone body other than a parallelepiped can be lit by $3\cdot2^{n-2}$ pencils of parallel rays or less.