  We prove a discrete analog of a certain four-vertex theorem for space curves.
The smooth case goes back to the work of Beniamino Segre and states that a
closed and smooth curve whose tangent indicatrix has no self-intersections
admits at least four points at which its torsion vanishes. Our approach uses
the notion of discrete tangent indicatrix of a (closed) polygon. Our theorem
then states that a polygon with at least four vertices and whose discrete
tangent indicatrix has no self-intersections admits at least four flattenings,
i.e., triples of vertices such that the preceding and following vertices are on
the same side of the plane spanned by this triple.
