An infinite sequence of non-realizable weavings

A weaving is a number of lines drawn in the plane so that no three lines intersect at a point, and the intersections are drawn so as to show which of the two lines is above the other. For each integer n⩾4 we construct a weaving of n lines, which is not realizable as a projection of a number of lines in 3-space, all of whose subfigures are realizable as such projections.