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I don't know if the figure can be considered a circular path or a polygon, but if so, then it intersects.
The figure resembles a Ment figure (the number of teeth is such that there are 111 segments), only it is located diagonally; the only problem is whether it can be considered an intersection when a straight path passes through the point where the segments connect, marked with an X.
There is also a version that this problem is solved not in a plane, but in a volume, that is, the polygon has an element protruding beyond the plane, or even more than one, which allows the straight line to intersect it.
Or, in general, the polygon itself is located in a volume, like a staircase, that is, it does not have 3 segments that lie in the same plane.