[kpreid]

For 35 degrees, you don't need 3D; a ring of 72 35-degree angles is a cycle (with a star pattern, rather than a polygon). There is a similar solution for any rational fraction of a full revolution (equivalently, any angle which is rational when measured in degrees (or gradians), but not radians).

However, the article said “about 35 degrees” so the actual number is probably something 34.5 ≤ x ≤ 35.5 but not actually 35.

My geometric intuition says that in 3D you can always construct a cycle but I don't know how to formalize it. Imagine a flat zig-zag chain of alternating bends; you can reshape it to a curve of arbitrary radius (around the axis of the width of the chain) by turning each bend slightly relative to its neighbors (about the axis of the beam), in alternating directions. Then you can choose a radius which makes the ends meet exactly.