Beaded Helicoid

Finally, I almost have a beaded helicoid. Although it is still in progress, the overall structure of the helix can be seen easily. Before I started to do this one, I still have some doubt about whether the resulting structure will look close to the real helically coiled carbon nanotube or not. This is because at the beginning stage, the beaded structure is so flexible and does not seem to work. But when the one-fourth of the first pitch is done, the structure is already very stable. This is really amazing. Now I have one pitch of the helicoid finished and still have some more to go.




By the way, the structure of helicoid is essentially derived from the twisted type of toroids. The twisted type of toroid is not stable for the small toroidal systems. But if we change the cyclic boundary condition, which apparantly induces very large strain energy in the twisted type toroid, and let the two ends of the tube go freely, then we will have the helicoid.

Of course, there is an additional constraint to be satisfied in order to avoid the intersection of the tube. Then not every twisted toroid can generate a stable helicoid.