Catenoid-Helicoid vs Torus-Nanospring

Two most famous minimal surfaces are the catenoid and helicoid as shown by the figures from the Indiana university.


In fact, we have already created these two surfaces at the intermediate stages in weaving torus and nanospring. One can obtain these two kinds of minimal surfaces simply by throwing away all pentagons.

I don't have good examples to illustrate this point, hopefully, we can create some beaded models to demonstrate this. Here is a picture that I tried to show how to make T120. Interestingly, in the intermediate stage, I have a catenoid.