Recreating Collapsible Bucket

I am currently in the process of trying to recreate aspects of this collapsible bucket within Rhino. I was wondering if anyone might have any suggestions of any tools or methods for creating these two aspects please.

If you want to simulate it, here are a couple of previous discussions with examples that might be helpful:

With a bit of work you could probably also get a reasonable approximation of the form in Rhino without Grasshopper just by manipulating the control points of a SubD cylinder