The shape shown the most in the video is a tensegrity tetrahedron although they do have snapshots of an icosahedron.
I have built tensegrity tetrahedrons. Here is a video how to:
And Bucky Fuller (my inspiration) on tensegrity.
There are no solids. The whole universe is made of rubber with varying degrees of stiffness. I taught that to my 5th grade science teacher long before I had ever heard of Bucky.
Tensegrity with soda straws.
Here are some posts I did on Buckminster Fuller (some of them are attributed to Dave – that error was created when the blog was updated a while back)