I have a simpler example and I see that its idea is similar to the above one.

![Example of a polyhedron][1]

Cut the vertices of a cube to form 8 small triangles and suppose the triangles are rigid but the faces are not. Then rotate the triangles, 4 of them clockwise and the rest counter-clockwise, in an alternating manner.

![Animating the above example][2]

The images are drawn using Geogebra 3D.


  [1]: https://i.sstatic.net/3G9ZP.png
  [2]: https://i.sstatic.net/qrZvp.gif