@mrdk @unnick
I'm not sure that these are related to the Jitterbug transformation.
This is my recreation of unnick's original cube/octahedron loop. I used the rhombic dodecahedron and rhombic triacontahedron for this and the previous loop. They remind me of tensegrity structures.
BTW, I made a couple of origami versions of the Jitterbug transformation many years ago. This one https://foldworks.net/wp-content/uploads/2018/06/jitterbug.pdf works better than the first version https://britishorigami.org/academic/davidpetty/origamiemporium/lam_jitterbug.htm