Few days ago I tried to design Mixup Cube with symmetry other than that in standard one. After few failed attempts I decided to make hexagonal prism with 3 mixup slices on hexagonal faces. Here are some pictures:
As you can see middle slices can be turned by 30 degrees. I wanted also add one cut (not mixup) on rectangular faces which would divide all hexagonal pieces in 6. But I gave it up, because of too big number of small pieces.
Still, this is only a visualization, I haven't design a mechanism, I'm not even sure how to start and how to make it work.
What do you think? Is it possible to build?