Thanks for all the kind words, they are always so nice to read!
Can you explain why it jumbles? It looks unbandageable to me but I'm probably missing something.
Sure thing. The proof is similar to the jumbling proof for the QuadStar puzzle. Here is an image of one face of the Fractured Cube, with a few additional cuts:
jumbling proof.JPG [ 60.97 KiB | Viewed 1094 times ]
As you can see, the new cuts do not line up to create equal size and shaped pieces. In order for the puzzle to be unbandaged, the cut lines shown would need to form a five-pointed star, but the proportions of the triangular faces do not allow this.
It wasn't obvious to me that a symmetrical version couldn't be made, but I see why now after mentally walking around the shape a little.
Interestingly, you could arrange the pieces so that every "face" has the same pattern (in this case the "butterfly" pattern). Four corners would have three edges reversed, and four would have no edges reversed. Even though it might seem like a more appealing starting pattern (being somewhat more symmetrical), this would prohibit the three correctly oriented edges at the four axes with three edges reversed from ever becoming scrambled, since those four axes would be permanently limited to 120 degree moves.