A bandaged cube like the one above can't turn. So far so true.
DragonCube got it right. The edges with bonds are the ones which are cut away. The result in this case is:
21E0800104C84.JPG [ 92.25 KiB | Viewed 876 times ]
(an emergency-built just for this picture)
And if you extend the non-truncated faces you get the mod shown above.
I'm pretty sure you have the most complete and extensive puzzle collection imaginable.
Depends. You might ask Rox or Georges about that. But thank you anyway.