The 1x2x2 is a simple transformation that has been seen in various forms for many years. The only thing that distinguishes mine from any other is that I attempted to make one using the 19mm cubies off of a standard Rubik's Cube and combined them with a 20mm micro cube necklace. The results were unfortunately less than satisfactory.
Given that the 20mm necklace cube is slightly bigger than a standard 19mm cubie and that it needs to be significantly smaller than that to be jammed inside, the inner core had to be reduced in size significantly, including a tiny bit of sanding down of the metal screws.
The puzzle itself is built very much like a Domino transformation. The biggest difference is that the bandaging only allows for the four corners to move. I will not go through great lengths to explain it, there isn't much point, honestly and the picture below shows about as much detail as is really necessary.
Sadly, shortly after completing this puzzle the internal mechanism gave up the ghost and broke apart. At this point I wrote off the core as being far too fragile and lacking another for the build, I shelved the project permanently. At least it was a nifty little experiment and it did last for about half a dozen turns before breaking apart in my hands.