it works like a cut down 4x4x4 actually.
Someone finally got it right!
(or at least close enough)
The Floppy 3x3x3 is incredibly complicated to look at, but I believe
it is isomorphic to (the same as) a 4x4x4 with the following properties:
1) One 2x2x2 corner is all bandaged together
2) The opposite (1x1x1) corner remains present on the puzzle
3) The other 6 (1x1x1) corners are all missing from the puzzle
4) The center pieces of the 3 faces surrounding the single remaining (1x1x1) corner have orientations marked, while the center pieces of the other 3 faces do not (keeping in mind that 1 of these centers on each of these other 3 faces are part of the bandaged 2x2x2 corner
This means all parities and restrictions from the normal 4x4x4 remain intact, with the extra apparent abilities to indepently swap 2 corners or rotate just 1 (but since there is only 2, one of which barely counts.... the swapping doesn't mean much). However this should mean that the Floppy 3x3x3 can reach EVERY state it can be properly assembled into, which is kind of exciting
(It also simplifies the calculation of possible permutations)
Again, I'm not quite as confident about this one as some of my previous claims, so it's possible I missed something, but for now I will sign my name on this explanation
PS: Looking through some of the pictures again, I noticed that there seems to be 2 (distinct!) small blue/blue edge pieces where I was expecting blue/red (both). Oskar, if you are reading this, is that a strange glare in the pictures, a mistake, or am I not fully understanding your color scheme? Did anyone else notice this?