ubuntucuber wrote:
I calculated only 8 possible permutations to a half turn 2x2
There are 24 possible permutations.
If you keep the DLB corner fixed (i.e. only do U2, R2, F2 moves) then the 4 corners UFR, UBL, DFL, DBR can be permuted in all possible ways. Every move swaps UFR with one of the others. This gives at least 4!=24 positions.
The other three corners cannot be moved independently, and orientation is fixed, so those 24 positions are all there are.