A Simple "One Algorithm" Method

[TMOY]

This is not always possible because of parity issues
Allowing at most one U move as a parity fix, it's fun. I solve first the edges then the corners (it's IMHO easier because (sexy move)^3 is edge-preserving).

 

[Tim Major]

I am pretty sure that it is IMPOSSIBLE to solve the cube with just the sexy move. This is because if you have a parity, there is NO way to solve it using the sexy move (since the sexy move has an even number of moves). So there goes all your hopes and dreams. :|

Yes, but you can solve up to the point where you are a U off, and I think most solvers could fill in the rest.

Heard of plus 2? I guess that wouldn't count though. It is pretty cool just using sexy move, and quite fun too.