The only face turning icosahedrons mass produced are:
- icosaix, may be something similar to what you want.
- radiolarian ii. Iis exactly like the icosaix but with a tiny edges exposed on the corners, making the turning slightly better (from what I've seen on youtube reviews), since this tiny pieces cause catches and lockups on the icosaix. This also reduces the accidental corner twisting, because the corners are smaller and you don't need to touch them in order to make a turn.
- eithan star. I similar to the radiolarian, but the big edges (that also are visible on the icosaix) are hidden, and the center of the face is now exposed (on the other two isn't).
Them all are produced by mf8 and cost around $75-$90.
If I had the money I would buy the radiolarian.