Banach-Tarski doesn't work in 2-dimensional space; there isn't a finite collection of subsets of the plane which can be assembled to make both one disc of radiu

Banach-Tarski doesn't work in 2-dimensional space; there isn't a finite collection of subsets of the plane which can be assembled to make both one disc of radius one and two discs of radius one. I believe that Banach-Tarski would make it much easier to disect a sphere and make a cube.