The problem with slicing is that here in 3d we would slice with 2d plane, but when you are in 4d, should you slice with 2d plane or 3d something? (3-1=2 so 4-1=3) or is slicing always 2d plane, says who?
To "slice" something you need a "plane" in one dimension lower. To get some sense of why, think about a ball in three dimensions. You can "slice off" some of its volume with a plane (one dimension less), but if you have a line all you do is have a line through it ... the ball is still connected, and you haven't sliced anything from it.
