You can't have interlocking rings in 2D without having some kind of intersection. You have a similar problem with moebius rings and klein bottles: moebius rings

You can't have interlocking rings in 2D without having some kind of intersection. You have a similar problem with moebius rings and klein bottles: moebius rings are 2D objects but you have to represent them in a 3D world if you don't want them to be self-intersecting. If you attempt to represent a moebius ring in 2D it'll necessarily self-intersect. Klein bottles are the same thing but with an added dimensions: any representation of a klein bottle in 3D makes it look like it's going through itself, even though in 4D it wouldn't: http://s3files.core77.com/blog/images/2013/06/klein-bottle-02.jpg http://s3files.core77.com/blog/images/2013/06/klein-bottle-0... It's also true if you remove a dimension: a 1D moebius strip would simply be a circle, but if you try to draw it in 1D you end up with a segment where both halves of the circle are overlapped. So every time we have a N-dimensional object that can only be properly represented in N+1 dimensions. That's also the same reason you can't solve the problem of connected three objects to three other objects on a 2D planes without intersecting: A B C X Y Z You can't distribute a, b and c to x, y and z on a 2D plane without intersection. Topology is fun.