Knot Theory is Geometrically Interesting...

Cube with Borromean Rings Cut Out by Charlie Gunn
Cube with Borromean Rings Cut Out by Charlie Gunn

Borromean Ring Complement Manifold 1 by Charlie Gunn
Borromean Ring Complement Manifold 1 by Charlie Gunn

Images from http://www.geom.umn.edu/graphics/pix/Video_Productions/Not_Knot/.