Here are some links to a table of knots, up to 9 crossings, built as three-dimensional objects.

If you can achieve stereoscopic vision with two adjacent pictures, you can see the knots "in 3D".


Which Knots?

Mathematica was used to construct each curve; each figure in the table was made with OpenGLViewer and points to Java applet, which uses LiveGraphics3D. (If you have never used this program before, see the corresponding help on how to manipulate the object with the mouse).

(*) The routines for the creation of the 3D curves were written essentially by Vítor Sousa, according to a detailed plan previously suggested in the scope of "Estágio". (Ramo Educacional da Licenciatura em Matemática - F.C.U.P - 2000/2001.). That subject acted as a guideline for a first contact with Mathematica.

Difficulty level: University