Some Links

The three linked trefoil knots shown were constructed using MATLAB. A hexagonal configuration of 6 small circles in a plane was revolved in space about a fixed vertical axis, while simultaneously being rotated through a twist of t = 3/2 revolutions in its own vertical plane (just as the familiar Moebius strip is generated by revolving a line segment with a twist of 1/2 revolution). This construction yields

• Six unknotted and unlinked tori if t = 1
  
  
• Three linked and knotted tori if t = 3/2
  
  
• Two linked and knotted tori if t = 4/3
  
  
• A single knotted torus if t = 7/6

For details see the paper Twisted Tubes, The Mathematica Journal 3 (1993), 10-13. We provide a Mathematica notebook that you can use to generate these links for yourself. However, the links actually pictured were generated using MATLAB.