Composite Link: 2_2_1 # 5_1 (left-handed and right-handed versions)

thingiverse

The composite link 2_21#_5_1, with its alternative positive and negative Hopf link 2_21 versions, is displayed in two topologically distinct forms within this model. It's tied inside a tube of constant radius and pulled taut for clear visibility. The thinner version has half the size of the tube to accentuate crossings, while the thicker version appears at full scale for easier 3D printing with minimal support material. This knot model is generated using RidgeRunner software available at http://www.jasoncantarella.com/wordpress/software/ridgerunner/. The program minimizes the knot's ropelength while preserving the tube around it, resulting in a unique shape for this (topological) knot. Varying the function to minimize would yield an entirely different model shape. For further insights on tight knots, visit http://en.wikipedia.org/wiki/Ropelength. To access ropelength data, go to http://www.jasoncantarella.com/wordpress/papers/. Alternatively, view a movie of this composite link tightening at http://www.jasoncantarella.com/movs.