Prime Link: 7_3_1

thingiverse

The prime link 7_3_1 is portrayed in two versions, thin and thick, tied within a constant-radius tube when pulled taut. The thin version's tube size has been halved to enhance visibility of crossings. These are more effortless to print with minimal support material. For further details about this prime link, refer to its Knot Atlas page at http://katlas.math.toronto.edu/wiki/L7a7. This model is generated by RidgeRunner, a knot tightening program freely accessible at http://www.jasoncantarella.com/wordpress/software/ridgerunner/. RidgeRunner utilizes a numerical algorithm to minimize the length of a knot while maintaining a tube around it. Note that this shape is just one possible configuration for the topological knot; optimizing different functions would yield alternative models. A movie showcasing the prime link tightening process can be viewed at http://www.jasoncantarella.com/movs. For more insights about tight knots, consult http://en.wikipedia.org/wiki/Ropelength. Rope length data is available at http://www.jasoncantarella.com/wordpress/papers/.