Prime Link: 6_3_3

thingiverse

This prime link, referred to as 6_3_3, features in a tube with constant radius and tightened form. The thin version reduces the tube size by half while maintaining visibility of crossings. Conversely, the thick version presents the full-scale tube. These are advantageous for printing with reduced support material. For more information on this specific knot, visit its page at Knot Atlas (http://katlas.math.toronto.edu/wiki/L6n1). Tight knots' details can be explored through Wikipedia (http://en.wikipedia.org/wiki/Ropelength), while ropelength data can be found on Jason Cantarella's site (http://www.jasoncantarella.com/wordpress/papers/). Witnessing a movie of this prime link tightening is also possible via the provided link (http://www.jasoncantarella.com/movs). This knot shape was created using RidgeRunner, a freely available software by Jason Cantarella, which utilizes a numerical algorithm to minimize knot length while preserving a tube around it. The presented shape is only one of the numerous possible forms that this topological knot could adopt if minimizing different functions.