Prime Link: 8_3_7

thingiverse

The prime link 8_3_7, exhibited in two versions - thin and thick, is displayed within a tube of constant radius when pulled taut. In the compact version, the tube's size is halved to enhance visibility of crossings. The thick version features a full-scale tube, easier to print with minimal support material. To learn more about this specific prime knot, visit its page on Knot Atlas (http://katlas.math.toronto.edu/L8n3). For insights into tight knots, refer to Wikipedia (http://en.wikipedia.org/wiki/Ropelength). If you're curious about ropelength data, consult Jason Cantarella's website (http://www.jasoncantarella.com/wordpress/papers/). To visualize the knot's tightening process, watch the movie on Jason Cantarella's site (http://www.jasoncantarella.com/movs). This intricate knot model was generated by RidgeRunner, a free software available at http://www.jasoncantarella.com/wordpress/software/ridgerunner/. RidgeRunner uses numerical algorithms to optimize the knot's length within a tube structure. Remember, varying the optimization function can result in different knot shapes.