Prime Link: 8_3_4

thingiverse

This prime link, 8_3_4, is demonstrated in two versions - thin and thick, with a consistent tube radius. The thin version helps visualize crossings while the thick one requires less support material during printing. To learn more about this specific knot, visit its Knot Atlas page at http://katlas.math.toronto.edu/L8a20. For insights on tight knots, refer to Wikipedia (http://en.wikipedia.org/wiki/Ropelength). For ropelength data, check out Jason Cantarella's website (http://www.jasoncantarella.com/wordpress/papers/). If you want to see a movie of this prime link tightening, visit http://www.jasoncantarella.com/movs. The knot shape is generated by RidgeRunner, a free software available at http://www.jasoncantarella.com/wordpress/software/ridgerunner/. This program uses an algorithm to minimize the length of the knot while preserving the tube around it, and different function minimization could result in other shapes for the same topological knot.