Prime Link: 6_3_1

thingiverse

The prime link 6_3_1 is represented in the given model, tied within a constant-radius tube and tightened. The thin version has reduced tube size to enhance visibility of crossings. Conversely, the thick version showcases the full scale tube. These versions are more convenient for printing with minimal support material. To learn more about this prime link, visit its page on Knot Atlas (http://katlas.math.toronto.edu/wiki/L6a5). For information regarding tight knots, refer to Wikipedia (http://en.wikipedia.org/wiki/Ropelength). Access ropelength data at Jason Cantarella's website (http://www.jasoncantarella.com/wordpress/papers/). To visualize this prime link tightening, watch the movie available on Cantarella's site (http://www.jasoncantarella.com/movs). This model was created using RidgeRunner, a free software developed by Jason Cantarella. RidgeRunner uses a numerical algorithm to minimize knot length while maintaining a tube around the knot. Different functions and minimization criteria can yield alternative shapes for this topological knot. Download RidgeRunner from Cantarella's website (http://www.jasoncantarella.com/wordpress/software/ridgerunner/).