Prime Link: 8_3_9

thingiverse

This text illustrates a prime link 8_3_9, tied within a constant-radius tube and tightened. The slim version features halved tubes to showcase crossings more clearly, while the thick version portrays full-scale tubes. These knots require less support material for printing. For further details on this specific prime link, visit its page in Knot Atlas (http://katlas.math.toronto.edu/L8n5). To learn about tight knots, refer to Wikipedia (http://en.wikipedia.org/wiki/Ropelength), and for ropelength data, check Jason Cantarella's website (http://www.jasoncantarella.com/wordpress/papers/). Observe a movie of this prime link tightening on Cantarella's site too (http://www.jasoncantarella.com/movs). The knot shape was generated by RidgeRunner, a program available for download at http://www.jasoncantarella.com/wordpress/software/ridgerunner/. RidgeRunner uses an algorithm to minimize the knot's length while preserving a tube around it; different functions can result in distinct knot shapes.