Prime Knot: 8_17

thingiverse

This text demonstrates a prime knot 8_17, tied inside a constant-radius tube and stretched taut. The slim version features halved tubing to aid visibility of crossings, while the thick version appears at full scale, easier to print with minimal support material. For further details on this prime knot, visit its page in the Knot Atlas (http://katlas.math.toronto.edu/wiki/8_17). To learn about tight knots, refer to Wikipedia (http://en.wikipedia.org/wiki/Ropelength). Rope-length data can be found at Jason Cantarella's site (http://www.jasoncantarella.com/wordpress/papers/). View a movie of the prime knot tightening at http://www.jasoncantarella.com/movs. This unique shape is generated by RidgeRunner, a free software accessible at http://www.jasoncantarella.com/wordpress/software/ridgerunner/. RidgeRunner utilizes numerical algorithms to minimize knot length while preserving a tube around the knot. Different functions can yield distinct model shapes for this topological knot.