Prime Knot: 8_4

thingiverse

This text showcases a model of prime knot 8_4, tied in a constant radius tube and pulled tight. The thin version reduces the tube size for better visibility, while the thick version is at full scale, easier to print with minimal support material. For more information about this knot, visit its Knot Atlas page at http://katlas.math.toronto.edu/wiki/8_4. Understand tight knots further through Wikipedia's ropelength guide (http://en.wikipedia.org/wiki/Ropelength), and for ropelength data, access Jason Cantarella's site (http://www.jasoncantarella.com/wordpress/papers/). To witness a movie of this prime knot tightening, visit http://www.jasoncantarella.com/movs. The intricate design is generated by RidgeRunner, a free software available at http://www.jasoncantarella.com/wordpress/software/ridgerunner/. This program uses a numerical algorithm to minimize knot length while preserving a tube around it; different functions could yield distinct shapes for the model.