Prime Link: 8_2_7

thingiverse

The prime link 8_2_7 can be visualized through a tube of constant radius, pulled tight. The thin version reduces the tube size by half for better visibility, while the thick version displays it at full scale. These models are easier to print with minimal support material. For details about this prime knot, refer to its page in Knot Atlas (http://katlas.math.toronto.edu/L8a8). The concept of tight knots is further explained on Wikipedia (http://en.wikipedia.org/wiki/Ropelength), and ropelength data can be found at Jason Cantarella's website (http://www.jasoncantarella.com/wordpress/papers/). To witness a movie of this prime knot tightening, visit http://www.jasoncantarella.com/movs. The creation of these shapes is credited to the RidgeRunner software, available for free at http://www.jasoncantarella.com/wordpress/software/ridgerunner/. This program uses a numerical algorithm that minimizes knot length while preserving a tube around it, and different functions can yield alternative models.