Prime Knot: 8_10

thingiverse

This prime knot 8_10 model showcases a unique formation tied within a constant-radius tube, stretched tautly. The thin version displays a halved tube size to enhance crossings visibility, while the thick version appears at full scale, requiring less support material for printing. To explore more about this specific prime knot, consult its Knot Atlas page (http://katlas.math.toronto.edu/wiki/8_10). For an in-depth understanding of tight knots, refer to Wikipedia (http://en.wikipedia.org/wiki/Ropelength), while ropelength data can be found at Jason Cantarella's website (http://www.jasoncantarella.com/wordpress/papers/). To witness the intriguing process of this prime knot tightening, visit Cantarella's movie collection (http://www.jasoncantarella.com/movs). The captivating visualizations are made possible through RidgeRunner, a free software by Jason Cantarella that utilizes numerical algorithms to minimize knot length while maintaining a tube surrounding it. Different functions can yield alternative shapes for the model. RidgeRunner is available for download at http://www.jasoncantarella.com/wordpress/software/ridgerunner/.