Prime Knot: 6_2

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The prime knot 6_2 is intricately illustrated in a constant radius tube, tightened to its peak form. The slim version boasts a reduced tube half-size, enhancing crossings visibility. Conversely, the thick version maintains full-scale tube appearance, easier for printing with minimal support material. For comprehensive details on this knot, visit its Knot Atlas page (http://katlas.math.toronto.edu/wiki/6_2). The intricacies of tight knots and ropelength are further explained in Wikipedia (https://en.wikipedia.org/wiki/Ropelength) and ropelength data sources (http://www.jasoncantarella.com/wordpress/papers/). To visually witness this prime knot's tightening, check out the video on http://www.jasoncantarella.com/movs. This exceptional visualization is made possible by RidgeRunner, a freely available software (http://www.jasoncantarella.com/wordpress/software/ridgerunner/) that uses numerical algorithms to minimize knot length while maintaining a tube around it. Different functions can yield different knot shapes.