Prime Knot: 8_1

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The prime knot 8_1 is illustrated with a constant radius tube, tightened to showcase its structure. In the slim version, the tube halves in size to accentuate crossings. The thick version showcases the full-scale tube for easier printing and minimal support material. To learn more about this specific knot, visit the Knot Atlas' 8_1 page (http://katlas.math.toronto.edu/wiki/8_1). Understand tight knots further through the Ropelength Wikipedia page (http://en.wikipedia.org/wiki/Ropelength). For ropelength data, refer to Jason Cantarella's website (http://www.jasoncantarella.com/wordpress/papers/). Witness a movie of this knot tightening on Jason Cantarella's movie site (http://www.jasoncantarella.com/movs). This intricate knot model is generated by RidgeRunner, a free software available at http://www.jasoncantarella.com/wordpress/software/ridgerunner/. RidgeRunner optimizes the knot's shape by minimizing its length while maintaining a tube around it, though different functional optimization could yield alternative shapes.