Prime Knot: 8_5

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This model demonstrates the prime knot 8_5, formed within a constant-radius tube and tightened. The thin version reduces the tube size, enhancing visibility of crossings. In contrast, the thick version showcases the full-scale tube. These versions require less support material for printing. To learn more about this particular prime knot, visit its page in the Knot Atlas (http://katlas.math.toronto.edu/wiki/8_5). For insights on tight knots, refer to Wikipedia (http://en.wikipedia.org/wiki/Ropelength), and for ropelength data, check Jason Cantarella's website (http://www.jasoncantarella.com/wordpress/papers/). To view a movie of this prime knot tightening, go to http://www.jasoncantarella.com/movs. This knot shape is a result of RidgeRunner, a freely available software from Jason Cantarella's website (http://www.jasoncantarella.com/wordpress/software/ridgerunner/) that uses a numerical algorithm to minimize the knot length while maintaining a tube around it. Remember, this is only one possible shape for this topological knot; different functions minimized would yield distinct models.