Prime knot: 8_12

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This text demonstrates a prime 8_12 knot, tied in a tube with constant radius and pulled tight. The thin version reduces the tube size to enhance visibility of crossings while the thick version displays the full-scale tube. These versions require less support material during printing. For more information about the 8_12 prime knot, refer to its Knot Atlas page (http://katlas.math.toronto.edu/wiki/8_12). To learn about tight knots and ropelength, visit Wikipedia (http://en.wikipedia.org/wiki/Ropelength). For ropelength data, check Jason Cantarella's website (http://www.jasoncantarella.com/wordpress/papers/). A movie of the prime knot tightening is available at (http://www.jasoncantarella.com/movs). This knot model was created using RidgeRunner, a free software accessible at (http://www.jasoncantarella.com/wordpress/software/ridgerunner/). The software uses an algorithm that minimizes knot length while preserving a tube around it, resulting in various shapes depending on the function being optimized.