Prime Link: 2_2_1 (Hopf Link)

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The prime link 2_2_1, or Hopf link, is modeled here in a constant radius tube and tightened to its minimum ropelength. In the thin version, the tube size is halved for clearer visibility of crossings. The thick version appears at full scale, requiring less support material during printing. For more details on this knot, visit its Knot Atlas page (http://katlas.math.toronto.edu/wiki/L2a1). This 3D model was created using RidgeRunner software, available for free at http://www.jasoncantarella.com/wordpress/software/ridgerunner/. This program employs a numerical algorithm to minimize knot length while maintaining a tube around the knot. The presented shape is just one possible configuration for this topological knot, as varying functions can result in different models. To witness this knot tightening, watch the movie at http://www.jasoncantarella.com/movs.