Prime Link: 7_2_1

thingiverse

The prime link 7_2_1 model showcases a tube of constant radius, tightened and depicted in both thin and thick versions. The thin version has a reduced tube size for clearer visibility of crossings, while the thick version appears at full scale. These models require less support material when printed. To learn more about this prime knot, visit its Knot Atlas page (http://katlas.math.toronto.edu/wiki/L7a6). RidgeRunner software, available at http://www.jasoncantarella.com/wordpress/software/ridgerunner/, creates such knots by minimizing their ropelength using a numerical algorithm while maintaining a tube around the knot. This model is just one possible shape for the knot, as optimizing different functions would result in distinct models. To visualize this prime link tightening, watch the movie at http://www.jasoncantarella.com/movs.