Composite Knot: 3_1 # 3_1 (square and granny versions)
thingiverse
The composite knot 31#_3_1, formed by joining two overhand or trefoil knots, has two versions - the square knot 3_1 # 3_1_m with left and right-handed trefoils and the granny knot 3_1 # 3_1 with same-handed trefoils. This intricate structure is visualized through a numerical algorithm called RidgeRunner, which minimizes knot length while maintaining a tube around it. The program is freely available at http://www.jasoncantarella.com/wordpress/software/ridgerunner/. Note that different function minimizations yield distinct shapes for this topological knot. For additional information on tight knots, ropelength data, and a movie of this composite knot's tightening process, visit http://en.wikipedia.org/wiki/Ropelength, http://www.jasoncantarella.com/wordpress/papers/, and http://www.jasoncantarella.com/movs respectively.
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