Composite Knot: 3_1 # 5_1 (square and granny versions)

thingiverse

This is a model of the composite knot 31#_5_1. Since both of these knots come in left and right-handed versions, there are two versions of this composite: a "square" version where a left-handed and right-handed knot are spliced together, and a "granny" version where both knots have the same handedness. Both versions are given here. They are tied in a tube of constant radius, and pulled tight. In the thin version, the tube has been reduced to half-size in order to help you see the crossings. In the thick version, the tube appears at full scale. These are easier to print without as much support material. For more information about tight knots, see http://en.wikipedia.org/wiki/Ropelength. For ropelength data, see http://www.jasoncantarella.com/wordpress/papers/. To see a movie of this composite knot tightening, visit http://www.jasoncantarella.com/movs. Instructions This knot shaped is created by my knot tightening program RidgeRunner, which is freely available at http://www.jasoncantarella.com/wordpress/software/ridgerunner/ RidgeRunner uses a numerical algorithm to minimize the length of a knot while preserving a tube around the knot. This is only one possible position for this (topological) knot; minimizing a function other than length would give you a different shape for the model.