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