Today we have two torus knot conformations of 7_1. A torus knot is one that can be drawn on the surface of torus (“inner tube” shape) without intersecting itself. A *T*(*p*,*q*) torus knot wraps around the torus like a clock *p* times, and around the handle of the torus *q* times. The standard conformation of 7_1 in the knot table is shown on the left, in the form of a *T*(2,7) torus knot. The blue conformation on the right is the same knot but in the *T*(7,2) torus knot conformation.

Thingiverse link: http://www.thingiverse.com/make:82264

Settings: Printed on a MakerBot Replicator 2 with our custom knot slicing settings to minimize supports. Printing the knot on its side results in far, far less support material than printing knot horizontally.

Technical notes, OpenSCAD flavor: This knot was printed by JMU student Taylor Meador, who used a modified version of the OpenSCAD code for our trefoil torus knot models from Day 150 (thanks as always to kitwallace).

$fn=24; /* // trefoil as the torus knot T(7,2) // http://mathworld.wolfram.com/Torus.html // take parameterization of torus (u,v)->R^3 // and let u=2t, v=3t // scaled to 40mm before tubifying function f(t) = [ 3.9*(3+1.6*cos(7*t))*cos(2*t), 3.9*(3+1.6*cos(7*t))*sin(2*t), 3.9*(1.6*sin(7*t)) ]; // create the knot with given radius and step tubify(1.6, 1, 360); */ module tubify(r, step, end) { for (t=[0: step: end+step]) { hull() { translate(f(t)) sphere(r); translate(f(t+step)) sphere(r); } };

These look good but I think you have p and q mixed up.