Three Interlocking Trefoil Knots

thingiverse

Three intricately intertwined trefoil knots, crafted by Hayley Archer-McClelland and refined by Dave Pfaff and myself as part of my rigorous Math 341 Introduction to Topology course in Fall 2014. Each trefoil knot is elegantly linked with the two others. Print Settings: Printer Brand: Formlabs Printer: Form 1 Rafts: Yes Supports: Yes Resolution: 0.2 Infill: 10% Notes: Be aware that you may need to upscale this object by a factor of ten in Makerware, as it is scaled in centimeters not millimeters. You may also need to reposition the knot onto the platform, which I believe is situated just above it. The model measures approximately nine centimeters by ten centimeters by five centimeters in size. These intricate knots were first brought to life on a Project 260 3D Systems printer. Later, they were expertly printed on a FormLabs 1+ printer using clear resin (02). How I Designed This Conceived entirely within Cinema4D. The parametric equations of a trefoil knot are x(t) = (2 + cos(3t))cos(2t), y = (2 + cos(3t))sin(2t), z = -sin(3t) from t = -pi to t = pi. We first created the curve with the Formula function, spanning t = -3.14 to t = 3.14. We then added a SweepNurb (with no caps) consisting of a circle with radius 0.2cm wrapped around the curve. The choice of t resulted in a small gap between the tube's ends. This was skillfully sealed using the Stitch and Sew tool in Edge mode.