Trefoil Knot

thingiverse

A 3-D rendering of a trefoil knot, by taking a parametric path representation and "thickening" to form a solid (but not so much that the knot self-intersects). The design starts in Sage, export to X3D (resulting file included), edit X3D in Blender (to remove some artifacts Sage leaves behind, like a cube of lines around the figure) and export to STL, import STL into Cura, scale (because graph units in Sage become millimeters in Cura) and situate figure on print platform, then export STL again to form the STL thing file here. Here is the Sage code to generate the figure: t = var('t') parametric_plot3d([sin(t)+2*sin(2*t), cos(t)-2*cos(2*t), -1*sin(3*t)],(t,0,2*pi), thickness=50, aspect_ratio=1) Since Sage is Python-based, be sure to check line breaks. Note that the surface is defined parametrically and plotted using the parametric_plot3d() method, with a large enough "thickness" setting to make the knot pretty substantial. Obligatory nod to artist M.C. Escher:http://www.mcescher.com/Gallery/recogn-bmp/LW444.jpg