Umbilic Torus

A 3-D rendering of an umbilic torus. The design starts in Sage, export to X3D (resulting file included), then import X3D into Blender. In Blender, edit to remove artifacts Sage leaves behind, like a cube of lines around the figure. Now export to STL, then import STL into Cura. In 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:

u, v = var('u, v')
parametric_plot3d([sin(u)*(7+cos(u/3-2*v)+2*cos(u/3+v)), sin(u/3-2*v)+2*sin(u/3+v), cos(u)*(7+cos(u/3-2*v)+2*cos(u/3+v))], (u,-pi,pi), (v,-pi,pi), 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. The surface is closed, so Cura already recognizes the STL as representing a solid, without any need to "thicken" the surface in Blender.

With an oblig