Congratulation to me, I'm making an eternity ring! In my experiments I tried a variety of shapes, each is swept around a major axis while twisting round the minor axis. Now you can try these too! Click 'Open in Customizer' and play: try changing the cross-section shape from triangle, ellipse to a Reuleaux Triangle (a curve of constant width which looks like a rounded triangle), and adjust the other dimensions too.

Note: If Thingiverse can't render this, please try downloading OpenSCAD, download mobius_ring.scad from Thing Files and experiment with it there.

Prusa

i3 MK2S

Doesn't Matter

Yes

0.1 Fine

100%

Was getting bad prints until I set Cura to 215C (it defaulted to 200C for Generic PLA).