About this project
A torus knot pendant: one continuous strand that weaves around a ring, over and under itself, and closes back on its start. Pick how many lobes it has and how many times it wraps around the centre - 3 lobes is the classic trefoil, 5 the cinquefoil. A hanging loop on one lobe lets it hang as an ornament or on a chain.
How it's built
- Knot path - the (p, q) torus knot curve: x = (R + r cos qt) cos pt, y = (R + r cos qt) sin pt, z = r sin qt. p is wraps, q is lobes.
- Strand - a round tube traced along the path.
- Loop - a ring of the same thickness, fused through the outermost point of one lobe. Every torus knot has that point, so the loop stays attached whatever you choose.
- The pendant is turned so the loop points up.
Parameters
| Group | Slider | What it does |
|---|---|---|
| Knot | Lobes | 3-11 lobes around the outside |
| Knot | Wraps | 2-5 turns around the centre |
| Size | Radius, depth | Overall size, and how far strands weave in and out |
| Size | Strand thickness | Tube radius; the readout shows the gap left between strands |
| Hanging loop | On/off, hole radius | Size the hole for your cord or ornament hook |
Printing
The knot is truly 3D, so print it flat with tree supports (or in resin). A strand radius of 1.5 mm or more prints cleanly on FDM. Silk or metallic filaments show off the curves nicely.
UpdatedOct 30, 2026
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