Villarceau mesh torus (customisable)

thingiverse

This is a donut shape, defined by a set of "Villarceau circles" making a mesh. The object is highly customizable. You can pick the radius of the hole through the middle of the donut, the radius for the hole around the inside of the donut, and the radius of the little rails of the mesh. You can also select the number of pairs of Villarceau circles making up the mesh, and you can decide if you want to make a complete torus (donut), or a half slice, or a small wedge. If you select a half torus, or a wedge, then you can glue them together to get the complete model. You can either glue two halves together, or you can print a lot of wedges -- the same number of wedges are needed as there are Villarceau circles making up the mesh. There is a parameter giving the number of VillarceauPairs: double that to get the number of wedges you would need to print. The picture shows a complete torus with a marble trapped inside. This was made with two halves glued together with the marble inside. There are also a few wedges in the background. Experiment with the customiser to see what is possible. If you are printing the model, the wedge should be able to print without supports, but you will need quite a few to make up the whole torus. You need some support for the half torus, and I have never even tried to print a complete torus as one print job. But it might be possible... To keep the overhang low on a wedge, you can increase the number of Villarceau circles, or the radius of the rails, or reduce the ratio of the minor radius over the major radius. Roughly speaking, increasing the hole radius parameter or decreasing the passage radius, will reduce overhangs, I think.