This model features a unique assembly of Villarceau (vee-yar-kow) circles which are elegant, ring-shaped figures that intersect each other to form a torus. To build the complete torus, you will need to print 12 sets of these paired circles, resulting in a total of 24 individual pieces. Once printed, these pieces come together in a seamless fashion, showcasing the beauty and symmetry of geometric design.

The process of assembling the torus from these 3D-printed components is straightforward and requires no cutting or folding, making it accessible to a wide range of users, from hobbyists to educators and students. But it can be challenging to add the final circles to the torus.

This project not only provides a tangible way to explore complex geometric shapes but also serves as a decorative piece or an educational tool. Whether you are looking to expand your collection of 3D models, engage in a hands-on project, or simply appreciate the intricate patterns of geometric forms, this torus assembly offers a rewarding and aesthetically pleasing experience.

Printing the Villarceau Circles

There are two sizes available: the large size produces a torus that is about 240 mm in diameter and the small size results in a 120 mm torus. On a larger 255x255 mm print bed, you can print up to 12 of the smaller inner or outer circles simultaneously. In contrast, the A1 mini can accommodate only one of the larger inner or outer circles at a time. Regardless of the printing method, a complete set requires 24 separate circles—12 outer and 12 inner circles.
 

Assembling the Torus

As you put it together, pay attention to which side of each circle was on the print bed and orient them all the same way to keep the look consistent. Begin by attaching an 'A' (outer) circle to a 'B' (inner) circle, aligning them at the central slots. Continue adding each circle, ensuring each is shifted one slot from the last. See the videos for the details of how this is done.

Complete the assembly with all but the last three outer circles. Once the remaining inner circles are in place, the next major step is connecting the torus ends, presenting a significant challenge. After linking the torus, the final task involves attaching the last three outer circles. Again, see the videos for details of how this is done.
 

Included are a few instructional videos for assembling paper versions of the torus, which are fully applicable to the 3D printed version. Unfortunately, there doesn’t seem to be an “easy” way to assemble them. Completing the assembly is satisfying but extremely difficult.

https://youtu.be/W50J-tgBJ2M

https://youtu.be/4L43ncFOQTo

https://youtu.be/rft4EJkVZ9Y

https://youtu.be/-d4IQT_phlQ

And here's a video of me removing and adding back the final circle to the torus. https://youtu.be/Q6TUq1BwdCE (sorry for going out of frame). To add the final circle to the torus, start by aligning the center slots of the two circles without attempting to slide the slots together until the end. If you compress the torus, you can position all the blue slots onto the corresponding green circles. Begin at the center of the blue circle and slide it along the green circles, systematically adjusting each slot starting from the center. When you have aligned all but the last slot on one side, slide the blue circle back to the opposite side, which will position the slots on the other side near their intended interleave points. Once all the blue slots are correctly straddling the green circles, you can begin to push the green and blue slots together.

The final circles may prove difficult to integrate into the structure. Pace yourself and don't hesitate to pause if needed. Deciding whether it’s better to attach these circles with the torus compressed or expanded can be tricky, likely requiring a mix of both methods and plenty of manipulation. Good Luck!