The Borromean rings are a set of three rings that are linked, but do not interlock:
The structure cannot be pulled apart, but cutting any one of the rings allows you to separate the other two. They cannot be physically constructed with regular tori in three dimensions, you have to deform the rings like this:
Which might look like perfect circles from one viewpoint only.
These are not Borromean rings, whatever the listing says, as they actually interlock and cutting one of them does not release the other two:
I would like to render an 'alien artefact' that appears to be a set of Borromean rings made out of perfect circles, indicating that they somehow stretch into additional dimensions. The rings don't need to move in relation to each other (although that would be amazing), but the camera does need to pan around them, showing them from several angles. I was thinking to use the geometry of the 'false rings' from the last link, but shade them in such a way that they render some parts of the structure in the wrong layer order to create the Borromean effect, but I couldn't think where to begin to make something like that happen. Any suggestions? Any rendering engine would be acceptable.