The circles that generate the nested tori of the Hopf fibration are so beautiful that I thought to use pearl necklaces to represent them. These Villarceau circles are all linked, which is quite astounding as they also fill up three-dimensional space. Technically, these are not circles as I'm using necklaces. My guess is that the pearls form catenaries: certainly in the vertical direction as they are subject to the earth's gravitation; and the acceleration in the radial direction ought to be constant (because of constant angular velocity), which should induce catenaries radially.