The Borromean rings, also called the Borromean links are three mutually interlocked rings, named after the Italian Renaissance family who used them on their coat of arms. The configuration of rings is also known as a “Ballantine,” and a brand of beer has been brewed under this name. In the Borromean rings, no two rings are linked, so if any one of the rings is cut, all three rings fall apart. Any number of rings can be linked in an analogous manner (Steinhaus 1999, Wells 1991).

sigma_1^(-1)sigma_2sigma_1^(-1)sigma_2sigma_1^(-1)sigma_2

The Borromean rings are a prime link. They have link symbol 06-0302, braid word , and are also the simplest Brunnian link.

It turns out that rigid Borromean rings composed of real (finite thickness) tubes cannot be physically constructed using three circular rings of either equal or differing radii. However, they can be made from three congruent elliptical rings.

More info: http://mathworld.wolfram.com/BorromeanRings.html

Gif via matthen: https://blog.matthen.com/

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