Borromean Rings

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Three mutually interlocked rings named after the Italian Renaissance family who used them on their coat of arms. No two rings are linked, so if one of the rings is cut, all three rings fall apart. They are given the Link symbol 06-03-02, and are also called the Ballantine. The Borromean rings have Braid Word ${\sigma_1}^{-1}\sigma_2{\sigma_1}^{-1}\sigma_2{\sigma_1}^{-1}\sigma_2$ and are also the simplest Brunnian Link.

References

Cundy, H. and Rollett, A. Mathematical Models, 3rd ed. Stradbroke, England: Tarquin Pub., pp. 58-59, 1989.

Gardner, M. The Unexpected Hanging and Other Mathematical Diversions. Chicago, IL: University of Chicago Press, 1991.

Jablan, S. ``Borromean Triangles.'' http://members.tripod.com/~modularity/links.htm.

Pappas, T. ``Trinity of Rings--A Topological Model.'' The Joy of Mathematics. San Carlos, CA: Wide World Publ./Tetra, p. 31, 1989.