The Borromean Rings

These three rings cannot be separated from each other without breaking them, but once one of the three is broken the other two can be separated without breaking.

This configuration of three rings appears numerous times in the history of art and iconography (it was one of the symbols of the Borromeo family from Milan, hence the name "Borromean rings") and plays a key role in a branch of modern mathematics, hyperbolic geometry.