Brunnian Links

http://commons.wikimedia.org/wiki/File:Braid_final.jpg
Image: Wikimedia Commons

The standard braid has a curious property: If we remove any one of the three strands, the other two are seen to be unconnected. If we remove the black strand above, the blue and red strands simply snake along one above the other. Similarly, removing the red or the blue strand reveals that the remaining strands are not braided together.

See Borromean Rings.