The Coxeter arrangement of type B3, a.k.a., the planes of symmetry of the cube.

3 
2 
1 
 3
 2
 1

4 
3 
2 
1 
 4
 3
 2
 1

4 
3 
2 
1 
 4
 3
 2
 1

These are examples of Brunnian braids. If one strand is deleted, the resulting braid on the remaining strands can be "unbraided." The "closure" of the first of these braids (obtained by tying the strands labeled 1 together and so on) is a famous link known as the Borromean rings. The last of these braids recently played a role in proving that the pure braid group does not have a property known as residual freeness.