In the relations above, indices are taken modulo n, so that the third relation includes as a particular case s 0 s n − − 1 s 0 = s n − − 1 s 0 s n − − 1 . (The second and third relation are sometimes called the braid relations.) When n = 2 , the affine symmetric group S ~ ~ 2 is the infinite dihedral group generated by two elements s 0 , s 1 subject only to the relations s 0 2 = s 1 2 = 1 .