Bose-Einstein condensates of atoms with arbitrary spin

We show that the ground state of a Bose-Einstein condensate of atoms with hyperfine spin f = 2 can be either spin aligned, condensed into pairs of atoms coupled to F = 0, or condensed into triplets of atoms coupled to F = 0. The complete phase diagram is constructed for f = 2 and the generic properties of the phase diagram are obtained for f > 2.