  In the highly frustrated pyrochlore magnet spins form a lattice of corner
sharing tetrahedra. We show that the tetrahedral ``molecule'' at the heart of
this structure undergoes a Jahn-Teller distortion when lattice motion is
coupled to the antiferromagnetism. We extend this analysis to the full
pyrochlore lattice by means of Landau theory and argue that it should exhibit
spin-Peierls phases with bond order but no spin order. We find a range of Neel
phases, with collinear, coplanar and noncoplanar order. While collinear Neel
phases are easiest to generate microscopically, we also exhibit an interaction
that gives rise to a coplanar state instead.
