  We show the existence of an emergent SO(6) symmetry in the low energy
description of the iron pnictides. This approximate symmetry provides a
unifying framework for the occurrence of spin density wave (SDW) and
superconductivity (SC) in these materials. We use this symmetry to make several
predictions for future experiments, including the topology of the phase diagram
and the presence of various resonant modes in neutron scattering experiments in
both the SC and SDW phases. We also predict the existence of a new "Orbital
Density Wave" state, which competes with both SDW and SC orders.
