  Second harmonic generation (SHG) on the pyrochlore metal Cd2Re2O7 indicates
the presence of three order parameters setting in below an inversion breaking
transition. Here, we explore a possible structural explanation and relate it
not only to the SHG data, but also to neutron and x-ray diffraction, where we
find that such a structural scenario can explain certain reflection extinctions
observed in single crystal x-ray data. From this analysis, we suggest future
experiments that could be done to resolve this matter. Finally, we comment on
the Landau-violating nature of the inversion breaking transition and its
relation to similar phenomena observed in improper ferroelectrics.
