  Perovskite photovoltaic ABX$_3$ systems are being studied due to their high
energy-conversion efficiencies with current emphasis placed on pure inorganic
systems. In this work, synchrotron single-crystal diffraction measurements
combined with second harmonic generation measurements reveal the absence of
inversion symmetry below room temperature in CsPbBr$_3$. Local structural
analysis by pair distribution function and X-ray absorption fine structure
methods are performed to ascertain the local ordering, atomic pair
correlations, and phase evolution in a broad range of temperatures. The
currently accepted space group assignments for CsPbBr$_3$ are found to be
incorrect in a manner that profoundly impacts physical properties. New
assignments are obtained for the bulk structure: $Im$$\bar{3}$ (above $\sim$
410 K), $P$2$_1$/$m$ (between $\sim$ 300 K and $\sim$ 410 K), and the polar
group $Pm$ (below $\sim$ 300 K), respectively. The newly observed structural
distortions exist in the bulk structure consistent with the expectation of
previous photoluminescence and Raman measurements. High-pressure measurements
reveal multiple low-pressure phases, one of which exists as a metastable phase
at ambient pressure. This work should help guide research in the perovskite
photovoltaic community to better control the structure under operational
conditions and further improve transport and optical properties.
