The development of colloidal nanocrystals as next-generation semiconductors relies heavily on understanding their structure with atomic precision, which is critical for interpreting the interaction between charge carriers and their lattice. In particular, lead halide perovskites are characterised by highly deformable octahedral frameworks, which makes conventional phase diagrams inadequate to capture their structural subtleties. Through this experiment down to cryogenic temperatures, we aim to reconstruct with atomic-level precision the interplay between local and average evolution of lead halide perovskites inorganic sublattice, within a unified structural picture that is still missing, and over the 4 -300K temperature range, which is relevant for understanding some of their exceptional optoelectronic features.