Diamond is a material of immense technological importance and an ancient signifier for wealth and societal status. In geology, diamond forms as part of the deep carbon cycle and typically displays a highly ordered cubic crystal structure. Impact diamonds, however, often exhibit structural disorder in the form of complex combinations of cubic and hexagonal stacking motifs. The structural characterization of such diamonds remains a challenge. Here, impact diamonds from the Popigai crater were characterized with a range of techniques. Using the MCDIFFaX approach for analysing X-ray diffraction data, hexagonality indices up to 40% were found. The effects of increasing amounts of hexagonal stacking on the Raman spectra of diamond were investigated computationally and found to be in excellent agreement with trends in the experimental spectra. Electron microscopy revealed nanoscale twinning within the cubic diamond structure. Our analyses lead us to propose a systematic protocol for assigning specific hexagonality attributes to the mineral designated as lonsdaleite among natural and synthetic samples.