What has the Penrose tiling to do with the icosahedral phases? Geometrical aspects of the icosahedral quasicrystal problem

SUMMARY The Penrose tiling is indeed a geometrical model appropriate for the description of the phenomena of icosahedral quasicrystals, although it is probably a related example, rather than the central theory itself, but many aspects of the theory remain to be developed. The transition from X‐ray crystal structure analysis (XRCSA) to high resolution electron microscopy (HREM) as the paradigmatic method for the investigation of crystal structures has facilitated this development and promises other advances from classical crystallography.