The ash heap of crystallography: restoring forgotten basic knowledge

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A critical analysis of some basic notions often overlooked in crystallographic education is presented to correct some common oversights occurring both in the literature and in textbooks. The crystal forms (face forms), defined in terms of their geometric eigensymmetry, are 47 in number, not 48 as often found in the literature. The split of the dihedron into dome and sphenoid calls for the consideration of the physical properties of the faces building a form; in that case, however, the same criterion should be used for all forms. By taking the handedness of the faces as representative of the physical properties of the faces, the occurrence of 130 crystallographic face forms (97 affine face forms and 33 enantiomorphic pairs) is demonstrated. Next, the correct use of non-coprime Miller indices when a centred unit cell is adopted is shown, and the inconsistent multiplication of Miller indices in the Bravais–Friedel–Donnay–Harker law is pointed out. A geometric derivation of the reflection conditions is reviewed. Finally, the inconsistent presentation of metric restrictions imposed by the structural symmetry is pointed out and corrected.