Comments on the relationship between The Archimedean truncated octahedron, and packing of geometric units in cubic crystal structures by C. Chieh and On the choice of origins in the description of space groups by H. Burzlaff & H. Zimmermann

The results of the investigation of the choice of origins in the description of space groups [Burzlaff & Zimmermann (1980). Z. Kristallogr. 153, 151-179] can be used to give group-theoretical reasons for the classification of cubic space groups by the aid of Archimedean truncated octahedron as was proposed by Chieh [Acta Cryst. (1979), A35, 946-952]. The division into units is independent of the choice of origin; however, it is found to be advantageous to place the centers of the geometric units at proper or privileged origins in dealing with cubic space groups without the site of cubic point-group symmetry, so as to simplify description of the geometric units. A modification is proposed in the representations of geometric-unit sequences. If the new symbols for the sequences of geometric units are extended by the symmetry of the centers of the units, there is a one-to-one correspondence between these extended sequence symbols and the non-isomorphic space group. Moreover, the extension of this concept to orthorhombic space groups with 'cubic' affine normalizers may be useful.