Some comments on the theory of space-group representations. III. The completeness of the identification of stars in the representation domain for each space group

Abstract

For pt.II see ibid., vol.3, p.619, 1970. Published sets of tables of the irreducible representations of the space groups are restricted to k vectors within Omega , the basic domain, whereas for a complete identification of all the irreducible representations it is necessary to consider phi , the representation domain, rather than just Omega . The representation domain, phi , is identified for every space group. A general procedure is described that enables one to identify all those additional special k vectors in ( phi - Omega ) that must be included in order to ensure that one, and only one, k vector from each star is identified.