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

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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.