Allowable irreducible representations of the point groups with five-fold rotational axes

摘要

Allowable irreducible representations of the point groups with five-fold rotations – that represent the symmetry of the quasicrystals in two and three dimensions – are derived by employing the little group technique in conjunction with the solvability property. The point groups D $_{5h} ({overline {10} {text{{emph m}}}2})$ and ${text{{emph I}}}_h (frac{2}{text{{emph m}}}overline 3 ,overline 5)$ are taken to illustrate the method.