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The method of tensor invariants is systematically summarized and generalized. With the help of the theorem of `shadow' and the theorem of the number of independent bases, the whole family of isovariant orthogonal basis functions for pentagonal, icosahedral, octagonal, decagonal and dodecagonal point groups is obtained. On the basis of these results, the Hall-coefficient tensors for quasicrystalline point groups are identified and tabulated. The results of this group-theoretical study are briefly discussed and summarized.
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