Abstract
The maximum number of independent third-order elastic and second-order piezomagnetic constants required by the seven pentagonal point groups 5, 5, 10, 52, 5m, 52m, and 10m2 and the two icosahedral point groups 235 and 2/m35 that represent the symmetries of quasi-crystals in two and three dimensions are obtained in this paper. The non-vanishing and independent tensor components needed by each of these nine point groups with fivefold rotations are identified and tabulated. The results of this group-theoretical study are briefly discussed and summarized.
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