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Group-theoretical methods have been accepted as exact and reliable tools in studying the physical properties of crystals and quasicrystalline materials. By group representation theory, the maximum number of non-vanishing and independent secondorder piezoelectric coefficients required by the seven pentagonal and two icosahedral point groups -that describe the quasicrystal symmetry groups in two and three dimensionsis determined. The schemes of non-vanishing and independent second-order piezoelectric tensor components needed by the nine point groups with five-fold rotations are identified and tabulated employing a compact notation. The results of this group-theoretical study are briefly discussed.

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