The maximum number of non-vanishing and independent second order photoelastic coefficients required by the seven pentagonal and the two icosahedral point groups 5(C₅),$$\bar 5$$(S₁₀),$$\overline {10} $$(C_5h),$$\overline {10} $$ m2(D_5h), 52(D₅), 5m(C_5v),$$\bar 5$$ 2m(D_5d); 235(I), 2/m$$\bar 3$$$$\bar 5$$(I_h)—that describe the quasicrystals symmetry groups in two and three dimensions—is obtained. The schemes of non-vanishing and independent coefficients have been calculated and listed. Finally the results of this group-theoretical study are briefly discussed.

The transport coefficients for the nine point groups$$5(C_5 ), \bar 5(S_{10} ), \overline {10} (C_{5h} ), \overline {10} m2(D_{5h} ), 52(D_5 ), 5m(C_{5\upsilon } ), \bar 5 2m(D_{5d} ), 235(I), 2/m \bar 3 \bar 5(I_h )$$ —which represent the symmetry groups of the quasicrystals in two and three dimensions—have been evaluated and tabulated in this work, employing group-theoretical methods.

Surface harmonics for the seven pentagonal point groups 5(C₅), {ie859-1}(S₁₀), {ie859-2}(C_5h), {ie859-3}m2(D_5h), {ie859-4} 2(D₅), 5m(C_5v) and 5 2m(D_5d) that represent the symmetries of quasicrystals in two and three dimensions are obtained, employing the projection operator method [11] and the simplified (authors) method. The results obtained are tabulated and are briefly discussed.