Practical Electron Microscopy and Database

The point group -53m () of icosahedral quasicrystals (e.g. AlMnPd, Al_5.5Li_3.3Cu, Al₆₅Fe₁₅Cu₂₀, Al_63.5Cu₂₄Fe_12.5, and almost spherical C₆₀ molecule) is a 6-dimensional (6-D) group. This group acts on the 21-dimensional space of rank 4 tensors (T_ijkm = T_jikm = T_ijmk = T_kmij) with the symmetry of the elasticity tensor. Since this group contains a 2-dimesional pointwise invariant subspace, the elasticity tensor has 2 free parameters. Figure 1438 shows the schematic illustration of symmetry operations of point group .

Figure 1438. Schematic illustration of symmetry operations of point group .