Icosahedral quasicrystals as twins of cubic crystals containing large icosahedral clusters of atoms: The 1012-atom primitive cubic structure of Al(6)CuLi(3), the C-phase Al(37)Cu(3)Li(21)Mg(3), and GaMg(2)Zn(3)

Single-grain precession x-ray diffraction photographs of Al₆CuLi₃ have been successfully indexed on the basis of icosahedral twinning of cubic crystals with a 1012-atom primitive cubic unit with edge 25.70 Å, giving support to the proposal that the so-called icosahedral quasicrystals are twins of crystals containing eight large icosahedral clusters in the β-W arrangement. In this compound two of the clusters consist of 104 atoms and six consist of 136 atoms, with 24 atoms shared. The same structure is assigned to the C-phase, Al₃₇Cu₃Li₂₁Mg₃, and to GaMg₂Zn₃. A theory of icosahedral quasicrystals and amorphous metals is described.