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 Al(6)CuLi(3) have been successfully indexed on the basis of icosahedral twinning of cubic crystals with a 1012-atom primitive cubic unit with edge 25.70 A, giving support to the proposal that the so-called icosahedral quasicrystals are twins of crystals containing eight large icosahedral clusters in the beta-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, Al(37)Cu(3)Li(21)Mg(3), and to GaMg(2)Zn(3). A theory of icosahedral quasicrystals and amorphous metals is described.