So-called icosahedral and decagonal quasicrystals are twins of an 820-atom cubic crystal.

Abstract

It is proposed that a molten alloy may contain a 104-atom cluster with icosahedral symmetry and largely icosahedral packing. The cluster may be described as involving twenty interpenetrating Friauf polyhedra. On rapid freezing these clusters form cubic crystals related to the \ensuremath{\beta}-W structure. The structure is compatible with x-ray and neutron powder diffraction patterns, the single-crystal precession x-ray patterns of ${\mathrm{CuLi}}_{3}$${\mathrm{Al}}_{6}$, the electron diffraction photographs, and the high-resolution electron micrographs.