Neutron-diffraction data were obtained from single-phase icosahedral powder of the system ${\mathrm{Al}}_{74}$${\mathrm{Si}}_5$${\mathrm{Mn}}_{21}$ and its modification by isomorphous substitution on the Mn sites. Amplitudes and phase differences of the partial structure factors ($F_{\mathrm{Al}}, F_{\mathrm{Mn}}$) were determined. From their $Q_{\perp }$ dependences, and within a strip-projection approach, phases were reconstructed. Atomic densities calculated in the physical 3D space show that Mackay icosahedra, the structural units usually invoked for quasicrystal models, do not emerge as the basic ingredients of the atomic arrangements.

• Received 3 February 1988

DOI:https://doi.org/10.1103/PhysRevLett.62.450