Six-dimensional Fourier analysis of the icosahedral ${\mathrm{Al}}_{73}$${\mathrm{Mn}}_{21}$${\mathrm{Si}}_6$ alloy

Fourier analysis of x-ray and neutron diffraction data of an icosahedral alloy are displayed both as a three-dimensional (3D) quasiperiodic function and as a six-dimensional (6D) periodic function. The 6D analysis leads to a simpler description that contains the same information as the 3D analysis. The 6D function has only two elongated peaks in the unit cell, but each peak contains much chemical detail.