The superstructure in decagonal Al-Ni-Co has a unit cell in 5D space 5 times larger than that of the normal structure. A 3D model of this structure proposed recently [K. Hiraga, W. Sun, and A. Yamamoto, Mater. Trans. JIM 35, 657 (1994)] has a 20 Å cluster on each vertex of the Penrose pattern with an edge length of 20 Å. This Letter shows a corresponding 5D model. There are 20 occupation domains in a unit cell, two of which are independent under the symmetry of ${P10\mathrm{}}_5/\mathrm{mcm}\left({10}^{7}1mm\right)$. This 5D model shows diffraction patterns similar to those of the superstructure. The phase transition from the normal phase to the superstructure occurs by a phason jump.

• Received 30 July 1996

DOI:https://doi.org/10.1103/PhysRevLett.78.4430