By Levi S. Shively

Spanish translation of the vintage college-level glossy geometry textbook

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Lett. 61, 2774 (1988). Y. L. V. Chester, Phys. Rev. B 39, 446 (1989). P. Bak, Scripta Met. 20, 1199 (1986). B. M. Lang-;-M. Tanaka, P. Sainfort and M. Audier, Nature 324, 48 (1986). ~Jaric, Anniversary Adriatico Research Conference on Quasicrystals, Trieste, July 4-7, 1989 (to be published by Yorld Scientific, Singapore). M. de Boissieu, M. Audier, Ch. M. Dubois, P. Guyot and B. Dubost, Ibidem. P. Tsai, A. Inoue and T. Masumoto, Japan J. Appl. Phys. 26, L1505 (1987) S. Ebalard and F. Spaepen, J.

Complicating factor is that the 6D-density function describing a single atom is not known, contrary to the case for atoms in 3D, physical space. All vertices of the 3D Penrose tiling can be obtained as a 3D section of a hypercubic lattice in 6D space, when each 6D lattice point is decorated with a object which has the shape of a triacontahedron (TR) in perpendicular space and is infinitely thin in physical space. 10- 12 It immediataly follows that a decoration of the 3D Penrose tiling with an atom on each vertex is represented in 6D space by a 60-atom, which is the convolution of an ordinary density in physical space and the triacontahedron in perpendicular space.

The two coordinate axis are two-fold symmetry axis. The peaks 0, A, Band G are obtained for atoms on the vertices of a Penrose tiling. The peaks C, E and F can be explained by assuming both the vertices and middle-edge positions to be decorated by atoms. 45 ( X,X,X,D, D, D) Fig. 3. Section of the 60 Patterson function for icosahedral Al6CuLi3, obtained by Fourier transformation of the measured X-ray diffraction intensities. Contour lines are drawn at intervals of 10% of the maximum value. This section incorporates the origin.