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Phil. Mag. Β 53, L43-L51. , and Dubost, B. (1986). A simple construction of the AlCuLi quasicrystalline structure related to the (Al,Zn) Mg cubic structure type. Phil. Mag. Β 54, L105-L111. , and Shoemaker, D. P. (1954). The determination of the crystal structure of the sigma phase in the Fe-Cr and the Fe-Mo systems. Acta Cryst. 7, 857-865. , Waugh, J. L. , and Pauling, L. (1957). The crystal structure of the metallic phase Mg (Al,Zn) . Acta Cryst. 10, 254-259. Boren, B. (1933). Rontgenuntersuchung der Legierungen von Si mit Cr, Mn, Co und Ni.

And Kentgen, G. (1983). Total synthesis of dodecahedrane. J. Am. Chem. Soc. 105, 5446-5450. Pauling, L. (1955). The stochastic method and the structure of proteins. Am. Sci. 43, 285-297. Pauling, L. (1960). The Nature of the Chemical Bond. 3d ed. Y. Pauling, L. (1985). Apparent icosahedral symmetry is due to directed multiple twinning of cubic crystals. ) 317, 512-514. 4 2 4 3 057 04 3 2 2 6

The first three shells are similar to the first three described in the previous sections. The fourth shell is different. The 60-atom shell in the T-phase structure is obtained by placing two atoms against each rhombic face of the tria­ contahedron. The 30-vertex icosidodecahedron in the polytope projection is obtained by placing a single vertex outward from the center of each (planar) rhombic face of the rhombic triacontahedron (as is understandable from the fact that the icosidodecahedron is the dual of the rhombic do­ decahedron).

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