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Icosahedral crystals: Where are the atoms?

1986; American Physical Society; Volume: 56; Issue: 8 Linguagem: Inglês

10.1103/physrevlett.56.861

1092-0145

Per Bak,

Mineralogy and Gemology Studies

The positions of atoms in icosahedral crystals are shown to correspond to arrangements of three-dimensional hypersurfaces in six-dimensional periodic lattices. The six-dimensional space-group symmetry allows for crystals which cannot be formed by space-filling decorated tilings (quasicrystals). Structures with continuously varying ``unit cells'' are possible. The connection between tilings, projections, cuts, and density-wave descriptions is pointed out.