Three-periodic nets and tilings: minimal nets
نویسندگان
چکیده
منابع مشابه
Three-periodic nets and tilings: minimal nets.
The 15 3-periodic minimal nets of Beukemann & Klee [Z. Kristallogr. (1992), 201, 37-51] have been examined. Seven have collisions in barycentric coordinates and are self-entangled. The other eight have natural tilings. Five of these tilings are self-dual and the nets are the labyrinth nets of the P, G, D, H and CLP minimal surfaces of genus 3. Twelve ways have been found for subdividing a cube ...
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Regular nets are defined as those with symmetry that requires the coordination figure to be a regular polygon or polyhedron. It is shown that this definition leads to five regular 3-periodic nets. There is also one quasiregular net with a quasiregular coordination figure. The natural tiling of a net and its associated essential rings are also defined, and it is shown that the natural tilings of...
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28 three-periodic nets with two kinds of vertex and one kind of edge are identified. Some of their crystallographic properties and their natural tilings are described. Restrictions on site symmetry and coordination number of such nets are discussed and examples of their occurrence in crystal structures are given.
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Acta Crystallographica Section A: Foundations of Crystallography covers theoretical and fundamental aspects of the structure of matter. The journal is the prime forum for research in diffraction physics and the theory of crystallographic structure determination by diffraction methods using X-rays, neutrons and electrons. The structures include periodic and aperiodic crystals, and non-periodic d...
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ژورنال
عنوان ژورنال: Acta Crystallographica Section A Foundations of Crystallography
سال: 2004
ISSN: 0108-7673
DOI: 10.1107/s0108767304015442