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Three-periodic nets and tilings: regular and quasiregular nets

Three-periodic nets and tilings: regular and quasiregular nets 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 the regular nets have the property that there is just one kind of vertex, one kind of edge, one kind of ring and one kind of tile, i.e. transitivity 1111. The quasiregular net has two kinds of natural tile and transitivity 1112. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Acta Crystallographica Section A: Foundations of Crystallography International Union of Crystallography

Three-periodic nets and tilings: regular and quasiregular nets

Three-periodic nets and tilings: regular and quasiregular nets


Abstract

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 the regular nets have the property that there is just one kind of vertex, one kind of edge, one kind of ring and one kind of tile, i.e. transitivity 1111. The quasiregular net has two kinds of natural tile and transitivity 1112.

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References (42)

Publisher
International Union of Crystallography
Copyright
Copyright (c) 2003 International Union of Crystallography
Subject
three-periodic nets, three-periodic tilings
ISSN
0108-7673
eISSN
1600-5724
DOI
10.1107/S0108767302018494
Publisher site
See Article on Publisher Site

Abstract

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 the regular nets have the property that there is just one kind of vertex, one kind of edge, one kind of ring and one kind of tile, i.e. transitivity 1111. The quasiregular net has two kinds of natural tile and transitivity 1112.

Journal

Acta Crystallographica Section A: Foundations of CrystallographyInternational Union of Crystallography

Published: Dec 21, 2002

Keywords: three-periodic nets ; three-periodic tilings .

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