TY - JOUR
T1 - Three-periodic nets and tilings
T2 - Regular and quasiregular nets
AU - Delgado Friedrichs, Olaf
AU - O'Keeffe, Michael
AU - Yaghi, Omar M.
PY - 2003/1
Y1 - 2003/1
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=0037273070&partnerID=8YFLogxK
U2 - 10.1107/S0108767302018494
DO - 10.1107/S0108767302018494
M3 - Article
SN - 0108-7673
VL - 59
SP - 22
EP - 27
JO - Acta Crystallographica Section A: Foundations of Crystallography
JF - Acta Crystallographica Section A: Foundations of Crystallography
IS - 1
ER -