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High‐symmetry embeddings of interpenetrating periodic nets. Essential rings and patterns of catenation
Author(s) -
Bonneau Charlotte,
O'Keeffe Michael
Publication year - 2015
Publication title -
acta crystallographica section a
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.742
H-Index - 83
ISSN - 2053-2733
DOI - 10.1107/s2053273314019950
Subject(s) - catenation , net (polyhedron) , lattice (music) , mathematics , combinatorics , crystallography , pure mathematics , topology (electrical circuits) , physics , geometry , chemistry , dna , biochemistry , acoustics
Symmetrical embeddings are given for multiply intergrown sets of some commonly occurring nets such as dia (diamond), qtz (quartz), pcu (net of primitive cubic lattice) and srs (labyrinth net of the G minimal surface). Data are also given for all known pairs of nets which have edge‐transitive self‐dual tilings. Examples are given for symmetrical polycatenation of the 2‐periodic nets sql (square lattice) and hcb (honeycomb). The idea that the rings that are the faces of natural tilings form a complete basis set (essential rings) is explored and patterns of catenation of such rings described.