Author:
Moreira de Oliveira Montauban,Eon Jean-Guillaume
Abstract
Non-crystallographic (NC) nets are periodic nets characterized by the existence of non-trivial bounded automorphisms. Such automorphisms cannot be associated with any crystallographic symmetry in realizations of the net by crystal structures. It is shown that bounded automorphisms of finite order form a normal subgroupF(N) of the automorphism group of NC nets (N,T). As a consequence, NC nets are unstable nets (they display vertex collisions in any barycentric representation) and, conversely, stable nets are crystallographic nets. The labelled quotient graphs of NC nets are characterized by the existence of an equivoltage partition (a partition of the vertex set that preserves label vectors over edges between cells). A classification of NC nets is proposed on the basis of (i) their relationship to the crystallographic net with a homeomorphic barycentric representation and (ii) the structure of the subgroupF(N).
Publisher
International Union of Crystallography (IUCr)
Subject
Inorganic Chemistry,Physical and Theoretical Chemistry,Condensed Matter Physics,General Materials Science,Biochemistry,Structural Biology
Cited by
9 articles.
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