Non-crystallographic nets: characterization and first steps towards a classification

DOI10.1107/S2053273314000631zbMath1337.05054OpenAlexW1975825297WikidataQ87849909 ScholiaQ87849909MaRDI QIDQ2808924

Montauban Jun. Moreira de Oliveira, Jean-Guillaume Eon

Publication date: 27 May 2016

Published in: Acta Crystallographica Section A Foundations and Advances (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1107/s2053273314000631

zbMATH Keywords

labelled quotient graphsnon-crystallographic netsunstable nets

Mathematics Subject Classification ID

Applications of graph theory (05C90) Three-dimensional polytopes (52B10) Statistical mechanics of crystals (82D25) Graphs and abstract algebra (groups, rings, fields, etc.) (05C25)

Related Items (2)

Symmetry and topology: the 11 uninodal planar nets revisited ⋮ High-symmetry embeddings of interpenetrating periodic nets. Essential rings and patterns of catenation

Cites Work

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• Equilibrium placement of periodic graphs and convexity of plane tilings
• Non-crystallographic nets with freely acting, non-abelian local automorphism groups
• Nomenclature and generation of three-periodic nets: the vector method
• Graph-theoretical characterization of periodicity in crystallographic nets and other infinite graphs
• Infinite geodesic paths and fibers, new topological invariants in periodic graphs
• Edge-transitive lattice nets
• Euclidian embeddings of periodic nets: definition of a topologically induced complete set of geometric descriptors for crystal structures
• Nets with collisions (unstable nets) and crystal chemistry
• Non-crystallographic nets with finite blocks of imprimitivity for bounded automorphisms
• Notes on infinite permutation groups

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