Archetypes and Other Embeddings of Periodic Nets Generated by Orthogonal Projection

Archetypes are defined as embeddings of minimal nets with maximal symmetry. A simple geometrical construction is proposed to construct the archetype associated with two-line-connected graphs with more than one cycle and without loops and a criterion is derived to check the embedding. The periodicity...

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Bibliographic Details
Published in:Journal of solid state chemistry 1999-11, Vol.147 (2), p.429-437
Main Author: Eon, Jean-Guillaume
Format: Article
Language:English
Subjects:
Condensed matter: structure, mechanical and thermal properties
Crystalline state (including molecular motions in solids)
Exact sciences and technology
Physics
Structure of solids and liquids
crystallography
Theory of crystal structure, crystal symmetry
calculations and modeling
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Summary:Archetypes are defined as embeddings of minimal nets with maximal symmetry. A simple geometrical construction is proposed to construct the archetype associated with two-line-connected graphs with more than one cycle and without loops and a criterion is derived to check the embedding. The periodicity of the archetype is equal to the cyclomatic number of the quotient graph of the net, and the factor group of its space group with respect to the normal subgroup of all translations is isomorphic to the automorphism group of the quotient graph. Orthogonal projections are considered to ensure the generation of periodic structures with three-dimensional coordination polyhedra.
ISSN:0022-4596
1095-726X
DOI:10.1006/jssc.1999.8379