✦ LIBER ✦

Archetypes and Other Embeddings of Periodic Nets Generated by Orthogonal Projection

✍ Scribed by Jean-Guillaume Eon

Publisher: Elsevier Science
Year: 1999
Tongue: English
Weight: 165 KB
Volume: 147
Category: Article
ISSN: 0022-4596
DOI: 10.1006/jssc.1999.8379

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✦ Synopsis

Archetypes are de5ned 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.

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