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A groupoid and graph-theoretical analysis of the biopyribole–palysepiole series

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The modular analysis of the biopyriboles–palysepioles polysomatic series is extended to take into account the local symmetry of each module and the partial operations mapping pairs of modules, to build the corresponding space groupoids. We show that the presence of pseudo-partial mirror in sepiolite and jimthompsonite leads to 40 (pseudo)-isometries, of which eight are total operations appearing in the space groups of the two structures. Chesterite can be described as a contracted twin in which a transmutation operation maps a portion of the larger module (Z8) onto the smaller module (Z5). The graph-theoretical analysis of these minerals confirms the results obtained by the application of the groupoid theory.
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Keywords: :BIOPYRIBOLES; CONTRACTED TWIN; GRAPH-THEORY; LABELLED QUOTIENT GRAPHS; MODULAR CRYSTAL STRUCTURES; MODULARITY; PALYSEPIOLES; PSEUDO-SYMMETRY; SPACE GROUPOIDS; TROPOCHEMICAL CELL-TWINNING

Document Type: Research Article

Publication date: June 1, 2018

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  • The European Journal of Mineralogy publishes original papers, review articles and letters dealing with the mineralogical sciences s.l. These include primarily mineralogy, petrology, geochemistry, crystallography and ore deposits, as well as environmental, applied and technical mineralogy. Nevertheless, papers in any related field, including cultural heritage, will be considered.
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