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

Abstract : The modular analysis of the biopyriboles-palysepioles polysomatic series recently presented by Nespolo and Bouznari (2017) 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 (Z 8) onto the smaller module (Z 5). The graph-theoretical analysis of these minerals confirms the results obtained by the application of the groupoid theory.
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Massimo Nespolo, Akihiro Umayahara, Jean-Guillaume Eon. A groupoid and graph-theoretical analysis of the biopyribole-palysepiole series. European Journal of Mineralogy, E Schweizerbart Science Publishers, 2018, Minerals and materials: building principles and applications, 30 (3), pp.413 - 428. ⟨10.1127/ejm/2018/0030-2726⟩. ⟨hal-01872490⟩

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