ISSN:
1600-5724
Quelle:
Crystallography Journals Online : IUCR Backfile Archive 1948-2001
Thema:
Chemie und Pharmazie
,
Geologie und Paläontologie
,
Physik
Notizen:
Aperiodic crystalline structures, commonly called quasicrystals, display a great variety of combinatorially possible local configurations. The local configurations of first order are the vertex configurations. This paper investigates, catalogues and classifies in detail the latter in the following important two-dimensional cases: the Penrose tiling, the decagonal triangle tiling and some twelve-fold tilings, including the patterns of Stampfli, Gähler, Niizeki and Socolar, as well as the square-triangle and the shield patterns. The main result is a comprehensive study of the three-dimensional primitive icosahedral tiling in its random version. All its 10 527 combinatorially possible noncongruent vertex configurations are constructed, coded, listed and classified. Methods for coding and representation of local configurations by formulae and diagrams, in particular those of Schlegel, are discussed. The paper also describes the algorithm used to generate them. The formal classification of local configurations by the characteristic integers rank, degree and order is also discussed.
Materialart:
Digitale Medien
URL:
http://dx.doi.org/10.1107/S0108767394001649
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