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Zeitschrift für Kristallographie - Crystalline Materials

Editor-in-Chief: Pöttgen, Rainer

Ed. by Antipov, Evgeny / Bismayer, Ulrich / Boldyreva, Elena V. / Huppertz, Hubert / Petrícek, Václav / Tiekink, E. R. T.

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Volume 223, Issue 11-12 (Dec 2008)


Integer Cech cohomology of icosahedral projection tilings

Franz Gähler / John R. Hunton / Johannes Kellendonk
Published Online: 2009-09-25 | DOI: https://doi.org/10.1524/zkri.2008.1070


The integer Cech cohomology of canonical projection tilings of dimension three and codimension three is derived. These formulae are then evaluated for several icosahedral tilings known from the literature. Rather surprisingly, the cohomologies of all these tilings turn out to have torsion. This is the case even for the Danzer tiling, which is, in some sense, the simplest of all icosahedral tilings. This result is in contrast to the case of two-dimensional canonical projection tilings, where many examples without torsion are known.

Keywords: Tilings; Cohomology; Torsion

About the article

* Correspondence address: Stuttgart, Deutschland,

Published Online: 2009-09-25

Published in Print: 2008-12-01

Citation Information: Zeitschrift für Kristallographie International journal for structural, physical, and chemical aspects of crystalline materials, ISSN (Print) 0044-2968, DOI: https://doi.org/10.1524/zkri.2008.1070.

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