# Integer Cech cohomology of icosahedral projection tilings

Gähler F, Hunton J, Kellendonk J (2008)
ZEITSCHRIFT FUR KRISTALLOGRAPHIE 223(11-12): 801-804.

Journal Article | Published | English

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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.
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Gähler F, Hunton J, Kellendonk J. Integer Cech cohomology of icosahedral projection tilings. ZEITSCHRIFT FUR KRISTALLOGRAPHIE. 2008;223(11-12):801-804.
Gähler, F., Hunton, J., & Kellendonk, J. (2008). Integer Cech cohomology of icosahedral projection tilings. ZEITSCHRIFT FUR KRISTALLOGRAPHIE, 223(11-12), 801-804.
Gähler, F., Hunton, J., and Kellendonk, J. (2008). Integer Cech cohomology of icosahedral projection tilings. ZEITSCHRIFT FUR KRISTALLOGRAPHIE 223, 801-804.
Gähler, F., Hunton, J., & Kellendonk, J., 2008. Integer Cech cohomology of icosahedral projection tilings. ZEITSCHRIFT FUR KRISTALLOGRAPHIE, 223(11-12), p 801-804.
F. Gähler, J. Hunton, and J. Kellendonk, “Integer Cech cohomology of icosahedral projection tilings”, ZEITSCHRIFT FUR KRISTALLOGRAPHIE, vol. 223, 2008, pp. 801-804.
Gähler, F., Hunton, J., Kellendonk, J.: Integer Cech cohomology of icosahedral projection tilings. ZEITSCHRIFT FUR KRISTALLOGRAPHIE. 223, 801-804 (2008).
Gähler, Franz, Hunton, John, and Kellendonk, Johannes. “Integer Cech cohomology of icosahedral projection tilings”. ZEITSCHRIFT FUR KRISTALLOGRAPHIE 223.11-12 (2008): 801-804.
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arXiv 0809.4442