Baake, M. and Grimm, U.
Averaged coordination numbers of planar aperiodic tilings.
Philosophical Magazine, 86(3-5)
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We consider averaged shelling and coordination numbers of aperiodic tilings. Shelling numbers count the vertices on radial shells around a vertex. Coordination numbers, in turn, count the vertices on coordination shells of a vertex, defined via the graph distance given by the tiling. For the Ammann–Beenker tiling, we find that coordination shells consist of complete shelling orbits, which enables us to calculate averaged coordination numbers for rather large distances explicitly. The relation to topological invariants of tilings is briefly discussed.
||Preprint version math-ph/0509038 available at http://arxiv.org/abs/math-ph/0509038
Proceedings of the 9th International Conference on Quasicrystals, 22ï¿½26 May 2005, Part 1. Guest Editors: Cynthia J. Jenks, Daniel J. Sordelet and Patricia Thiel
||aperiodic order; shelling numbers; coordination numbers; averages
||Mathematics, Computing and Technology > Mathematics and Statistics
||14 Jul 2006
||22 Jan 2011 10:49
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