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Averaged coordination numbers of planar aperiodic tilings

Baake, M. and Grimm, U. (2006). Averaged coordination numbers of planar aperiodic tilings. Philosophical Magazine, 86(3-5) pp. 567–572.

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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.

Item Type: Journal Article
ISSN: 1478-6435
Extra Information: Preprint version math-ph/0509038 available at

Proceedings of the 9th International Conference on Quasicrystals, 22�26 May 2005, Part 1. Guest Editors: Cynthia J. Jenks, Daniel J. Sordelet and Patricia Thiel
Keywords: aperiodic order; shelling numbers; coordination numbers; averages
Academic Unit/Department: Mathematics, Computing and Technology > Mathematics and Statistics
Mathematics, Computing and Technology
Item ID: 4927
Depositing User: Uwe Grimm
Date Deposited: 14 Jul 2006
Last Modified: 24 Feb 2016 05:24
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