The Open UniversitySkip to content

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.

Full text available as:
PDF (Not Set) - Requires a PDF viewer such as GSview, Xpdf or Adobe Acrobat Reader
Download (165kB)
DOI (Digital Object Identifier) Link:
Google Scholar: Look up in Google Scholar


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 Item
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/School: Faculty of Science, Technology, Engineering and Mathematics (STEM) > Mathematics and Statistics
Faculty of Science, Technology, Engineering and Mathematics (STEM)
Item ID: 4927
Depositing User: Uwe Grimm
Date Deposited: 14 Jul 2006
Last Modified: 07 Dec 2018 12:39
Share this page:


Altmetrics from Altmetric

Citations from Dimensions

Download history for this item

These details should be considered as only a guide to the number of downloads performed manually. Algorithmic methods have been applied in an attempt to remove automated downloads from the displayed statistics but no guarantee can be made as to the accuracy of the figures.

Actions (login may be required)

Policies | Disclaimer

© The Open University   contact the OU