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.

DOI: https://doi.org/10.1080/14786430500269022

URL: http://www.tandf.co.uk/journals/titles/14786435.ht...

Abstract

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.

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About

• Item ORO ID
• 4927
• Item Type
• Journal Item
• ISSN
• 1478-6435
• Extra Information
• Preprint version math-ph/0509038 available at http://arxiv.org/abs/math-ph/0509038
  
  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 or School
• Faculty of Science, Technology, Engineering and Mathematics (STEM) > Mathematics and Statistics
  Faculty of Science, Technology, Engineering and Mathematics (STEM)
• Depositing User
• Uwe Grimm