Coordination numbers of the vertex graph of a Penrose tiling-Reference-Cited by-同舟云学术

Coordination numbers of the vertex graph of a Penrose tiling

Published:2018-02-15 Issue:2 Volume:74 Page:112-122
ISSN:2053-2733
Container-title:Acta Crystallographica Section A Foundations and Advances
language:
Short-container-title:Acta Cryst Sect A

Author:

Shutov Anton^ORCID,Maleev Andrey^ORCID

Abstract

A new approach to study coordination shells and coordination sequences of quasiperiodic graphs is suggested. The structure of the coordination shells in the vertex graph of a Penrose tiling is described. An asymptotic formula for its coordination numbers is obtained. An essentially different behaviour of the coordination numbers for even and odd shells is revealed.

Funder

Russian Foundation for Basic Research

Publisher

International Union of Crystallography (IUCr)

Subject

Inorganic Chemistry,Physical and Theoretical Chemistry,Condensed Matter Physics,General Materials Science,Biochemistry,Structural Biology

Link

http://journals.iucr.org/a/issues/2018/02/00/eo5079/eo5079.pdf

Reference25 articles.

1. Averaged coordination numbers of planar aperiodic tilings

2. Baake, M. & Grimm, U. (2013). Aperiodic Order, Vol. 1, A Mathematical Invitation. Cambridge University Press.

3. Baake, M., Grimm, U., Repetowicz, P. & Joseph, D. (1998). Proceedings of the 6th International Conference on Quasicrystals, edited by S. Takeuchi & T. Fujiwara, pp. 124-127. Singapore: World Scientific.

4. Discrete tomography of Penrose model sets

Cited by 4 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. An application of singular traces to crystals and percolation;Journal of Geometry and Physics;2022-09

2. Growth forms of grid tilings;Acta Crystallographica Section A Foundations and Advances;2022-05-13

3. Coordination sequences of crystals are of quasi-polynomial type;Acta Crystallographica Section A Foundations and Advances;2021-02-18

4. Coordination shells and coordination numbers of the vertex graph of the Ammann–Beenker tiling;Acta Crystallographica Section A Foundations and Advances;2019-08-23