Premium
Coordination numbers of the vertex graph of a Penrose tiling
Author(s) -
Shutov Anton,
Maleev Andrey
Publication year - 2018
Publication title -
acta crystallographica section a
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.742
H-Index - 83
ISSN - 2053-2733
DOI - 10.1107/s2053273318000062
Subject(s) - penrose tiling , quasiperiodic function , coordination number , vertex (graph theory) , quasicrystal , combinatorics , mathematics , graph , discrete mathematics , physics , geometry , ion , quantum mechanics , mathematical analysis
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.