Crystallographic Properties of Local Groups of a Delone Set in a Euclidean Plane

It is proved that, in any Delone set on a Euclidean plane, a subset of points with a crystallographic local group, i.e., with local rotations of order or , is also a Delone set. This result has a number of important implications for regular systems and crystalline structures. By the local group at a...

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Bibliographic Details
Published in:Computational mathematics and mathematical physics 2022-08, Vol.62 (8), p.1265-1274
Main Authors: Dolbilin, N. P., Shtogrin, M. I.
Format: Article
Language:English
Subjects:
Computational Mathematics and Numerical Analysis
Crystallography
Disks
Euclidean geometry
General Numerical Methods
Mathematics
Mathematics and Statistics
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Summary:It is proved that, in any Delone set on a Euclidean plane, a subset of points with a crystallographic local group, i.e., with local rotations of order or , is also a Delone set. This result has a number of important implications for regular systems and crystalline structures. By the local group at a point of a set we mean the group of the cluster of radius centered at this point, where is the radius of a covering of the plane by equal disks with centers in
ISSN:0965-5425
1555-6662
DOI:10.1134/S0965542522080048