Delone sets and tilings: local approach

DOI10.1134/S0081543822040071zbMath1503.52031OpenAlexW4312774486MaRDI QIDQ2099703

Nikolai P. Dolbilin, Mikhail Shtogrin

Publication date: 18 November 2022

Published in: Proceedings of the Steklov Institute of Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1134/s0081543822040071

zbMATH Keywords

Delone setsregular systemsisogonal tilingsDelone tiling

Mathematics Subject Classification ID

Combinatorial aspects of tessellation and tiling problems (05B45) Tilings in (2) dimensions (aspects of discrete geometry) (52C20) Tilings in (n) dimensions (aspects of discrete geometry) (52C22)

Cites Work

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• Uniqueness theorem for locally antipodal Delaunay sets
• Combinatorial and metric theory of planigons
• Crystallographic properties of local groups of a Delone set in a Euclidean plane
• On the regularity radius of Delone sets in \({\mathbb{R}}^3\)
• Delone sets in \(\mathbb{R}^3\) with \(2R\)-regularity conditions
• Local Groups in Delone Sets
• Local groups in Delone sets: a conjecture and results
• On the origin of crystallinity: a lower bound for the regularity radius of Delone sets

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