On the regularity radius of Delone sets in \({\mathbb{R}}^3\)

DOI10.1007/s00454-021-00292-6zbMath1477.52023arXiv1909.05805OpenAlexW3158897302MaRDI QIDQ2230916

Undine Leopold, Marjorie Senechal, Alexey I. Garber, Nikolai P. Dolbilin, Egon Schulte

Publication date: 29 September 2021

Published in: Discrete \& Computational Geometry (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1909.05805

zbMATH Keywords

symmetry groupregular systemregularity radiusDelone setcluster group

Mathematics Subject Classification ID

Lattices and convex bodies in (n) dimensions (aspects of discrete geometry) (52C07) Combinatorial aspects of tessellation and tiling problems (05B45) Tilings in (n) dimensions (aspects of discrete geometry) (52C22) Quasicrystals and aperiodic tilings in discrete geometry (52C23)

Related Items (4)

Local groups in Delone sets: a conjecture and results ⋮ Crystallographic properties of local groups of a Delone set in a Euclidean plane ⋮ Delone sets and tilings: local approach ⋮ Local Groups in Delone Sets

Cites Work

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• Classical topics in discrete geometry
• Multiregular point systems
• Delone sets: local identity and global symmetry
• Delone sets in \(\mathbb{R}^3\) with \(2R\)-regularity conditions
• Locally antipodal Delaunay sets
• Struktur der Materie
• A Remark on Stirling's Formula
• On the origin of crystallinity: a lower bound for the regularity radius of Delone sets
• The Open Mathematics of Crystallization

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