A. Garber

activity

20102025

most citedOn the Origin of Crystallinity: a Lower Bound for the Regularity Radius of Delone Sets

23 citations · 112 across the 26 of their papers we have counts for

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Showing 2019Show all

2 papers · 1 filter

math.MG2019★ 17 cited

On the regularity radius of Delone sets in $R^{3}$

Nikolay Dolbilin, Alexey Garber, Undine Leopold +1

We complete the proof of the upper bound $ρ^_{3} \leq 10 R$ for the regularity radius of Delone sets in three-dimensional Euclidean space. Namely, summing up the results obtained ea…

math.CO2019★ 7 cited

Voronoi conjecture for five-dimensional parallelohedra

Alexey Garber

We prove the Voronoi conjecture for five-dimensional parallelohedra. Namely, we show that if a convex five-dimensional polytope $P$ tiles $R^{5}$ with translations, then $P$ …

On the regularity radius of Delone sets in R3

Voronoi conjecture for five-dimensional parallelohedra

On the regularity radius of Delone sets in $R^{3}$