17 citations · 22 across the 5 of their papers we have counts for
5 papers
On the regularity radius of Delone sets in
Nikolay Dolbilin, Alexey Garber, Undine Leopold +1
We complete the proof of the upper bound for the regularity radius of Delone sets in three-dimensional Euclidean space. Namely, summing up the results obtained ea…
On the Optimality of Functionals over Triangulations of Delaunay Sets
Nikolay P. Dolbilin, Herbert Edelsbrunner, Oleg R. Musin
In this short paper, we consider the functional density on sets of uniformly bounded triangulations with fixed sets of vertices. We prove that if a functional attains its minimum o…
The Delone Peak
N. P. Dolbilin
One of beautifull mountains in the neighborhood of the Belukha, the tallest summit in the Altai (in Siberia), is called the Delone Peak in the name of Boris Nikolaevich Delone (Del…
A Local Characterization of Combinatorial Multihedrality in Tilings
Nikolai Dolbilin, Egon Schulte
A locally finite face-to-face tiling of euclidean d-space by convex polytopes is called combinatorially multihedral if its combinatorial automorphism group has only finitely many o…
Properties of Böröczki tilings in high dimensional hyperbolic spaces
N. Dolbilin, D. Frettlöh
We consider families of Böröczky tilings in hyperbolic space in arbitrary dimension, study some basic properties and classify all possible symmetries. In particular, it is shown th…