23 citations · 112 across the 26 of their papers we have counts for
5 papers · 1 filter
On the Voronoi Conjecture for combinatorially Voronoi parallelohedra in dimension five
Mathieu Dutour Sikirić, Alexey Garber, Alexander Magazinov
In a recent paper Garber, Gavrilyuk and Magazinov proposed a sufficient combinatorial condition for a parallelohedron to be affinely Voronoi. We show that this condition holds for…
Periodic triangulations of
Mathieu Dutour Sikirić, Alexey Garber
We consider in this work triangulations of that are periodic along . They generalize the triangulations obtained from Delaunay tessellations of lattice…
On triangular paperfolding patterns
Alexey Garber
We introduce patterns on a triangular grid generated by paperfolding operations. We show that in case these patterns are defined using a periodic sequence of foldings, they can als…
On the Origin of Crystallinity: a Lower Bound for the Regularity Radius of Delone Sets
Igor A. Baburin, Mikhail Bouniaev, Nikolay Dolbilin +4
The local theory of regular or multi-regular systems aims at finding sufficient local conditions for a Delone set to be a regular or multi-regular system. One of the main goals…
On a Helly-type question for central symmetry
Alexey Garber, Edgardo Roldán-Pensado
We study a certain Helly-type question by Konrad Swanepoel. Assume that is a set of points such that every -subset of is in centrally symmetric convex position, is it tr…