Vestnik Chelyabinsk. Gos. Univ., 2015, Issue 17, Pages 6–17
This article is cited in 1 scientific paper (total in 1 paper)
Geometry and Topology
Crystal criterion and antipodal Delaunay sets
N. P. Dolbilin
V.A. Steklov Mathematical Institute of Russian Academy of Sciences, Moscow, Russian Federation
It is proved that a discrete set of points repeatability local configurations under certain conditions implies the so-called «global order», which includes the presence of a plurality of crystallographic symmetry group. It is also proved that the set of Delaunay, in which all $2R$-clusters are antipodal, that is centrally symmetric, is itself a centrally symmetric with respect to each of its points. Moreover, if in addition to this cluster are identical, then the set is correct, i. e. its symmetry group acts transitively.
This article based on a lecture delivered at the International Conference «Quantum topology» (5-17 July 2014), organized by the Laboratory of Quantum Topology of Chelyabinsk State University.
Delaunay set, cluster, the right system, crystallographic group.
PDF file (1191 kB)
N. P. Dolbilin, “Crystal criterion and antipodal Delaunay sets”, Vestnik Chelyabinsk. Gos. Univ., 2015, no. 17, 6–17
Citation in format AMSBIB
\paper Crystal criterion and antipodal Delaunay sets
\jour Vestnik Chelyabinsk. Gos. Univ.
Citing articles on Google Scholar:
Related articles on Google Scholar:
This publication is cited in the following articles:
N. P. Dolbilin, A. N. Magazinov, “Locally antipodal Delaunay sets”, Russian Math. Surveys, 70:5 (2015), 958–960
|Number of views:|