Uniqueness theorem for locally antipodal Delaunay sets
We prove theorems on locally antipodal Delaunay sets. The main result is the proof of a uniqueness theorem for locally antipodal Delaunay sets with a given 2R-cluster. This theorem implies, in particular, a new proof of a theorem stating that a locally antipodal Delaunay set all of whose 2R-clusters are equivalent is a regular system, i.e., a Delaunay set on which a crystallographic group acts transitively.
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- 1.E. S. Fedorov, An Introductionto the Theory of Figures (St. Petersburg, 1885); 2nd ed. (Akad. Nauk SSSR, Moscow, 1953), Classics of Science [in Russian].Google Scholar
- 3.A. Schoenflies, Krystallsystemeund Krystallstructur (B.G. Teubner, Leipzig, 1891).Google Scholar
- 10.R. P. Feynman, R. B. Leighton, and M. Sands, TheFeynman Lectures on Physics (Addison Wesley, Reading, MA, 1964), Vol. II, Ch. 30.Google Scholar