Yurii G. Nikonorov - Finite homogeneous metric spaces with special properties

This talk is devoted to some recent results on finite homogeneous metric spaces obtained in joint papers with Prof. V.N. Berestovskii. Every finite homogeneous metric subspace of an Euclidean space represents the vertex set of a compact convex polytope with the isometry group that is transitive on the set of vertices, moreover, all these vertices lie on some sphere. Consequently, the study of such subsets is closely related to the theory of convex polytopes in Euclidean spaces.