Angular properties of Delaunay diagrams in any dimension (Q1283736)

The authors characterize the Delone diagrams in \(d\)-dimensional Euclidean space through a property of its facets. Then they introduce a new definition of angles being a generalization of the usual definition of angles used to establish the equiangularity of Delone triangulations in two-dimensional case. These new angles are used for a characterization of some Delone diagrams. The paper also characterizes Delone diagrams in spaces of dimension over 2 considering only solid angles. A kind of local equiangularity of the Delone diagrams is shown. Moreover, the paper presents an angular characterization of those Delone diagrams for which every region contains its circumcenter.