A Delaunay simplex is the dual of the Voronoi diagram. Delaunay simplexes were developed by Борис Николаевич Делоне. In two-dimensions it is more commonly known as Delaunay triangulation, and in three-dimensions , as Delaunay tetrahedralisation.
A Delaunay triangulation fulfils the empty circle property (also called Delaunay property): the circumscribing circle of any facet of the triangulation contains no data point in its interior. For a point set with no subset of four co-circular points the Delaunay triangulation is unique. A similar property holds for tetrahedralisation in three dimensions.
- Математические основы структурного анализа кристаллов (совместно с А.Д.Александровым и Н.Падуровым), Москва, Матем. литература, 1934 г.
- A. V. Anikeenko, M. L. Gavrilova and N. N. Medvedev "A Novel Delaunay Simplex Technique for Detection of Crystalline Nuclei in Dense Packings of Spheres", Lecture Notes in Computer Science 3480 pp. 816-826 (2005)