Given a set of n linearly independent points in a Euclidean space Ed, P = {p1, … , pn} with n > d, a Delaunay tessellation with at lease one d-dimensional simplex can be constructed. This tessellation is unique up to degenerate linearity conditions. The cardinality of the set of unique k-dimensional simplexes, k ≤ d, in the tessellation is bounded and the bound can be computed, given the dimension of the space, d, and the number of points in the tessellation generating set, n. These bounds can be refined if the number of points on the convex hull of P, m, is known. The bounds on cardinality are developed using constructive geometric arguments presented in the sequence necessary to construct the tessellation. The cardinality of simplexes in the Voronoi diagram is then related to the Delaunay tessellation by geometric duality. An example is given.
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机译：在欧几里德空间E d ，p = {p1，...，pn}中给定一组线性独立点，用n> d，可以构造具有租约的delaunay tessellation。 。这种曲面细分是彻底的线性条件。在镶嵌在镶嵌中的唯一k维单位，k≤d的组的基数被界限，并且鉴于空间，d的尺寸和镶嵌生成组中的点数，可以计算绑定。如果已知p，m的凸壳上的点数，则可以改进这些界限。基数的界限是使用在构建曲面细分所需的序列中呈现的建设性的几何参数来开发。然后，Voronoi图中单纯X的基数与几何二元性的Delaunay Telsellation有关。给出一个例子。
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