Delaunay tesselations and convex hulls According to Wikipedia the Delaunay tesselation in $d$ dimensions can be viewed as a convex hull problem in $d+1$ dimensions. Given a countable set of points $S\subset \mathbb{R}^d$ and a point $p\in S$, find the largest subset $X\subset S\setminus\{p\}$ with the following properties:


Every point in $X$ is a vertex of the convex hull of $X$.
$p$ is the only point in $S$ that lies in the interior of the convex hull of $X$. 


Is there a relationship between the $d$-dimensional Delaunay tesselation and the set of polytopes for each point $p\in S$ as described?
The relationship I remember is that the Delaunay tessalation is the "visual complement" of Voronoi cells.

I just found this paper on Google which has a nice figure as to why finding the convex hull in d+a dimensions is equivalent to finding the Delaunay tessalation:

http://www.cs.mtu.edu/~shene/PUBLICATIONS/2004/Hull2VD.pdf

What's also interesting from a theoretical cs perspective is that the knn problem can be mapped to the Voronoi cell problem, and by extension to the Delaunay tesselation and the convex hull problem. Known algorithms in d-dimensions typically have an exponential dependency on dimension.