In $\mathbb{R}^2$ it's known that with a "random" point configuration, the average degree of a vertex in its Delaunay triangulation is 6. 


Does anyone know of a similar result in higher dimension? I am particularly interested in the case of $\mathbb{R}^3$.



Average vertex degree in finite Delaunay triangulations in high dimensions
There is a good survey (of experimental and theoretical results) in [Tanemura's 2003 paper.](http://wildfire.stat.ucla.edu/pdflibrary/tanemura.pdf)


