[math-fun] Statistics for a class of random solids

Suppose we have a random point generator, that generates points in R^3 with all three coordinates normally distributed around 0, say with a standard deviation of 1, though it doesn't really matter. Take N random points in this manner, and form the convex closure. This will be a polyhedron. What are the expected numbers of faces, vertices, and edges, in terms of N? Do they approach finite limits as N increases? I imagine that the surface area grows without bound. What about the expected number of faces that have 3, 4, 5, 6 edges, and so on? I can think of many more questions of this sort, and am wondering if anybody here knows what's known.