Let me add that there is a paper on asymptotics of the number of vertices, perimeter, and area of a convex hull for standard normally distributed independent points in the plane: Irene Hueter, The Convex Hull of a Normal Sample, Adv. App. Prob. 26 855-875 (1994). It is available at JSTOR. She proves that the number of vertices for the convex hull N satisfies: (N-2\sqrt(2*pi*ln n)) —> sqrt(2\sqrt(2*pi*ln n)*(1+pi*c)) times N(0,1), c_2 about 0.1 So average number of vertices grows like square root of logarithm of n. Steve