This reminds me very much of a question I don't recall mentioning here before: Consider real random variables U, V, W having a joint distribution on R^3. Assume that the means E(U) = E(V) = E(W) = 0 and the variances E(U^2) = E(V^2) = E(W^2) = 1. Let rho denotes the Pearson correlation coefficient. Note that rho(U,V) = E(UV), rho(V,W) = E(VW), rho(W,X) = E(WX) PUZZLE: What is the set of possible triples of correlations T = {(x,y,z) in [-1,1]^3}, where x = rho(U,V), y = rho(V,W), z = rho(W,U). ??? Find a closed form polynomial inequality that describes the set T as a subset of [-1,1]^3. --Dan RWG wrote: << The equation of the samosa! ParametricPlot3D[{Cos[t], Cos[u], Cos[u + t]}, {t, 0, 2 π}, {u, 0, π}] (Rounded regular tetrahedron, four vertices, no edges, but contains the line segments joining the vertices.) Implicit equation: acos(z)=acos(x)+acos(y) Volume pi^2/2 Area (empirical) 5 pi, but I can't get Mma to do the integral. This can't be new. Does this surface have a legitimate name? Can anyone prove the area?