Three Desks, One Common Correlation

Three trading desks report daily P\&L. A risk manager finds that every pair of desks has exactly the same correlation $r$: $\mathrm{corr}(X,Y) = \mathrm{corr}(Y,Z) = \mathrm{corr}(Z,X) = r$. What is the full set of values $r$ can take? Then generalize to $n$ desks.