[math-fun] Volume puzzle

The regular n-simplex delta_n(S_n) of side S_n is the convex span of n+1 points in n-space any two of which are a distance of S_n apart. PUZZLE: Assume S_n = K*n for some constant K > 0. Define f(n) = the n-volume of delta_n(S_n) Given that f(n) approaches a finite limit L > 0 as n -> oo, find L. --Dan