Abstract: Let K be a hypercube in R n. The asymptotic properties of two affine invariant m2(K) and S2(K) of a random simplex inside K are studied. As an application of the method, the isotropic constant L K of parallelotope with volume |K|=1 and center of mass at the origin is obtained.

Key words: hypercube, isotropic constant, parallelotope, Sylvester's problem, convex body