Learning the intersection of halfspaces is of interest in theoretical learning theory.
In this thesis, we consider two special cases of learning polytopes, cube and simplex. We show that the rotation of an arbitrarily oriented cube can be determined by computing the minima of the moment-generating function, given uniformly distributed samples from the cube. We also provide computational experiment results to suggest that the rotation of a simplex can be determined by computing the minima or maxima of the 3rd moment function and the (2n)th moment function.