The inverse moment problem for convex polytopes: implementation aspects
  We give a detailed technical report on the implementation of the algorithm presented in Gravin et al. (Discrete & Computational Geometry'12) for reconstructing an $N$-vertex convex polytope $P$ in $\mathbb{R}^d$ from the knowledge of $O(Nd)$ of its moments. 
Nick Gravin, Danny Nguyen, Dmitrii Pasechnik, Sinai Robins
math.NA