Before revision:  We offer an open-source , optimized C++ implementation , and analyze its performance to show that it outperforms state-of-the-art software for H-polytopes by Cousins-Vempala (2016) and Emiris-Fisikopoulos (2018), while it undertakes volume computations that were intractable until now, as it is the first polynomial-time, practical method for V-polytopes and zonotopes that scales to high dimensions (currently 100). We further focus on zonotopes, and characterize them by their order (number of generators over dimension), because this largely determines sampling complexity. We analyze a related application, where we evaluate methods of zonotope approximation in engineering .
After revision:  We offer an open-source , optimized C++ implementation , and analyze its performance to show that it outperforms state-of-the-art software for H-polytopes and in the hundreds for V- and Z-polytopes on moderate hardware. Last, we illustrate our software in evaluating Z-polytope approximations .