Contemporary time-stepping methods used in the dynamic simulation of rigid bodies suffer from problems in accuracy, performance, and robustness. Significant allowances for tuning, coupled with careful implementation of a broad phase collision detection scheme is required to make dynamic simulation useful for practical applications. A recently developed formulation method is presented herein that is more robust, and not dependent on broad-phase collision detection or system tuning for its behavior. Several uncomplicated benchmark examples are presented to give an analysis and make a comparison of the new Polyhedral Exact Geometry time-stepping method with the well-known Stewart-Trinkle time-stepping method. The behavior and performance for the two methods are discussed. This includes specific cases where contemporary time-steppers fail, and how they are ameliorated by the new method presented here. The goal of this work is to complete the groundwork for further research into high performance simulation.