The Dempster-Shafer (DS) theory to statistical inference extends the Bayesian approach by allowing the use of partial and vacuous prior information. It yields three-valued uncertainty assessments representing probabilities for, against, and don’t know about formal assertions of interest. This talk presents a Gibbs algorithm that targets the distribution of a class of random convex polytopes, first described in Dempster (1972) to encapsulate the DS inference for Categorical distributions. Our sampler relies on an equivalence between the iterative constraints of the vertex configuration and the non-negativity of cycles in a fully connected directed graph. Joint work with Pierre E. Jacob, Paul T. Edlefsen and Arthur P. Dempster.