2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/65228It is shown how the Beneath-and-Beyond algorithm can be used to yield another proof of the equivalence of V- and H-representations of convex polytopes. In this sense this paper serves as the sketch of an introduction to polytope theory with a focus on algorithmic aspects. Moreover, computational results are presented to compare Beneath-and-Beyond to other convex hull implementations.21 pages, 2 figures; v2: added the bibliography which was erroneously omitted in v1Metric GeometryCombinatorics52B11; 52B55; 68Q25text