2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/130920A reflexive polytope, respectively its associated Gorenstein toric Fano variety, is called pseudo-symmetric, if the polytope has a centrally symmetric pair of facets. Here we present a complete classification of pseudo-symmetric simplicial reflexive polytopes together with some applications. This generalizes a result of Ewald on pseudo-symmetric nonsingular toric Fano varieties.AMS-LaTeX, 16 pages; references updated, introduction correctedCombinatoricsAlgebraic Geometry52B20, 14M25, 14J45, 52B12text