2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/143637We use methods of combinatorics of polytopes together with geometrical and computational ones to obtain the complete list of compact hyperbolic Coxeter n-polytopes with n+3 facets, 3<n<8. Combined with results of Esselmann (1994), Andreev (1970) and Poincare (1882) this gives the classification of all compact hyperbolic Coxeter n-polytopes with n+3 facets.v4: paper is rewritten. Complete proofs added, errors corrected. 36 pages, a lot of figuresMetric GeometryGroup Theory51M20; 51F15; 20F55text