2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/60179We investigate some combinatorial properties of convex polytopes simple in edges. For polytopes whose nonsimple vertices are located sufficiently far one from another, we prove an analog of the Hard Lefschetz theorem. It implies Stanley's conjecture for such polytopes.Rewritten. The first version contained fatal errors. 16 pages, to be published in Func. Anal. and ApplAlgebraic GeometryCombinatorics14M25 (Primary) 52B05, 14F43 (Secondary)text