2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/106129This paper presents a technique for constructing new chiral or regular polyhedra (or maps) from self-dual abstract chiral polytopes of rank 4. From improperly self-dual chiral polytopes we derive "Petrie-Coxeter-type" polyhedra (abstract chiral analogues of the classical Petrie-Coxeter polyhedra) and investigate their groups of automorphisms.15 pages. Contributions to Algebra and Geometry, to appearMetric GeometryCombinatorics51M20text