2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/115369We give a geometric realization of cluster categories of type $D_n$ using a polygon with $n$ vertices and one puncture in its center as a model. In this realization, the indecomposable objects of the cluster category correspond to certain homotopy classes of paths between two vertices.20 pages (v3: section 5.3 amended, some other editorial changes and typos fixed)Representation TheoryRings and Algebras16G20; 16G70; 18E30; 05E15text