2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/61243We develop the basic topological properties of compact polygons, i.e. of compact topological Tits buildings of rank two. It is proved that the Coxeter diagram of such a building is always crystallographic, that is, compact connected n-gons exist only for n=3,4,6. We classify compact polygons which admit a transitive group action, showing that such a polygon is Moufang and thus related to a real Lie group of rank 2.Differential GeometryGeometric Topology51H 57P 51Etext