  We 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.
