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.

翻译：我们开发了紧凑多边形的基本地貌特性,即2级的紧凑地表层天体建筑。可以证明,这种建筑的Coxeter图始终是晶体学的,也就是说,只有n=3,4,6的紧凑连接的正形存在。 我们对允许过渡性集团行动的紧凑多边形进行了分类,表明这种多边形是Moufang,因此与2级的真正利族集团有关。