A Tits polygon is a bipartite graph in which the neighborhood of each vertex is endowed with an “opposition relation” satisfying certain axioms. Moufang polygons are precisely the Tits polygons in which these opposition relations are all trivial. Every Tits polygon has a distinguished set of circuits. A Tits quadrangle is a Tits polygon in which these circuits all have length 8. There is a standard construction that produces a Tits polygon from certain pairs (∆, T), where ∆ is an irreducible spherical building and T is a Tits index of relative rank 2. We call a Tits quadrangle exceptional if it arises from such a pair (∆, T) for ∆ the spherical building associated to the group of rational points of an exceptional algebraic group. In this paper, we characterize the exceptional Tits quadrangles as extensions of orthogonal Tits quadrangles in a suitable sense.

Tits多边形是一个二部图，其中每个顶点的邻域具有满足某些公理的“对立关系”。Moufang多边形恰好是Tits多边形，其中这些对立关系都是微不足道的。每个山雀多边形都有一组独特的电路。一个Tits四边形是一个Tits多边形，其中所有电路的长度均为8。存在一个标准构造，该构造从某些对（∆，T）生成Tits多边形，其中∆是不可约的球形建筑物，T是相对的Tits指数等级2。如果Tits四角形来自这样的一对（∆，T）对于∆，与例外代数群的有理点群相关的球面建筑物。在本文中，我们将特殊的Tits四边形表征为在适当意义上正交Tits四边形的扩展。