One of the most fundamental results in the theory of regular near polygons is the result that every regular near 2d-gon, \(d \ge 3\), whose parameters \(s,t,t_i\), \(i \in \{ 0,1,\ldots ,d \}\), satisfy \(s,t_2 \ge 2\) and \(t_3=t_2^2+t_2\) is a dual polar space. The proof of that theorem heavily relies on Tits’ theory of buildings, in particular on Tits’ strong results on covering of chamber systems. In this paper, we give an alternative proof which only employs geometrical and algebraic combinatorial arguments.

中文翻译：

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在近多边形上，所有他的六角形都是对偶极空间

正则近多边形理论中最基本的结果之一是每个正则近2 d -gon \（d \ ge 3 \）的结果，其参数\（s，t，t_i \），\（i \在\ {0,1，\ ldots，d \} \）中，满足\（s，t_2 \ ge 2 \）和\（t_3 = t_2 ^ 2 + t_2 \）是一个双极空间。该定理的证明在很大程度上依赖于Tits的建筑物理论，特别是Tits在覆盖腔室系统方面的出色结果。在本文中，我们给出了仅使用几何和代数组合论证的替代证明。