We give a construction which takes a rank two incidence geometry with three points on a line and returns a geometry of the same type, i.e., with three points on a line. It is also demonstrated that embeddings of the original geometry can be extended to the new geometry. It is shown that the family of dual polar spaces of type Sp(2n, 2) arise recursively from the construction starting with the geometry consisting of one point and no lines. Making use of this construction we inductively construct projective embeddings for these geometries, in particular the embedding in the spin module for the group Sp(2n, 7). We also show that if we apply the construction to a classical near polygon which is isometrically embedded in the near 2n-gon of type Sp(2n, 2) the resulting space is a near polygon. Examples of such classical, isometrically embedding spaces are near 2n-gon of Hamming type on a three letter alphabet and the product of dual polar spaces of types Sp(2k, 2) and Sp(2l, 2) with k + l = n. (C) 1997 Academic Press.
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机译：我们给出了一个结构，它在一条线上具有三个点的排名两个发病率几何，并返回相同类型的几何形状，即，在一行上有三个点。还证明了原始几何形状的嵌入可以扩展到新几何形状。结果表明，SP型（2n，2）的双极空间的家族从施工开始，从由一个点和无线组成的几何形状开始。利用这种结构，我们感应地构建投影嵌入的这些几何形状，特别是在旋转模块中嵌入群体SP（2N，7）。我们还表明，如果我们将结构应用于在SP型近2N（2N，2）的近2N-GON中的近2N嵌入的经典近多边形，所得到的空间是近多边形。这种经典的等法嵌入空间的示例在三个字母的字母表上靠近汉明型的2N-GON，以及SP（2k，2）和SP（2L，2）的双极性空间的乘积，其中k + L = n。 （c）1997年学术出版社。
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