A pentagonal geometry PENT($k,r$) is a partial linear space, where every line is incident with $k$ points, every point is incident with $r$ lines, and for each point $x$, there is a line incident with precisely those points that are not collinear with $x$. Here we generalize the concept by allowing the points not collinear with $x$ to form the point set of a Steiner system $S\left(2,k,w\right)$ whose blocks are lines of the geometry.

中文翻译：

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广义五边形几何

五边形几何体 PENT($克,r$) 是一个部分线性空间，其中每条线都与 $克$ 点，每个点都与 $r$ 线，对于每个点 $X$，有一条线恰好与那些不共线的点相交 $X$. 在这里，我们通过允许与不共线的点来概括这个概念$X$ 形成 Steiner 系统的点集 $秒\left(2,克,瓦\right)$ 其块是几何线。