Near polygon

In mathematics, a near polygon is an incidence geometry introduced by Ernest E. Shult and Arthur Yanushka in 1980. Shult and Yanushka showed the connection between the so-called tetrahedrally closed line-systems in Euclidean spaces and a class of point-line geometries which they called near polygons. These structures generalise the notion of generalized polygon as every generalized 2n-gon is a near 2n-gon of a particular kind. Near polygons were extensively studied and connection between them and dual polar space was shown in 1980s and early 1990s. Some sporadic simple groups, for example the Hall-Janko group and the Mathieu groups, act as automorphism groups of near polygons.

A near 2d-gon is an incidence structure (${\displaystyle P,L,I}$), where ${\displaystyle P}$ is the set of points, ${\displaystyle L}$ is the set of lines and ${\displaystyle I\subseteq P\times L}$ is the incidence relation, such that:

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