Generalized polygon

In combinatorial theory, a generalized polygon is an incidence structure introduced by Jacques Tits in 1959. Generalized n-gons encompass as special cases projective planes (generalized triangles, n = 3) and generalized quadrangles (n = 4). Many generalized polygons arise from groups of Lie type, but there are also exotic ones that cannot be obtained in this way. Generalized polygons satisfying a technical condition known as the Moufang property have been completely classified by Tits and Weiss. Every generalized n-gon with n even is also a near polygon.

A generalized 2-gon (or a digon) is an incidence structure with at least 2 points and 2 lines where each point is incident to each line.

For ${\displaystyle n\geq 3}$ a generalized n-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:

...
Wikipedia