Explore: Generalized Polygons

special cases projective planes (generalized triangles, n = 3) and generalized quadrangles (n = 4). Many generalized polygons arise from groups of Lie type

(axioms), such as projective planes, affine planes, generalized polygons, partial geometries and near polygons. Very general incidence structures can be obtained

geometric progression and let the sides be a, ar, ar2, ar3. Then the generalized polygon inequality requires that 0 < a < a r + a r 2 + a r 3 0 < a r < a

10 sides Hendecagram - star polygon with 11 sides Dodecagram - star polygon with 12 sides Apeirogon - generalized polygon with countably infinite set

In geometry, a generalized polygon can be called a polygram, and named specifically by its number of sides. All polygons are polygrams, but they can also

around the polygon makes one full turn, so the sum of the exterior angles must be 360°. This argument can be generalized to concave simple polygons, if external

Fermat theorem on polygonal numbers" in the Annals of Mathematics, "Representation by Extended Polygonal Numbers and by Generalized Polygonal Numbers" and

near polygons. In fact, any near polygon that has precisely two points per line must be a connected bipartite graph. All finite generalized polygons except

2 are precisely the generalized polygons, and a plethora of examples exist. (There are free constructions of infinite generalized n-gons for every n ≥

when they admit a suitable group of symmetries (the so-called Moufang polygons). In collaboration with François Bruhat he developed the theory of affine