The biggest little polygon with sides is the convex plane -gon of unit polygon diameter having largest possible area.
Reinhardt (1922) showed that for odd, the regular polygon on sides is the biggest little -gon. For , the square with diagonal 1 has maximum area, but an infinite number of other 4-gons are equally large (Audet et al. 2002). The case was solved by Graham (1975) and is known as Graham's biggest little hexagon, and the case was solved by Audet et al. (2002). The following table summarizes these results, showing the percentage that the given polygon is larger than the regular -gon.
|area||% larger than regular -gon||reference|
|8||0.726867||2.79%||Audet et al. (2002)|
The biggest little polygon graphs on and 8 nodes are implemented in the Wolfram Language as GraphData["BiggestLittlePolygon", n].