largest small hexagon | largest small octagon

The biggest little polygon with n sides is the convex plane n-gon of unit polygon diameter having largest possible area. The biggest little polygons for n = 6, 8, and 10 are illustrated above. In the figures, diagonals shown in red have unit length. Reinhardt showed that for n odd, the regular polygon on n sides is the biggest little n-gon. For n = 4, the square with diagonal 1 has maximum area, but an infinite number of other 4-gons are equally large . The n = 6 case was solved by Graham and is known as Graham's biggest little hexagon, and the n = 8 case was solved by Audet et al. (2002).

Graham's biggest little hexagon | polygon diameter