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 | |

6 | 0.674981 | 3.92% | Graham (1975) |

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*].