The biggest little polygon with 
sides is the convex plane 
-gon of unit polygon diameter
having largest possible area. The biggest little polygons
for 
,
8, and 10 are illustrated above. In the figures, diagonals shown in red have unit
length.
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 area of Graham's biggest little hexagon is given by an algebraic number with minimal polynomial of degree 10, and the area of the smallest little octagon has a minimal polynomial of degree 42 (Hurst 2025).
The following table summarizes these results, including the percentage that the given polygon is larger than the corresponding regular 
-gon.
 | area | OEIS | % larger | algebraic degree | references |
| 6 | 0.674981... | A111969 | 3.92% | 10 | Graham (1975) |
| 8 | 0.726868... | A381252 | 2.79% | 42 | Audet et al. (2002), Foster and Szaba (2007), Hurst (2025) |
| 10 | 0.749137... | A383173 | 1.96% | 152 | Hurst (2025) |
The biggest little polygon graphs on 
and 8 nodes are implemented in the Wolfram
Language as GraphData[
"BiggestLittlePolygon",
n
]
for 
,
8, and (in a future version of the Wolfram
Language) 10.
