**Background:** The *biggest little polygon with $n$ sides* is the convex plane $n$-gon of unit polygon diameter having largest possible area. For $n$ odd, the regular polygon on $n$ sides is known to be the biggest little $n$-gon. For even $n$, the regular polygon is suboptimal for $n$=6 (this optimal hexagon was found by Ron Graham) and $n$ = 8 (not sure about higher even numbers). The *Reinhardt polygons* are polygons maximizing *perimeter* for fixed diameter, maximizing width for their diameter, and maximizing width for their perimeter.

**Question:** If we try to keep diameter at 1 and try to find n-gons that maximize the *moment of inertia* about an axis thru the center of mass and normal to the plane, what happens?