Biggest little polygon

Biggest little polygon with 6 sides (on the left); on the right the regular polygon with same diameter but lower area.

In geometry, the biggest little polygon for a number n is the n-sided polygon that has diameter one (that is, every two of its points are within unit distance of each other) and that has the largest area among all diameter-one n-gons. One non-unique solution when n = 4 is a square, and the solution is a regular polygon when n is an odd number, but the solution is irregular otherwise.