We show that the Banach-Mazur distance between the parallelogram and the affine-regular hexagon is $\frac{ 3}{ 2}$ and we conclude that the diameter of the family of centrally-symmetric planar convex bodies is just $\frac{ 3}{ 2}$. A proof of this fact does not seem to be published earlier. Asplund announced this without a proof in his paper proving that the Banach-Mazur distance of any planar centrally-symmetric bodies is at most $\frac{ 3}{ 2}$. Analogously, we deal with the Banach-Mazur distances between the parallelogram and the remaining affine-regular even-gons.
Categories: math.MG math.FA