Abstract
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.
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