Zonoids whose polars are zonoids: the Banach--Mazur distance need not tend to one

Dmitry Ryabogin, Artem Zvavitch

For every $n\ge 2$, we consider a Gaussian zonoid of revolution $Z_n$ arising from works of Vitale and Mathis. We prove that $Z_n^{\ast }$ is also a zonoid and compute the Banach--Mazur…