Symplectically self-polar polytopes of minimal capacity

Abstract In this paper we continue the study of symplectically self-polar convex bodies started in [3]. We construct symplectically self-polar convex bodies of the minimal Ekeland–Hofer–Zehnder capacity. This in turn proves that the lower bound for the Ekeland–Hofer–Zehnder capacity for centrally symmetric convex bodies obtained in [1] cannot be improved. We also make some numerical experiments and speculations regarding the minimal volume of symplectically self-polar convex bodies.