Banach-Mazur distance between [$P_5$ and $P_3$ is $d(P_5,P_3)=1+\frac{\sqrt5}2$](https://arxiv.org/pdf/1707.04830.pdf) where $P_n$ is regular polygon in $n$ sides. What is the distance $d(P_n,P_k)$ in general case (closed form or approximate results?)?