We give an algorithm to route a multicommodity flow in a planar graph $G$
with congestion $O(\log k)$, where $k$ is the maximum number of terminals on
the boundary of a face, when each demand edge lie on a face of $G$. We also
show that our specific method cannot achieve a substantially better congestion.
It is known that in the Minkowski sum of $r$ polytopes in dimension $d$, with
$r<d$, the number of vertices of the sum can potentially be as high as the
product of the number of vertices in each summand. However, the number of
vertices for sums of more polytopes was unknown so far.