${\pi }_B$ in asymetric Minkowski normed spaces

We extend the classical results of Stanislaw Golab, on the values of pi in arbitrary normed planes, to asymmetric norms where the unit ball has one axis of symmetry. First, we characterize the values of ${\pi }_B$ for different families of polygons as unit ball B. Then we prove that ${\pi }_B\ge 3$, and can take all possible values and is not bounded in such spaces.