A Note on the Faces of the Dual Koch Arrangement

We analyze the faces of the dual Koch arrangement, which is the arrangement of $2^s+1$ lines obtained by projective duality from the Koch chain $K_s$. In particular, we show that this line arrangement does not contain any $k$-gons for $k>5$, and that the number of pentagons is $3\cdot 2^{s-1}-3$.