  For stationary first passage percolation in two dimensions, the existence and
uniqueness of semi-infinite geodesics directed in particular directions or
sectors has been considered by Damron and Hanson (Commun. Math. Phys., 2014),
Ahlberg and Hoffman (preprint, 2016), and others. However the main results do
not cover geodesics in the direction of corners of the limit shape
$\mathcal{B}$, where two facets meet. We construct an example with the
following properties: (i) the limiting shape is an octagon, (ii) semi-infinite
geodesics exist only in the four axis directions, and (iii) in each axis
direction there are multiple such geodesics. Consequently, the set of points of
$\partial \mathcal{B}$ which are in the direction of some geodesic does not
have all of $\mathcal{B}$ as its convex hull.
