  The geodesic between two points $a$ and $b$ in the interior of a simple
polygon~$P$ is the shortest polygonal path inside $P$ that connects $a$ to $b$.
It is thus the natural generalization of straight line segments on
unconstrained point sets to polygonal environments. In this paper we use this
extension to generalize the concept of the order type of a set of points in the
Euclidean plane to geodesic order types. In particular, we show that, for any
set $S$ of points and an ordered subset $\mathcal{B} \subseteq S$ of at least
four points, one can always construct a polygon $P$ such that the points of
$\mathcal{B}$ define the geodesic hull of~$S$ w.r.t.~$P$, in the specified
order. Moreover, we show that an abstract order type derived from the dual of
the Pappus arrangement can be realized as a geodesic order type.
