  In this paper we study the orthogonal momentum amplituhedron $\mathcal{O}_k$,
a recently introduced positive geometry that encodes the tree-level scattering
amplitudes in ABJM theory. We generate the full boundary stratification of
$\mathcal{O}_k$ and show that its boundaries can be labelled by so-called
orthogonal Grassmannian forests (OG forests). We also determine the generating
function for enumerating boundaries according to their dimension and show that
the Euler characteristic of $\mathcal{O}_k$ equals one. This provides a strong
indication that the orthogonal momentum amplituhedron is homeomorphic to a
ball. This paper is supplemented with the Mathematica package "orthitroids"
which contains useful functions for studying the positive orthogonal
Grassmannian and the orthogonal momentum amplituhedron.
