  The momentum amplituhedron is a positive geometry encoding tree-level
scattering amplitudes in $\mathcal{N}=4$ super Yang-Mills directly in
spinor-helicity space. In this paper we classify all boundaries of the momentum
amplituhedron $\mathcal{M}_{n,k}$ and explain how these boundaries are related
to the expected factorization channels, and soft and collinear limits of tree
amplitudes. Conversely, all physical singularities of tree amplitudes are
encoded in this boundary stratification. Finally, we find that the momentum
amplituhedron $\mathcal{M}_{n,k}$ has Euler characteristic equal to one, which
provides a first step towards proving that it is homeomorphic to a ball.
