  In this paper we provide a formula for the canonical differential form of the
hypersimplex $\Delta_{k,n}$ for all $n$ and $k$. We also study the
generalization of the momentum amplituhedron $\mathcal{M}_{n,k}$ to $m=2$, and
we conclude that the existing definition does not possess the desired
properties. Nevertheless, we find interesting momentum amplituhedron-like
logarithmic differential forms in the $m=2$ version of the spinor helicity
space, that have the same singularity structure as the hypersimplex canonical
forms.
