  In this paper, we define the momentum amplituhedron in the four-dimensional
split-signature space of dual momenta. It encodes scattering amplitudes at tree
level and loop integrands for N=4 super Yang-Mills in the planar sector. In
this description, every point in the tree-level geometry is specified by a null
polygon. Using the null structure of this kinematic space, we find a geometry
whose canonical differential form produces loop-amplitude integrands.
Remarkably, at one loop it is a curvy version of a simple polytope, whose
vertices are specified by maximal cuts of the amplitude. This construction
allows us to find novel formulae for the one-loop integrands for amplitudes
with any multiplicity and helicity. The formulae obtained in this way agree
with the ones derived via prescriptive unitarity. It makes prescriptive
unitarity naturally emerge from this geometric description.
