  In recent years, it has been understood that color-ordered scattering
amplitudes can be encoded as logarithmic differential forms on positive
geometries. In particular, amplitudes in maximally supersymmetric Yang-Mills
theory in spinor helicity space are governed by the momentum amplituhedron. Due
to the group-theoretic structure underlying color decompositions, color-ordered
amplitudes enjoy various identities which relate different orderings. In this
paper, we show how the Kleiss-Kuijf relations arise from the geometry of the
momentum amplituhedron. We also show how similar relations can be realised for
the kinematic associahedron, which is the positive geometry of bi-adjoint
scalar cubic theory.
