  We classify the rational Yangian invariants of the $m=2$ toy model of
$\mathcal{N}=4$ Yang-Mills theory in terms of generalised triangles inside the
amplituhedron $\mathcal{A}_{n,k}^{(2)}$. We enumerate and provide an explicit
formula for all invariants for any number of particles $n$ and any helicity
degree $k$. Each invariant manifestly satisfies cluster adjacency with respect
to the $Gr(2,n)$ cluster algebra.
