  Generalised bi-adjoint scalar amplitudes, obtained from integrations over
moduli space of punctured $\mathbb{CP}^{k-1}$, are novel extensions of the CHY
formalism. These amplitudes have realisations in terms of Grassmannian cluster
algebras. Recently connections between one-loop integrands for bi-adjoint cubic
scalar theory and $\mathcal{D}_n$ cluster polytope have been established. In
this paper using the $\text{Gr}\left(3,6\right)$ cluster algebra, we relate the
singularities of $\left(3,6\right)$ amplitude to four-point one-loop integrand
in the bi-adjoint cubic scalar theory through the $\mathcal{D}_{4}$ cluster
polytope. We also study factorisation properties of the $(3,6)$ amplitude at
various boundaries in the worldsheet.
