  We build upon the prior works of [1-3] to study tree-level planar amplitudes
for a massless scalar field theory with polynomial interactions. Focusing on a
specific example, where the interaction is given by $\lambda_3\phi^{3}\
+\lambda_4 \phi^{4}$, we show that a specific convex realization of a simple
polytope known as the accordiohedron in kinematic space is the positive
geometry for this theory. As in the previous cases, there is a unique planar
scattering form in kinematic space, associated to each positive geometry which
yields planar scattering amplitudes.
