Projectivizations of pointed polyhedral cones $C$ are positive geometries with canonical forms that look like $\Omega_C(x) = \frac{A(x)}{B(x)}dx$ with $A, B$ polynomials. We are going to see that the numerator $A(x)$ is given by the adjoint polynomial of the dual cone $C^\vee$, which cancels unwanted poles outside the polytope.