Is there a preferred way to characterize a cone in cohomology?

Question

In a Euclidean space, one can of course describe a cone using a generalization of polar coordinates, and since the de Rham cohomology spaces are themselves Euclidean spaces, one can do the same here. For example, in the Kodaira-Thurston manifold $KT$, we have $b_{2}=4$. If $(x,y,z,t)$ defines global coordinates for $H^{2}(KT;\mathbf{R})$, then it is not difficult to determine that the set of Hard Lefschetz symplectic forms on this manifold is the set determined by $xt-yz\neq 0$, $z\neq 0$, $t\neq 0$, and $z\neq t$. Are there more sophisticated, more illuminating ways of describing the Hard Lefschetz cone in KT?