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Given complete fan $\Delta$ defining a projective toric variety (so that $\Delta$ is the normal fan of some polytope). How do one go on to find a defining ideal of the toric variety in projective space? Or, going the other way, given binomial equations defining a projective toric variety, is there some way to recover the fan?

In my case, I am trying to recover the fan of the hypersurface $Z(x_0x_3-x_1x_2)$ in $\mathbb{P}^n$ ($n>3$).

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