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Toric What is the fan of the toric blow-up of $\mathbb{P}^3$ along the union of two intersecting lines?
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Is there a good way to find the fan and polytope of the blow-up of $\mathbb{P}^3$ along the union of two invariant (and so intersecting ) lines?

Everything I find in the literature is for blow-ups along smooth invariant centers.

Thanks!
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Toric blow-up of $\mathbb{P}^3$ along the union of two intersecting lines

Is there a good way to find the fan and polytope of the blow-up of $\mathbb{P}^3$ along the union of two invariant (and so intersecting) lines?

Everything I find in the literature is for blow-ups along smooth invariant centers.

Thanks!