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$K3$ surfaces in $\mathbb P^1 \times \mathbb P^1 \times \mathbb P^1$

In the generic case you'll have $\text{NS}(S)\otimes\mathbb R\cong\mathbb R^3$ and you can compute the $3$-by-$3$ matrix for the action of the three involutions $i_1,i_2,i_3$ on, say, a basis ...
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