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We prove that every K3 surface with automorphism group$(\mathbb{Z}/2\mathbb{Z})^2$ admits an explicit birational model as a doublesextic surface. This model is canonical for Picard number greater than 10. ForPicard number greater than 9, the K3 surfaces in question possess a secondbirational model, in the form of a projective quartic hypersurface,generalizing the Inose quartic.

On projective K3 surfaces $\mathcal{X}$ with $\mathrm{Aut}(\mathcal{X})=(\mathbb{Z}/2\mathbb{Z})^2$