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Smooth primitively polarized $\mathrm{K3}$ surfaces of genus 36 are studied.It is proved that all such surfaces $S$, for which there exists an embedding$\mathrm{R} \hookrightarrow \mathrm{Pic}(S)$ of some special lattice$\mathrm{R}$ of rank 2, are parameterized up to an isomorphism by some18-dimensional unirational algebraic variety. More precisely, it is shown thata general $S$ is an anticanonical section of a (unique) Fano 3-fold withcanonical Gorenstein singularities.

Remark on polarized K3 surfaces of genus 36