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We investigate a toroidal compactification of the moduli space of K3 surfacesof degree $2$ originating from the program formulated byGross-Hacking-Keel-Siebert. This construction uses Dolgachev's formulation ofmirror symmetry and the birational geometry of the mirror family. Our mainresult in an analysis of the toric fan. For this we use the methods developedby two of us in a previous paper.

On the GHKS compactification of the moduli space of K3 surfaces of degree two