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