  We find explicit equations of the fake projective plane
$(a=7,p=2,\emptyset,D_3 X_7)$, which lies in the same class as the fake
projective plane $(a=7,p=2,\emptyset,D_3 2_7)$ with $21$ automorphisms whose
equations were previously found by Borisov and Keum. The method involves
finding a birational model of a common Galois cover of these two surfaces.
