A JOURNEY FROM THE OCTONIONIC P-2 TO A FAKE P-2

We discover a family of surfaces of general type with K-2 = 3 and p(g) = q = 0 as free C-13 quotients of special linear cuts of the octonionic projective plane OP2. A special member of the family has 3 singularities of type A(2), and is a quotient of a fake projective plane. We use the techniques of earlier work of Borisov and Fatighenti to define this fake projective plane by explicit equations in its bicanonical embedding.