  Fake projective planes are smooth complex surfaces of general type with Betti
numbers equal to those of the usual projective plane. They come in complex
conjugate pairs and have been classified as quotients of the two-dimensional
ball by explicitly written arithmetic subgroups. In this paper we find
equations of a projective model of a conjugate pair of fake projective planes
by studying the geometry of the quotient of such surface by an order seven
automorphism.
