  We discover a simple construction of a four-dimensional family of smooth
surfaces of general type with $p_g(S)=q(S)=0$, $K^2_S=3$ with cyclic
fundamental group $C_{14}$. We use a degeneration of the surfaces in this
family to find (complicated) explicit equations of six new pairs of fake
projective planes. Our methods for finding new fake projective planes involve
nontrivial computer calculations which we hope will be applicable in other
settings.
