The Collaborative International Dictionary of English v.0.48:

fantail goldfish \fan"tail` gold"fish\, n. (Zool.)
   a type of goldfish bred artificially, having a realtively
   short oval body and a tail with four lobes arrayed somewhat
   like a folding fan, as though forming a part of the surface
   of a cone. Called also fantail.
   [PJC]