  Most known examples of subfactors occur in families, coming from algebraic
objects such as groups, quantum groups and rational conformal field theories.
The Haagerup subfactor is the smallest index finite-depth subfactor which does
not occur in one of these families. In this paper we construct the planar
algebra associated to the Haagerup subfactor, which provides a new proof of the
existence of the Haagerup subfactor. Our technique is to find the Haagerup
planar algebra as a singly generated subfactor planar algebra, contained inside
of a graph planar algebra.
