  We construct a new subfactor planar algebra, and as a corollary a new
subfactor, with the `extended Haagerup' principal graph pair. This completes
the classification of irreducible amenable subfactors with index in the range
$(4,3+\sqrt{3})$, which was initiated by Haagerup in 1993. We prove that the
subfactor planar algebra with these principal graphs is unique. We give a skein
theoretic description, and a description as a subalgebra generated by a certain
element in the graph planar algebra of its principal graph. In the skein
theoretic description there is an explicit algorithm for evaluating closed
diagrams. This evaluation algorithm is unusual because intermediate steps may
increase the number of generators in a diagram.
