  In this paper, we construct the "2221" subfactor planar algebra by finding it
as a subalgebra of the graph planar algebra of its principal graph. In
particular, we give a presentation of the "2221" subfactor planar algebra
consisting of generators and relations. As a corollary, we have a planar
algebra proof of the existence of a subfactor with principal graph "2221". To
show the subfactor property, we use the jellyfish algorithm for evaluating
closed diagrams. Lastly, we show uniqueness up to conjugation of "2221".
