  We give a realization of the infinity crystal for affine sl(2) using
decorated polygons. The construction and proof are combinatorial, making use of
Kashiwara and Saito's characterization of the infinity crystal in terms of the
* involution. The polygons we use have combinatorial properties suggesting they
are the analogues in this case of the Mirkovic-Vilonen polytopes defined by
Anderson and the third author in finite type. Using Kashiwara's similarity of
crystals we also give MV polytopes for $A_2^{(2)}$, the only other rank two
affine Kac-Moody algebra.
