  Using the twistor correspondence, we give a classification of toric
anti-self-dual Einstein metrics: each such metric is essentially determined by
an odd holomorphic function. This explains how the Einstein metrics fit into
the classification of general toric anti-self-dual metrics given in an earlier
paper (math.DG/0602423). The results complement the work of Calderbank-Pedersen
(math.DG/0105263), who describe where the Einstein metrics appear amongst the
Joyce spaces, leading to a different classification. Taking the twistor
transform of our result gives a new proof of their theorem.
