  We consider the set of permutations that are sorted after two passes through
a pop stack. We characterize these permutations in terms of forbidden patterns
(classical and barred) and enumerate them according to the ascent statistic.
Then we show these permutations to be in bijection with a special family of
polyominoes. As a consequence, the permutations sortable by this machine are
shown to have the same enumeration as three classical permutation classes.
