  An Alexander self-dual complex gives rise to a compactification of $M_{0,n}$,
called ASD compactification, which is a smooth algebraic variety. ASD
compactifications include (but are not exhausted by) the polygon spaces, or the
moduli spaces of flexible polygons. We present an explicit description of the
Chow rings of ASD compactifications. We study the analogues of Kontsevich
tautological bundles, compute their Chern classes, compute top intersections of
the Chern classes, and derive a recursion for the intersection numbers.
