  In \cite{MW}, B. Moonen and the author defined a new invariant, called
$F$-Zips, of certain varieties in positive characteristics. We showed that the
isomorphism classes of these invariants can be interpreted as orbits of a
certain variety $Z$ with an action of a reductive group $G$. In loc. cit. we
gave a combinatorial description of the set of these orbits.
  In this manuscript we give an explicit combinatorial recipe to decide which
orbits are in the closure of a given orbit. We do this by relating $Z$ to a
semi-linear variant of the wonderful compactification of $G$ constructed by de
Concini and Procesi. As an application we give an explicit criterion of the
closure relation for Ekedahl-Oort strata in the moduli space of principally
polarized abelian varieties.
